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A Sparse Bayesian Learning for Diagnosis of Nonstationary and Spatially Correlated Faults:References
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#correlated-faults#fault-diagnosis#multistage-assembly-systems#multistation-assembly-systems#nonstationary-faults#sparse-bayesian-learning#spatially-correlated-faults#variational-bayes-inference
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Interesting Papers for Week 36, 2024
Auditory Competition and Coding of Relative Stimulus Strength across Midbrain Space Maps of Barn Owls. Bae, A. J., Ferger, R., & Peña, J. L. (2024). Journal of Neuroscience, 44(21), e2081232024.
Volatile working memory representations crystallize with practice. Bellafard, A., Namvar, G., Kao, J. C., Vaziri, A., & Golshani, P. (2024). Nature, 629(8014), 1109–1117.
Maximum diffusion reinforcement learning. Berrueta, T. A., Pinosky, A., & Murphey, T. D. (2024). Nature Machine Intelligence, 6(5), 504–514.
Neuronal activation sequences in lateral prefrontal cortex encode visuospatial working memory during virtual navigation. Busch, A., Roussy, M., Luna, R., Leavitt, M. L., Mofrad, M. H., Gulli, R. A., … Martinez-Trujillo, J. C. (2024). Nature Communications, 15, 4471.
Heterogeneity in strategy use during arbitration between experiential and observational learning. Charpentier, C. J., Wu, Q., Min, S., Ding, W., Cockburn, J., & O’Doherty, J. P. (2024). Nature Communications, 15, 4436.
Belief Updating during Social Interactions: Neural Dynamics and Causal Role of Dorsomedial Prefrontal Cortex. Christian, P., Kaiser, J., Taylor, P. C., George, M., Schütz-Bosbach, S., & Soutschek, A. (2024). Journal of Neuroscience, 44(22), e1669232024.
A fear conditioned cue orchestrates a suite of behaviors in rats. Chu, A., Gordon, N. T., DuBois, A. M., Michel, C. B., Hanrahan, K. E., Williams, D. C., … McDannald, M. A. (2024). eLife, 13, e82497.
Mapping model units to visual neurons reveals population code for social behaviour. Cowley, B. R., Calhoun, A. J., Rangarajan, N., Ireland, E., Turner, M. H., Pillow, J. W., & Murthy, M. (2024). Nature, 629(8014), 1100–1108.
Spatial-Temporal Analysis of Neural Desynchronization in Sleeplike States Reveals Critical Dynamics. Curic, D., Singh, S., Nazari, M., Mohajerani, M. H., & Davidsen, J. (2024). Physical Review Letters, 132(21), 218403.
Simple visual stimuli are sufficient to drive responses in action observation and execution neurons in macaque ventral premotor cortex. De Schrijver, S., Decramer, T., & Janssen, P. (2024). PLOS Biology, 22(5), e3002358.
Intrinsic Neural Excitability Biases Allocation and Overlap of Memory Engrams. Delamare, G., Tomé, D. F., & Clopath, C. (2024). Journal of Neuroscience, 44(21), e0846232024.
Common neural dysfunction of economic decision-making across psychiatric conditions. Feng, C., Liu, Q., Huang, C., Li, T., Wang, L., Liu, F., … Qu, C. (2024). NeuroImage, 294, 120641.
Single trial Bayesian inference by population vector readout in the barn owl’s sound localization system. Fischer, B. J., Shadron, K., Ferger, R., & Peña, J. L. (2024). PLOS ONE, 19(5), e0303843.
Synergizing habits and goals with variational Bayes. Han, D., Doya, K., Li, D., & Tani, J. (2024). Nature Communications, 15, 4461.
Dynamic computational phenotyping of human cognition. Schurr, R., Reznik, D., Hillman, H., Bhui, R., & Gershman, S. J. (2024). Nature Human Behaviour, 8(5), 917–931.
Neural Reward Representations Enable Utilitarian Welfare Maximization. Soutschek, A., Burke, C. J., Kang, P., Wieland, N., Netzer, N., & Tobler, P. N. (2024). Journal of Neuroscience, 44(21), e2376232024.
Chimpanzees use social information to acquire a skill they fail to innovate. van Leeuwen, E. J. C., DeTroy, S. E., Haun, D. B. M., & Call, J. (2024). Nature Human Behaviour, 8(5), 891–902.
Paradoxical Boosting of Weak and Strong Spatial Memories by Hippocampal Dopamine Uncaging. Velazquez-Delgado, C., Perez-Becerra, J., Calderon, V., Hernandez-Ortiz, E., Bermudez-Rattoni, F., & Carrillo-Reid, L. (2024). eNeuro, 11(5), ENEURO.0469-23.2024.
Impact of early visual experience on later usage of color cues. Vogelsang, M., Vogelsang, L., Gupta, P., Gandhi, T. K., Shah, P., Swami, P., … Sinha, P. (2024). Science, 384(6698), 907–912.
Learning to Choose: Behavioral Dynamics Underlying the Initial Acquisition of Decision-Making. White, S. R., Preston, M. W., Swanson, K., & Laubach, M. (2024). eNeuro, 11(5), ENEURO.0142-24.2024.
#neuroscience#science#research#brain science#scientific publications#cognitive science#neurobiology#cognition#psychophysics#neurons#neural computation#neural networks#computational neuroscience
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How to Select Classes for Data Science That Will Help You Get a Job
It is always exciting and at the same time challenging as one can think of entering a career in data science. As much as organizations start practicing big data in their operations, they are likely to require data scientists. Performance in class greatly determines whether one will succeed in this competitive world hence the need to select the right courses. Read on for this step-by-step guide that will enable you to come up with a realistic plan on which classes to take to acquire skills and make yourself more marketable to employers. Here in this article, Advanto Software will guide you in the selection of classes for Data Science.
Defining the Essence of Classes for Data Science
We have to emphasize that, while considering courses, one should define the basic skills needed for a data scientist’s position. In simple words, data science is an interdisciplinary approach involving statistical analysis, programming, and domain knowledge. The primary skills needed include:
Statistical Analysis and Probability
Programming Languages (Python, R)
Machine Learning Algorithms
Data Visualization Techniques
Big Data Technologies
Data Wrangling and Cleaning
1. In this case, one should try to concentrate on those academic disciplines that form the basis for data science classes.
Statistical Analysis and Probability
Data science’s foundation is statistical analysis. This process comprises knowledge of distributions, testing of hypotheses, and inference-making processes out of data. Classes in statistical analysis will cover: Classes in statistical analysis will cover:
Descriptive Statistics: Arithmetic average, positional average, most frequent value, and measure of variation.
Inferential Statistics: Confidence Intervals, Hypothesis Testing, and Regression Analysis.
Probability Theory: Bayes’ Theorem, probability density and distribution functions and stochastic processes.
Programming for Data Science
To be precise, a data scientist cannot afford to have poor programming skills. Python and R are the two most popular languages in the area. Look for classes that offer:
Python Programming: Development skills in certain libraries, for instance, Pandas, NumPy, and Scikit-learn.
R Programming: This means focus on packages such as; ggplot, dplyr, and caret.
Data Manipulation and Analysis: Approaches to data management and analysis.
2. Master Level Data Science Concepts
Machine Learning and AI
Machine Learning is an important aspect of data science. Advanced courses should delve into:
Statistical Analysis and Probability
Supervised Learning: Supervised techniques like; decision trees, random forest, and Support Vector Machines both classification and regression.
Unsupervised Learning: Supervised methods such as decision trees, regression analysis, logistic regression, neural networks, support vector machines, and Naïve Bayes.
Deep Learning: Some of the most commonly referred neural networks include the following; neural networks, convolutional neural networks (CNNs), and recurrent neural networks (RNNs).
Big Data Technologies
Given the emergence of big data, big data technologies are becoming vital to be acquainted with. Classes to consider include:
Hadoop Ecosystem: Explaining Hadoop, MapReduce, and Hadoop file system (HDFS).
Spark: Learning Apache Spark about Big data faster data processing and analysis.
NoSQL Databases: Functions related to databases such as the use of MongoDB and Cassandra.
3. Emphasize Data Visualization Skills
Visualization Tools: Intensive analytical training in Tableau, Power BI, or D3 tools. Js.
Graphical Representation: Ways of effective and efficient making of charts, graphs, and dashboards required for business and other organizational units.
Interactive Visualization: Challenging language design and creating interesting data-driven narratives with the help of libraries like Plotly or Bokeh.
4. Field Work and Application organizations
Project-Based Learning
Hands-on experience is vital. Opt for classes that offer:
• Capstone Projects: Simulated business scenarios that replicate problems that organizations encounter.
• Case Studies: Solutions to data science problems in different domains and perspectives on the problems in depth.
• Internships and Co-ops: Companies and actual practice with them as a certain advantage.
Industry-Relevant Case Studies Classes For Data Science should include:
Domain-Specific Applications: Use of data science in various fields such as financial and banking, health services, sales, and marketing, or any other field of one’s choice.
Problem-Solving Sessions: Employing real-life business scenarios and finding quantitative solutions to the problems arising.
5. Evaluate the Fairness of the Credentials Presented by the Course Providers
Accreditation and Certification
It should be certain that the classes are from accredited institutions or offer certificates that are well-accepted in the market. Look for:
University-Backed Programs: University or Course / Curriculum offered by an accredited University or an Intuition.
Professional Certifications: Certifications from some of the many professional bodies like the Data Science Council of America or the Institute for Operations Research and the Management Sciences.
Instructor Expertise
The strengths of teachers prove to be very influential.
Instructor Background: Academic background or work experience, the author’s research papers and projects, and accomplishments in the field.
Course Reviews and Ratings: In the present study, information from past students about the usefulness of the course.
6. As for the factors making up the community, one has to consider Flexibility and Learning Formats.
Decide based on your preferences
Online Courses: In some cases, the students�� ability to set their own pace of learning and; Online programs are generally cheaper than their traditional counterparts.
On-Campus Classes: Close contact with the instructors as the students engage in a well-organized learning process.
Conclusion
Choosing the Advanto Software classes for data science is not a mere decision of choosing courses, but rather, it involves identifying the important competencies, extending the course topics to the basic and the modern levels, and also ensuring that the courses provide practical experience as much as possible with the 100% job assurance. It will therefore be beneficial to select courses that provide more extensive coverage on statistics, data programming, machine learning, and data visualization to enhance your chances of getting a job in data science. It is also important to evaluate the credibility of course providers and how learning formats can be adaptable to one’s career paths.
Join us now: advantosoftware.com/
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There’s something that seems really weird to me about the technique called “variational Bayes.”
(It also goes by various other names, like “variational inference with a (naive) mean-field family.” Technically it’s still “variational” and “Bayes” whether or not you’re making the mean-field assumption, but the specific phrase “variational Bayes” is apparently associated with the mean-field assumption in the lingo, cf. Wainwright and Jordan 2008 p. 160.)
Okay, so, “variational” Bayesian inference is a type of method for approximately calculating your posterior from the prior and observations. There are lots of methods for approximate posterior calculation, because nontrivial posteriors are generally impossible to calculate exactly. This is what a mathematician or statistician is probably doing if they say they study “Bayesian inference.”
In the variational methods, the approximation is done as follows. Instead of looking for the exact posterior, which could be any probability distribution, you agree to look within a restricted set of distributions you’ve chosen to be easy to work with. This is called the “variational family.”
Then you optimize within this set, trying to pick the one that best fits the exact posterior. Since you don’t know the exact posterior, this is a little tricky, but it turns out you can calculate a specific lower bound (cutely named ELBO) on the quality of the fit without actually knowing the value you’re fitting to. So you maximize this lower bound within the family, and hope that gets you the best approximation available in the family. (”Hope” because this is not guaranteed -- it’s just a bound, and it’s possible for the bound to go up while the fit goes down, provided the bound isn’t too tight. That’s one of the weird and worrisome things about variational inference, but it’s not the one I’m here to talk about.)
The variational family is up to you. There don’t seem to be many proofs about which sorts of variational families are “good enough” to approximate the posterior in a given type of problem. Instead it’s more heuristic, with people choosing families that are “nice” and convenient to optimize and then hoping it works out.
This is another weird thing about variational inference: there are (almost) arbitrarily bad approximations that still count as “correctly” doing variational inference, just with a bad variational family. But since the theory doesn’t tell you how to pick a good variational family -- that’s done heuristically -- the theory itself doesn’t give you any general bounds on how badly you can do when using it.
In practice, the most common sort of variational family, the one that gets called “variational Bayes,” is a so-called “mean field” or “naive mean field” family. This is a family of distributions with an independence property. Specifically, if your posterior is a distribution over variables z_1, ..., z_N, then a mean-field posterior will be a product of marginal distributions p_1(z_1), ..., p_N(z_N). So your approximate posterior will treat all the variables as unrelated: it thinks the posterior probability of, say, “z_1 > 0.3″ is the same no matter the value of z_2, or z_3, etc.
This just seems wrong. Statistical models of the world generally don’t have independent posteriors (I think?), and for an important reason. Generally the different variables you want to estimate in a model -- say coefficients in a regression, or latent variable values in a graphical model -- correspond to different causal pathways, or more generally different explanations of the same observations, and this puts them in competition.
You’d expect a sort of antisymmetry here, rather than independence: if one variable changes then the others have to change too to maintain the same output, and they’ll change in the “opposite direction,” with respect to how they affect that output. In an unbiased regression with two positive variables, if the coefficient for z_1 goes up then the coefficient for z_2 should go down; you can explain the data with one raised and the other lowered, or vice versa, but not with both raised or lowered.
This figure from Blei et al shows what variational Bayes does in this kind of case:
The objective function for variational inference heavily penalizes making things likely in the approximation if they’re not likely in the exact posterior, and doesn’t care as much about the reverse. (It’s a KL divergence -- and yes you can also do the flipped version, that’s something else called “expectation propagation”).
An independent distribution can’t make “high x_1, high_2″ likely without also making “high x_1, low x_2″ likely. So it can’t put mass in the corners of the oval without also putting mass in really unlikely places (the unoccupied corners). Thus it just squashes into the middle.
People talk about this as “variational Bayes underestimating the variance.” And, yeah, it definitely does that. But more fundamentally, it doesn’t just underestimate the variance of each variable, it also completely misses the competition between variables in model space. It can’t capture any of the models that explain the data mostly with one variable and not another, even though these models are as likely as any. Isn’t this a huge problem? Doesn’t it kind of miss the point of statistical modeling?
(And it’s especially bad in cases like neural nets, where your variables have permutation symmetries. What people call “variational Bayesian neural nets” is basically ordinary neural net fitting to find some local critical point, and placing a little blob of variation around that one critical point. It’s nothing like a real ensemble, it’s just one member of an ensemble but smeared out a little.)
#mathpost#you just gotta place your faith in a theorem called bayes#statpicking#(kinda stretching the scope of that last tag)
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SSC CGL Syllabus 2021-22| Exam Pattern For Tier I, II,III,IV
Tier I Syllabus:
Tier-I: General Intelligence & Reasoning:
It would include questions of both verbal and non-verbal type. This component may include questions on analogies, similarities and differences, space visualization, spatial orientation, problem solving, analysis, judgment, decision making, visual memory, discrimination, observation, relationship concepts, arithmetical reasoning and figural classification, arithmetic number series, non-verbal series, coding and decoding, statement conclusion, syllogistic reasoning etc. The topics are, Semantic Analogy, Symbolic/ Number Analogy, Figural Analogy, Semantic Classification, Symbolic/ Number Classification, Figural Classification, Semantic Series, Number Series, Figural Series, Problem Solving, Word Building, Coding & de-coding, Numerical Operations, symbolic Operations, Trends, Space Orientation, Space Visualization, Venn Diagrams, Drawing inferences, Punched hole/ pattern- folding & un-folding, Figural Pattern- folding and completion, Indexing, Address matching, Date & city matching, Classification of centre codes/roll numbers, Small & Capital letters/ numbers coding, decoding and classification, Embedded Figures, Critical thinking, Emotional Intelligence, Social Intelligence, Other sub-topics, if any.
General Awareness:
Questions in this component will be aimed at testing the candidates‟ general awareness of the environment around him and its application to society. Questions will also be designed to test knowledge of current events and of such matters of every day observations and experience in their scientific aspect as may be expected of any educated person. The test will also include questions relating to India and its neighbouring countries especially pertaining History, Culture, Geography, Economic Scene, General Policy & Scientific Research.
Quantitative Aptitude:
The questions will be designed to test the ability of appropriate use of numbers and number sense of the candidate. The scope of the test will be computation of whole numbers, decimals, fractions and relationships between numbers, Percentage. Ratio & Proportion, Square roots, Averages, Interest, Profit and Loss, Discount, Partnership Business, Mixture and Alligation, Time and distance, Time & Work, Basic algebraic identities of School Algebra & Elementary surds, Graphs of Linear Equations, Triangle and its various kinds of centres, Congruence and similarity of triangles, Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two or more circles, Triangle, Quadrilaterals, Regular Polygons, Circle, Right Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular Parallelepiped, Regular Right Pyramid with triangular or square base, Trigonometric ratio, Degree and Radian Measures, Standard Identities, Complementary angles, Heights and Distances, Histogram, Frequency polygon, Bar diagram & Pie chart.
English Comprehension:
Candidates‟ ability to understand correct English, his/ her basic comprehension and writing ability, etc. would be tested.
Tier II Syllabus:
Paper-I (Quantitative Abilities):
The questions will be designed to test the ability of appropriate use of numbers and number sense of the candidate. The scope of the test will be the computation of whole numbers, decimals, fractions and relationships between numbers, Percentage, Ratio & Proportion, Square roots, Averages, Interest, Profit and Loss, Discount, Partnership Business, Mixture and Alligation, Time and distance, Time & Work, Basic algebraic identities of School Algebra & Elementary surds, Graphs of Linear Equations, Triangle and its various kinds of centres, Congruence and similarity of triangles, Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two or more circles, Triangle, Quadrilaterals, Regular Polygons, Circle, Right Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular Parallelepiped, Regular Right Pyramid with triangular or square base, Trigonometric ratio, Degree and Radian Measures, Standard Identities, Complementary angles, Heights and Distances, Histogram, Frequency polygon, Bar diagram & Pie chart.
Paper-II (English Language and Comprehension):
Questions in this component will be designed to test the candidate’s understanding and knowledge of English Language and will be based on spot the error, fill in the blanks, synonyms, antonyms, spelling/ detecting misspelled words, idioms & phrases, one word substitution, improvement of sentences, active/ passive voice of verbs, conversion into direct/ indirect narration, shuffling of sentence parts, shuffling of sentences in a passage, cloze passage & comprehension passage.
Paper-III (Statistics):
Collection, Classification and Presentation of Statistical Data – Primary and Secondary data, Methods of data collection; Tabulation of data; Graphs and charts; Frequency distributions; Diagrammatic presentation of frequency distributions.
Measures of Central Tendency- Common measures of central tendency – mean median and mode; Partition values- quartiles, deciles, percentiles.
Measures of Dispersion- Common measures dispersion – range, quartile deviations, mean deviation and standard deviation; Measures of relative dispersion.
Moments, Skewness and Kurtosis – Different types of moments and their relationship; meaning of skewness and kurtosis; different measures of skewness and kurtosis.
Correlation and Regression – Scatter diagram; simple correlation coefficient; simple regression lines; Spearman’s rank correlation; Measures of association of attributes; Multiple regression; Multiple and partial correlation (For three variables only).
Probability Theory – Meaning of probability; Different definitions of probability; Conditional probability; Compound probability; Independent events; Bayes‟ theorem.
Random Variable and Probability Distributions – Random variable; Probability functions; Expectation and Variance of a random variable; Higher moments of a random variable; Binomial, Poisson, Normal and Exponential distributions; Joint distribution of two random variable (discrete).
Sampling Theory – Concept of population and sample; Parameter and statistic, Sampling and non-sampling errors; Probability and nonprobability sampling techniques (simple random sampling, stratified sampling, multistage sampling, multiphase sampling, cluster sampling, systematic sampling, purposive sampling, convenience sampling and quota sampling); Sampling distribution (statement only); Sample size decisions.
Statistical Inference - Point estimation and interval estimation, Properties of a good estimator, Methods of estimation (Moments method, Maximum likelihood method, Least squares method), Testing of hypothesis, Basic concept of testing, Small sample and large sample tests, Tests based on Z, t, Chi-square and F statistic, Confidence intervals.
Analysis of Variance - Analysis of one-way classified data and two-way classified data.
Time Series Analysis - Components of time series, Determinations of trend component by different methods, Measurement of seasonal variation by different methods.
Index Numbers - Meaning of Index Numbers, Problems in the construction of index numbers, Types of index number, Different formulae, Base shifting and splicing of index numbers, Cost of living Index Numbers, Uses of Index Numbers.
Paper-IV (General Studies-Finance and Economics):
Part A: Finance and Accounts-(80 marks):
Fundamental principles and basic concept of Accounting:
Financial Accounting: Nature and scope, Limitations of Financial Accounting, Basic concepts and Conventions, Generally Accepted Accounting Principles.
Basic concepts of accounting: Single and double entry, Books of original Entry, Bank Reconciliation, Journal, ledgers, Trial Balance, Rectification of Errors, Manufacturing, Trading, Profit & loss Appropriation Accounts, Balance Sheet Distinction between Capital and Revenue Expenditure, Depreciation Accounting, Valuation of Inventories, Non-profit organisations Accounts, Receipts and Payments and Income & Expenditure Accounts, Bills of Exchange, Self-Balancing Ledgers.
Part B: Economics and Governance-(120 marks):
Comptroller & Auditor General of India- Constitutional provisions, Role and responsibility.
Finance Commission-Role and functions.
Basic Concept of Economics and introduction to Micro Economics: Definition, scope and nature of Economics, Methods of economic study and Central problems of an economy and Production possibilities curve.
Theory of Demand and Supply: Meaning and determinants of demand, Law of demand and Elasticity of demand, Price, income and cross elasticity; Theory of consumer’s behaviour Marshall an approach and Indifference curve approach, Meaning and determinants of supply, Law of supply and Elasticity of Supply.
Theory of Production and cost: Meaning and Factors of production; Laws of production- Law of variable proportions and Laws of returns to scale.
Forms of Market and price determination in different markets: Various forms of markets-Perfect Competition, Monopoly, Monopolistic Competition and Oligopoly ad Price determination in these markets.
Indian Economy:
Economic Reforms in India: Economic reforms since 1991; Liberalisation, Privatisation, Globalisation and Disinvestment.
Money and Banking:
Role of Information Technology in Governance.
Nature of the Indian Economy Role of different sectors Role of Agriculture, Industry and Services-their problems and growth;
National Income of India-Concepts of national income, Different methods of measuring national income.
Population-Its size, rate of growth and its implication on economic growth.
Poverty and unemployment- Absolute and relative poverty, types, causes and incidence of unemployment
Infrastructure-Energy, Transportation, Communication.
Monetary/ Fiscal policy- Role and functions of Reserve Bank of India; functions of commercial Banks/RRB/Payment Banks.
Budget and Fiscal deficits and Balance of payments.
Fiscal Responsibility and Budget Management Act, 2003.
Note: Questions in Paper-I will be of Matriculation Level, Paper-II of 10+2 Level and in Paper-III and Paper-IV of Graduation Level.
Tier-IV Syllabus (Skill Test):
Date Entry Skill Test (DEST):
The “Data Entry Speed Test” Skill Test will be conducted for a passage of about 2000 (two thousand) key depressions for a duration of 15 (fifteen) minutes.
Computer Proficiency Test (CPT):
The Commission will hold Computer Proficiency Test (CPT), comprising of three modules: (i) Word Processing, (ii) Spread Sheet and (iii) Generation of Slides. The CPT will be conducted in the manner decided by the Commission for the purpose. No exemption from CPT is allowed for any category of PwD candidates. CPT will be of qualifying nature.
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300+ TOP STATA Interview Questions and Answers
STATA Interview Questions for freshers experienced :-
1. What is the elementary use of Stata? The integrated statistical software is fundamentally used as an integral part of research methodologies in the field of economics, biomedicine, and political science in order to examine data pattern. 2. What are the most advisable functions performed with the help of Stata? The program is best suited for processing time? the series, panel, and cross? sectional data. 3. What makes the tool more intuitive? The availability of both command line and graphical user interface makes the usage of the software more spontaneous. 4. What are the competencies of using Stata software? The incorporation of data management, statistical analysis, graphics, simulations, regression, and custom programming and at the same time it also accommodates a system to disseminate user-written programs that lets it grow continuously, making it an integral statistical tool. 5. List four major builds of Stata and state their purposes? STATA MP - Multiprocessor computer which includes dual-core and multicore processors. STATA SE - Majorly used for analyzing larger databases STATA IC - The standard version of the software Numerics by STATA support MP, SE AND IC data types in an embedded environment. 6. State the various disciplines which use Stata as an integral software for efficient results? STATA software acts as an effective analytical and statistical tools for major sectors, they are as follows : Behavioral sciences: Behavioral scientist entrust STATA for its accuracy, extensibility, reproducibility, and ease of use features. Whether it is an extensive research on cognitive development, studying personality traits or developing measurement instruments, The software accommodates all the required collateral to pursue a broad range of behavioral science questions. Education: In the process of developing new tests or researching diverse topics as learning and development, teacher effectiveness, or school finance, STATA establishes the relevant and accurate statistical methodology options forward. The analysis is consistently integrated with illustrations (graphics) and data management into one package in order to seek a wide range of educational questions. Medical: Medicinal researchers entrust to use STATA for its range of biostatistical methods and reproducibility approach towards the data. In the process of any medical research or while performing a clinical trial, the program provides accurate tools which helps conduct the study from power and sample-size calculations to data management to analysis. Biostatistics: Biostatisticians approve of STATA for its accuracy, extensibility, and reproducibility. Inconsiderate of the study’s statistical approach or focus area or whether it is a cross-sectional, longitudinal, or time-to-event. STATA equips the users with all the necessary statistics, graphics, and data management tools needed to implement and study a wide range of biostatistical methods. Economics: The researchers in the field of economics have always relied upon STATA for its accuracy and relevancy. Whether its a study on educational institution selection research process, Gross domestic price or stock trends, Stata provides all the statistics, graphics, and data management tools needed to complete the study with utmost authenticity. Business / Finance - Marketing: financial and marketing research analysts often rely on this tool in the case of researching asset pricing, capital market dynamics, customer-value management, consumer and firm behaviour, or branding, the reason being its accuracy and extensibility of providing all the statistics, graphics, and data management tools. Sociology: Apart from the above-listed sectors, STATA is also used in the study of demographic and geographic research processes. 7. What are the key features of Stata/ MP? STATA/ MP is termed as the fastest and largest version of the program. This version’s multiprocessing abilities provide the most comprehensive support (multi core) to all kinds of statistics and data administration. STATA/MP supports over 64 cores/processors, making it the fastest medium to analyze the data when compared to STATA/SE. This version interprets 10 to 20 billion observations in comparison to STATA/SE’s 2 billion observations. The program is 100% compatible with other versions and needs no modification of the analyses to obtain Stata/MP's speed improvements. 8. List down few highlights of new Stata 15? Extended regression modules which can address the problems such as Endogenous covariates, Nonrandom treatment assignment etc in any combination, unlike the previous Heckman and ivregress modules. STATA’S Latin Class Analysis helps to identify unobserved categories in the latent classes. STATA now supports Markdown - A standard markup language that allows text formatting from plain text input. Program's Dynamic stochastic general equilibrium command estimates the parameters of DSGE models that are linear in the variables but potentially nonlinear in the parameters. Bayes prefix, when combined with Bayesian features with STATA’S spontaneous and elegant specification of regression models, lets the users fit Bayesian regression models more conveniently and fit additional models. 9. What is the work function of Stata’S user interface? Primarily, STATA by default opens in four different windows : Results: This window displays all the commands and their results, with an exception being made for graphs which are showcased in their own window. Review: Only the commands are made visible in this particular window. When clicked on any specific command by the user it appears on a separate window. The review tab has an option of “ Save Review Contents ” which allows the user to save all documented files in the review window to a file for later use. ( This is not a substitute for log and do files.) Command: This is the space used to type the commands while working in an interactive mechanism. All the content typed here will be reflected in both results and review windows. “ Page Up “ and “ Page Down “ keys are used in order to view previously executed commands. Variables: Entire list of user ’s variables and their labels are displayed here. When clicked it will be pasted in the command window. 10. What are the various data format compatible with Stata software? STATA is compatible to import data from various formats, Inclusive of ASCII data formats (such as CSV or databank formats) and spreadsheet formats (including various Excel formats). It can as well read and write SAS XPORT format datasets natively, using the fdause and fdasave commands. The STATAS’s dominion file formats are platform independent, which enables the users from different operating systems comfortably exchange datasets and programs. Although there has been consistent change over the course of time with respect to STATA’S data format, still the users can read all older dataset formats and can write both the current and most recent previous dataset format, using the same old command.
STATA Interview Questions 11. Elaborate on Do, Log and CmdLog files? The User must always operate his work in a do-file, which ensures the output can be reproduced at a later time. One can start a do.file by simply clicking on the do.file editor button. The user has to also make sure to always turn on “Auto indent” and Auto save on do/run” options presented in the preferences tab. Another cardinal rule while working on STATA is the always maintain a log file running. These files have a record of the work done and even showcases the results. This function can be activated by giving "log using mylog.log" command. The usage of “.log” extension automatically creates the log as a plain text file that can then be opened in Microsoft Word or notepad as well as Stata's viewer. One can initiate command log with the command "cmdlog using mycmdlog.log". This ensures the file is saved in the text format. CmdLog has only the executed commands with no reflection of the output. Additionally, all the commands irrespective of where they are issued from are recorded in the command log. 12. Explain Stata salient features? Time series: This feature of the software allows the users to handle all the statistical challenges constitutional to time-series data, for example, common factors, autoregressive conditional heteroskedasticity, unit roots, autocorrelations etc. The program operates various activities like filtering to fitting compound multiple variate models and graphing which reveals the structure into the time series. Survival Analysis: With the help of specialized survival analytical tools provided by STATA, the user an analyze the duration of an outcome. They can estimate and plot the possibility of survival over time irrespective of discrepancies such as (unobserved event, delay entry or gaps in the study). hazard ratios, mean survival time, and survival probabilities can be predicted with the help of this model. Extended regression Models: ERM is the face name for the class of models addresses several complications that arise on a regular basis frequently. Example of ERMS are 1) endogenous covariates, 2) sample selection and 3) non random treatment assignment. These complications can either arise alone or with any combination. The ERMs grants the user to make authentic inferences. Structural Equation Modeling: SME performs an assessment of the mediation effects. It evaluates the relationship between unobserved latent concept and observed variables that measure the concerned latent concept. ANOVA / MANOVA: These are known as Fit one- and two-way models. They analyze the data enclosed, fixed or random factors or with repeated measures. ANOVA is used when the user faces continuous covariates, whereas MANOVA models when the user has multiple outcome variables. The relationship between the outcome and predictors can be explored by estimating effect sizes and computing least-squares and marginal means. 13. List down standards methods and advanced techniques provided by Stata program? STATA provides over 100 various authentic statistical tools. Here are the few examples: STANDARD METHODS ADVANCED TECHNIQUES Basic tabulations and summaries Time-series smoothers Multilevel models Binary, count, and censored outcomes Case-control analysis Contrasts and comparisons Dynamic panel-data (DPD) regressions Multiple imputations Power analysis SEM (structural equation modeling) ANOVA and MANOVA Latent class analysis (LCA) 14. Explain Publication - Quality graphics feature? STATA makes it convenient for the users to generate high-quality styled graphs and visual representations. A user can either point and click or write scripts to produce numerous graphs in a reproducible manner. In order to view the visual, it must be either converted into EPS or TIF for publication, to PNG or SVG for the web, or to PDF. With an additional feature of integrated graph editor, the user can alter the graph accordingly. 15. List the different graph styles provided by STATA? STATA is one of the recommended software to create graphical illustrations, the following are the types of graphs made available by STATA namely : Bar charts Box plots Histograms Spike plots Pie charts Scatterplot matrices Dot charts Line charts Area charts etc. 16. How does the reading and documentation function work in STATA? In order to write a program to read data into STATA, Then the user has two possible choices. “Infile” and “infix” . When compared to infix, the infile command has more capabilities but at the same time has a higher level of complexity. If the user’s codebook has “start” and “length” information for the variables or the variables are separated by spaces ( not commas or tabs) then it advisable to use infile. On the other hand, if the codebook contains “start” and “end” column information then, the user can go ahead with infix. 17. What are the advantages of using STATA program? STATA is a fast, accurate and easy to use interface, with an additional feature of intuitive command syntax making it a powerful statistical data analytical tool. STATA provides a wide range of statistical tools from standard methods such as Basic tabulations and summaries, Case-control analysis, Linear regression to advanced techniques for example: Multilevel models, Dynamic panel data regressions, SEM etc. Data administration feature of STATA allows complete control over all data types. The user can then combine and reshape data sets, manage variables, and collect statistics across groups or duplicates. The software is capable to manage unique data sets (survival/duration data, panel/longitudinal etc.) The program is cross-platform compatible which includes windows, MAC, Linux. 18. Explain the role of MATA programming language? MATA is a full-fledged programming language that compiles the data typed into bytecode, optimizes it, and executes it fast. Al though it is not a requirement in order to use STATA a fast and complex matrix programming language is an essential part of STATA. The language acts as both interactive environments for manipulating matrices and fully developed environment that can produce compiled and optimized code. It complies important features for the processing of panel data, performs operations on real or complex matrices and offers outright support for object-oriented -programming and is fully integrated with every form of STATA. 19. Explain describe and codebook commands? Once the data is loaded in STATA, User must document in order to know what are the variables and how they are coded. The describe and codebook commands furnish information about the user’s data. Describe command is the most basic form of a command. It projects a short description of the file and also lists variables and their required information in the datasets. Codebook drafts a detailed description of each variable. By default, the codebook command will list variables that have nine or less discrete values and means for those which are more than nine. STATA Interview Questions and Answers Pdf Download Read the full article
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Interesting Papers for Week 52, 2019
Happy Holidays!
A Novel Predictive-Coding-Inspired Variational RNN Model for Online Prediction and Recognition. Ahmadi, A., & Tani, J. (2019). Neural Computation, 31(11), 2025–2074.
Cortical and thalamic inputs exert cell type‐specific feedforward inhibition on striatal GABAergic interneurons. Assous, M., & Tepper, J. M. (2019). Journal of Neuroscience Research, 97(12), jnr.24444.
Corticostriatal plasticity in the nucleus accumbens core. Bamford, N. S., & Wang, W. (2019). Journal of Neuroscience Research, 97(12), jnr.24494.
Turing complete neural computation based on synaptic plasticity. Cabessa, J. (2019). PLOS ONE, 14(10), e0223451.
Robust Control in Human Reaching Movements: A Model-Free Strategy to Compensate for Unpredictable Disturbances. Crevecoeur, F., Scott, S. H., & Cluff, T. (2019). Journal of Neuroscience, 39(41), 8135–8148.
Invariant neural responses for sensory categories revealed by the time-varying information for communication calls. Elie, J. E., & Theunissen, F. E. (2019). PLOS Computational Biology, 15(9), e1006698.
Dynamic Integrative Synaptic Plasticity Explains the Spacing Effect in the Transition from Short- to Long-Term Memory. Elliott, T. (2019). Neural Computation, 31(11), 2212–2251.
Coordinated hippocampal-entorhinal replay as structural inference. Evans, T., & Burgess, N. (2019). In Advances in Neural Information Processing Systems 33 (NeurIPS 2019) (pp. 1729–1741). Vancouver, Canada.
Flexible information routing in neural populations through stochastic comodulation. Haimerl, C., Savin, C., & Simoncelli, E. (2019). In Advances in Neural Information Processing Systems 33 (NeurIPS 2019) (pp. 14379–14388). Vancouver, Canada.
Embodied Synaptic Plasticity With Online Reinforcement Learning. Kaiser, J., Hoff, M., Konle, A., Vasquez Tieck, J. C., Kappel, D., Reichard, D., … Dillmann, R. (2019). Frontiers in Neurorobotics, 13, 81.
Rats exhibit similar biases in foraging and intertemporal choice tasks. Kane, G. A., Bornstein, A. M., Shenhav, A., Wilson, R. C., Daw, N. D., & Cohen, J. D. (2019)e. Life, 8, e48429.
Great apes use self-experience to anticipate an agent’s action in a false-belief test. Kano, F., Krupenye, C., Hirata, S., Tomonaga, M., & Call, J. (2019). Proceedings of the National Academy of Sciences of the United States of America, 116(42), 20904–20909.
GABAergic Inhibition Gates Perceptual Awareness During Binocular Rivalry. Mentch, J., Spiegel, A., Ricciardi, C., & Robertson, C. E. (2019). Journal of Neuroscience, 39(42), 8398–8407.
Preserving Inhibition during Developmental Hearing Loss Rescues Auditory Learning and Perception. Mowery, T. M., Caras, M. L., Hassan, S. I., Wang, D. J., Dimidschstein, J., Fishell, G., & Sanes, D. H. (2019). Journal of Neuroscience, 39(42), 8347–8361.
Mice Discriminate Stereoscopic Surfaces Without Fixating in Depth. Samonds, J. M., Choi, V., & Priebe, N. J. (2019). Journal of Neuroscience, 39(41), 8024–8037.
Brian 2, an intuitive and efficient neural simulator. Stimberg, M., Brette, R., & Goodman, D. F. (2019). eLife, 8, e47314.
Complementary encoding of priors in monkey frontoparietal network supports a dual process of decision-making. Suriya-Arunroj, L., & Gail, A. (2019). eLife, 8, e47581.
Isolated cortical computations during delta waves support memory consolidation. Todorova, R., & Zugaro, M. (2019). Science, 366(6463), 377–381.
Adversarial Feature Alignment: Avoid Catastrophic Forgetting in Incremental Task Lifelong Learning. Yao, X., Huang, T., Wu, C., Zhang, R.-X., & Sun, L. (2019). Neural Computation, 31(11), 2266–2291.
A Normative Theory for Causal Inference and Bayes Factor Computation in Neural Circuits. Zhang, W., Wu, S., Doiron, B., & Lee, T. S. (2019). In Advances in Neural Information Processing Systems 33 (NeurIPS 2019) (pp. 3799–3808). Vancouver, Canada.
#science#Neuroscience#neurobiology#computational neuroscience#psychophysics#cognition#cognitive science#research#Brain science#scientific publications
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"[D] A blog post introducing variational inference"- Detail: Hello r/ml, recently I wrote a post giving a mathematical introduction and derivations of various models of variational inference.AbstractIn this post I give an introduction to variational inference, which is about maximising the evidence lower bound (ELBO).I use a top-down approach, starting with the KL divergence and the ELBO, to lay the mathematical framework of all the models in this post.Then I define mixture models and the EM algorithm, with Gaussian mixture model (GMM), probabilistic latent semantic analysis (pLSA) the hidden markov model (HMM) as examples.After that I present the fully Bayesian version of EM, also known as mean field approximation (MFA), and apply it to fully Bayesian mixture models, with fully Bayesian GMM (also known as variational GMM), latent Dirichlet allocation (LDA) and Dirichlet process mixture model (DPMM) as examples.Then I explain stochastic variational inference, a modification of EM and MFA to improve efficiency.Finally I talk about autoencoding variational Bayes (AEVB), a Monte-Carlo + neural network approach to raising the ELBO, exemplified by the variational autoencoder (VAE). I also show its fully Bayesian version.Link:https://ypei.me/posts/2019-02-14-raise-your-elbo.htmlAll feedback is welcome.. Caption by HomogeneousSpace. Posted By: www.eurekaking.com
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Toward the unambiguous identification of supermassive binary black holes through Bayesian inference. (arXiv:2004.10944v3 [astro-ph.HE] UPDATED)
Supermassive binary black holes at sub-parsec orbital separations have yet to be discovered, with the possible exception of blazar OJ~287. In parallel to the global hunt for nanohertz gravitational waves from supermassive binaries using pulsar timing arrays, there has been a growing sample of candidates reported from electromagnetic surveys, particularly searches for periodic variations in optical light curves of quasars. However, the periodicity search is prone to false positives from quasar red noise and quasi-periodic oscillations from the accretion disc of a single supermassive black hole---especially when the data span fewer than a few signal cycles. We present a Bayesian method for the detection of quasar (quasi-)periodicity in the presence of red noise. We apply this method to the binary candidate PG1302$-$102, and show that a) there is very strong support (Bayes factor $>10^6$) for quasi-periodicity, and b) the data slightly favour a quasi-periodic oscillation over a sinusoidal signal, which we interpret as modest evidence against the binary black hole hypothesis. We also find that the prevalent damped random walk red-noise model is disfavored with more than 99.9\% credibility. Finally, we outline future work that may enable the unambiguous identification of supermassive binary black holes.
from astro-ph.HE updates on arXiv.org https://ift.tt/2XYyKrc
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The 9 Best Free Online Big Information and Data Analytics Programs
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A Gentle Introduction to Generative Adversarial Networks (GANs)
Generative Adversarial Networks, or GANs for short, are an approach to generative modeling using deep learning methods, such as convolutional neural networks.
Generative modeling is an unsupervised learning task in machine learning that involves automatically discovering and learning the regularities or patterns in input data in such a way that the model can be used to generate or output new examples that plausibly could have been drawn from the original dataset.
GANs are a clever way of training a generative model by framing the problem as a supervised learning problem with two sub-models: the generator model that we train to generate new examples, and the discriminator model that tries to classify examples as either real (from the domain) or fake (generated). The two models are trained together in a zero-sum game, adversarial, until the discriminator model is fooled about half the time, meaning the generator model is generating plausible examples.
GANs are an exciting and rapidly changing field, delivering on the promise of generative models in their ability to generate realistic examples across a range of problem domains, most notably in image-to-image translation tasks such as translating photos of summer to winter or day to night, and in generating photorealistic photos of objects, scenes, and people that even humans cannot tell are fake.
In this post, you will discover a gentle introduction to Generative Adversarial Networks, or GANs.
After reading this post, you will know:
Context for GANs, including supervised vs. unsupervised learning and discriminative vs. generative modeling.
GANs are an architecture for automatically training a generative model by treating the unsupervised problem as supervised and using both a generative and a discriminative model.
GANs provide a path to sophisticated domain-specific data augmentation and a solution to problems that require a generative solution, such as image-to-image translation.
Let’s get started.
A Gentle Introduction to Generative Adversarial Networks (GANs) Photo by Barney Moss, some rights reserved.
Overview
This tutorial is divided into three parts; they are:
What Are Generative Models?
What Are Generative Adversarial Networks?
Why Generative Adversarial Networks?
What Are Generative Models?
In this section, we will review the idea of generative models, stepping over the supervised vs. unsupervised learning paradigms and discriminative vs. generative modeling.
Supervised vs. Unsupervised Learning
A typical machine learning problem involves using a model to make a prediction, e.g. predictive modeling.
This requires a training dataset that is used to train a model, comprised of multiple examples, called samples, each with input variables (X) and output class labels (y). A model is trained by showing examples of inputs, having it predict outputs, and correcting the model to make the outputs more like the expected outputs.
In the predictive or supervised learning approach, the goal is to learn a mapping from inputs x to outputs y, given a labeled set of input-output pairs …
— Page 2, Machine Learning: A Probabilistic Perspective, 2012.
This correction of the model is generally referred to as a supervised form of learning, or supervised learning.
Example of Supervised Learning
Examples of supervised learning problems include classification and regression, and examples of supervised learning algorithms include logistic regression and random forest.
There is another paradigm of learning where the model is only given the input variables (X) and the problem does not have any output variables (y).
A model is constructed by extracting or summarizing the patterns in the input data. There is no correction of the model, as the model is not predicting anything.
The second main type of machine learning is the descriptive or unsupervised learning approach. Here we are only given inputs, and the goal is to find “interesting patterns” in the data. […] This is a much less well-defined problem, since we are not told what kinds of patterns to look for, and there is no obvious error metric to use (unlike supervised learning, where we can compare our prediction of y for a given x to the observed value).
— Page 2, Machine Learning: A Probabilistic Perspective, 2012.
This lack of correction is generally referred to as an unsupervised form of learning, or unsupervised learning.
Example of Unsupervised Learning
Examples of unsupervised learning problems include clustering and generative modeling, and examples of unsupervised learning algorithms are K-means and Generative Adversarial Networks.
Discriminative vs. Generative Modeling
In supervised learning, we may be interested in developing a model to predict a class label given an example of input variables.
This predictive modeling task is called classification.
Classification is also traditionally referred to as discriminative modeling.
… we use the training data to find a discriminant function f(x) that maps each x directly onto a class label, thereby combining the inference and decision stages into a single learning problem.
— Page 44, Pattern Recognition and Machine Learning, 2006.
This is because a model must discriminate examples of input variables across classes; it must choose or make a decision as to what class a given example belongs.
Example of Discriminative Modeling
Alternately, unsupervised models that summarize the distribution of input variables may be able to be used to create or generate new examples in the input distribution.
As such, these types of models are referred to as generative models.
Example of Generative Modeling
For example, a single variable may have a known data distribution, such as a Gaussian distribution, or bell shape. A generative model may be able to sufficiently summarize this data distribution, and then be used to generate new variables that plausibly fit into the distribution of the input variable.
Approaches that explicitly or implicitly model the distribution of inputs as well as outputs are known as generative models, because by sampling from them it is possible to generate synthetic data points in the input space.
— Page 43, Pattern Recognition and Machine Learning, 2006.
In fact, a really good generative model may be able to generate new examples that are not just plausible, but indistinguishable from real examples from the problem domain.
Examples of Generative Models
Naive Bayes is an example of a generative model that is more often used as a discriminative model.
For example, Naive Bayes works by summarizing the probability distribution of each input variable and the output class. When a prediction is made, the probability for each possible outcome is calculated for each variable, the independent probabilities are combined, and the most likely outcome is predicted. Used in reverse, the probability distributions for each variable can be sampled to generate new plausible (independent) feature values.
Other examples of generative models include Latent Dirichlet Allocation, or LDA, and the Gaussian Mixture Model, or GMM.
Deep learning methods can be used as generative models. Two popular examples include the Restricted Boltzmann Machine, or RBM, and the Deep Belief Network, or DBN.
Two modern examples of deep learning generative modeling algorithms include the Variational Autoencoder, or VAE, and the Generative Adversarial Network, or GAN.
What Are Generative Adversarial Networks?
Generative Adversarial Networks, or GANs, are a deep-learning-based generative model.
More generally, GANs are a model architecture for training a generative model, and it is most common to use deep learning models in this architecture.
The GAN architecture was first described in the 2014 paper by Ian Goodfellow, et al. titled “Generative Adversarial Networks.”
A standardized approach called Deep Convolutional Generative Adversarial Networks, or DCGAN, that led to more stable models was later formalized by Alec Radford, et al. in the 2015 paper titled “Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks“.
Most GANs today are at least loosely based on the DCGAN architecture …
— NIPS 2016 Tutorial: Generative Adversarial Networks, 2016.
The GAN model architecture involves two sub-models: a generator model for generating new examples and a discriminator model for classifying whether generated examples are real, from the domain, or fake, generated by the generator model.
Generator. Model that is used to generate new plausible examples from the problem domain.
Discriminator. Model that is used to classify examples as real (from the domain) or fake (generated).
Generative adversarial networks are based on a game theoretic scenario in which the generator network must compete against an adversary. The generator network directly produces samples. Its adversary, the discriminator network, attempts to distinguish between samples drawn from the training data and samples drawn from the generator.
— Page 699, Deep Learning, 2016.
The Generator Model
The generator model takes a fixed-length random vector as input and generates a sample in the domain.
The vector is drawn from randomly from a Gaussian distribution, and the vector is used to seed the generative process. After training, points in this multidimensional vector space will correspond to points in the problem domain, forming a compressed representation of the data distribution.
This vector space is referred to as a latent space, or a vector space comprised of latent variables. Latent variables, or hidden variables, are those variables that are important for a domain but are not directly observable.
A latent variable is a random variable that we cannot observe directly.
— Page 67, Deep Learning, 2016.
We often refer to latent variables, or a latent space, as a projection or compression of a data distribution. That is, a latent space provides a compression or high-level concepts of the observed raw data such as the input data distribution. In the case of GANs, the generator model applies meaning to points in a chosen latent space, such that new points drawn from the latent space can be provided to the generator model as input and used to generate new and different output examples.
Machine-learning models can learn the statistical latent space of images, music, and stories, and they can then sample from this space, creating new artworks with characteristics similar to those the model has seen in its training data.
— Page 270, Deep Learning with Python, 2017.
After training, the generator model is kept and used to generate new samples.
Example of the GAN Generator Model
The Discriminator Model
The discriminator model takes an example from the domain as input (real or generated) and predicts a binary class label of real or fake (generated).
The real example comes from the training dataset. The generated examples are output by the generator model.
The discriminator is a normal (and well understood) classification model.
After the training process, the discriminator model is discarded as we are interested in the generator.
Sometimes, the generator can be repurposed as it has learned to effectively extract features from examples in the problem domain. Some or all of the feature extraction layers can be used in transfer learning applications using the same or similar input data.
We propose that one way to build good image representations is by training Generative Adversarial Networks (GANs), and later reusing parts of the generator and discriminator networks as feature extractors for supervised tasks
— Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks, 2015.
Example of the GAN Discriminator Model
GANs as a Two Player Game
Generative modeling is an unsupervised learning problem, as we discussed in the previous section, although a clever property of the GAN architecture is that the training of the generative model is framed as a supervised learning problem.
The two models, the generator and discriminator, are trained together. The generator generates a batch of samples, and these, along with real examples from the domain, are provided to the discriminator and classified as real or fake.
The discriminator is then updated to get better at discriminating real and fake samples in the next round, and importantly, the generator is updated based on how well, or not, the generated samples fooled the discriminator.
We can think of the generator as being like a counterfeiter, trying to make fake money, and the discriminator as being like police, trying to allow legitimate money and catch counterfeit money. To succeed in this game, the counterfeiter must learn to make money that is indistinguishable from genuine money, and the generator network must learn to create samples that are drawn from the same distribution as the training data.
— NIPS 2016 Tutorial: Generative Adversarial Networks, 2016.
In this way, the two models are competing against each other, they are adversarial in the game theory sense, and are playing a zero-sum game.
Because the GAN framework can naturally be analyzed with the tools of game theory, we call GANs “adversarial”.
— NIPS 2016 Tutorial: Generative Adversarial Networks, 2016.
In this case, zero-sum means that when the discriminator successfully identifies real and fake samples, it is rewarded or no change is needed to the model parameters, whereas the generator is penalized with large updates to model parameters.
Alternately, when the generator fools the discriminator, it is rewarded, or no change is needed to the model parameters, but the discriminator is penalized and its model parameters are updated.
At a limit, the generator generates perfect replicas from the input domain every time, and the discriminator cannot tell the difference and predicts “unsure” (e.g. 50% for real and fake) in every case. This is just an example of an idealized case; we do not need to get to this point to arrive at a useful generator model.
Example of the Generative Adversarial Network Model Architecture
[training] drives the discriminator to attempt to learn to correctly classify samples as real or fake. Simultaneously, the generator attempts to fool the classifier into believing its samples are real. At convergence, the generator’s samples are indistinguishable from real data, and the discriminator outputs 1/2 everywhere. The discriminator may then be discarded.
— Page 700, Deep Learning, 2016.
GANs and Convolutional Neural Networks
GANs typically work with image data and use Convolutional Neural Networks, or CNNs, as the generator and discriminator models.
The reason for this may be both because the first description of the technique was in the field of computer vision and used CNNs and image data, and because of the remarkable progress that has been seen in recent years using CNNs more generally to achieve state-of-the-art results on a suite of computer vision tasks such as object detection and face recognition.
Modeling image data means that the latent space, the input to the generator, provides a compressed representation of the set of images or photographs used to train the model. It also means that the generator generates new images or photographs, providing an output that can be easily viewed and assessed by developers or users of the model.
It may be this fact above others, the ability to visually assess the quality of the generated output, that has both led to the focus of computer vision applications with CNNs and on the massive leaps in the capability of GANs as compared to other generative models, deep learning based or otherwise.
Conditional GANs
An important extension to the GAN is in their use for conditionally generating an output.
The generative model can be trained to generate new examples from the input domain, where the input, the random vector from the latent space, is provided with (conditioned by) some additional input.
The additional input could be a class value, such as male or female in the generation of photographs of people, or a digit, in the case of generating images of handwritten digits.
Generative adversarial nets can be extended to a conditional model if both the generator and discriminator are conditioned on some extra information y. y could be any kind of auxiliary information, such as class labels or data from other modalities. We can perform the conditioning by feeding y into the both the discriminator and generator as [an] additional input layer.
— Conditional Generative Adversarial Nets, 2014.
The discriminator is also conditioned, meaning that it is provided both with an input image that is either real or fake and the additional input. In the case of a classification label type conditional input, the discriminator would then expect that the input would be of that class, in turn teaching the generator to generate examples of that class in order to fool the discriminator.
In this way, a conditional GAN can be used to generate examples from a domain of a given type.
Taken one step further, the GAN models can be conditioned on an example from the domain, such as an image. This allows for applications of GANs such as text-to-image translation, or image-to-image translation. This allows for some of the more impressive applications of GANs, such as style transfer, photo colorization, transforming photos from summer to winter or day to night, and so on.
In the case of conditional GANs for image-to-image translation, such as transforming day to night, the discriminator is provided examples of real and generated nighttime photos as well as (conditioned on) real daytime photos as input. The generator is provided with a random vector from the latent space as well as (conditioned on) real daytime photos as input.
Example of a Conditional Generative Adversarial Network Model Architecture
Why Generative Adversarial Networks?
One of the many major advancements in the use of deep learning methods in domains such as computer vision is a technique called data augmentation.
Data augmentation results in better performing models, both increasing model skill and providing a regularizing effect, reducing generalization error. It works by creating new, artificial but plausible examples from the input problem domain on which the model is trained.
The techniques are primitive in the case of image data, involving crops, flips, zooms, and other simple transforms of existing images in the training dataset.
Successful generative modeling provides an alternative and potentially more domain-specific approach for data augmentation. In fact, data augmentation is a simplified version of generative modeling, although it is rarely described this way.
… enlarging the sample with latent (unobserved) data. This is called data augmentation. […] In other problems, the latent data are actual data that should have been observed but are missing.
— Page 276, The Elements of Statistical Learning, 2016.
In complex domains or domains with a limited amount of data, generative modeling provides a path towards more training for modeling. GANs have seen much success in this use case in domains such as deep reinforcement learning.
There are many research reasons why GANs are interesting, important, and require further study. Ian Goodfellow outlines a number of these in his 2016 conference keynote and associated technical report titled “NIPS 2016 Tutorial: Generative Adversarial Networks.”
Among these reasons, he highlights GANs’ successful ability to model high-dimensional data, handle missing data, and the capacity of GANs to provide multi-modal outputs or multiple plausible answers.
Perhaps the most compelling application of GANs is in conditional GANs for tasks that require the generation of new examples. Here, Goodfellow indicates three main examples:
Image Super-Resolution. The ability to generate high-resolution versions of input images.
Creating Art. The ability to great new and artistic images, sketches, painting, and more.
Image-to-Image Translation. The ability to translate photographs across domains, such as day to night, summer to winter, and more.
Perhaps the most compelling reason that GANs are widely studied, developed, and used is because of their success. GANs have been able to generate photos so realistic that humans are unable to tell that they are of objects, scenes, and people that do not exist in real life.
Astonishing is not a sufficient adjective for their capability and success.
Example of the Progression in the Capabilities of GANs From 2014 to 2017. Taken from The Malicious Use of Artificial Intelligence: Forecasting, Prevention, and Mitigation, 2018.
Further Reading
This section provides more resources on the topic if you are looking to go deeper.
Posts
Books
Papers
Articles
Summary
In this post, you discovered a gentle introduction to Generative Adversarial Networks, or GANs.
Specifically, you learned:
Context for GANs, including supervised vs. unsupervised learning and discriminative vs. generative modeling.
GANs are an architecture for automatically training a generative model by treating the unsupervised problem as supervised and using both a generative and a discriminative model.
GANs provide a path to sophisticated domain-specific data augmentation and a solution to problems that require a generative solution, such as image-to-image translation.
Do you have any questions? Ask your questions in the comments below and I will do my best to answer.
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Multiset Dimension We introduce a variation of the metric dimension, called the multiset dimension. The representation multiset of a vertex $v$ with respect to $W$ (which is a subset of the vertex set of a graph $G$), $r_m (v|W)$, is defined as a multiset of distances between $v$ and the vertices in $W$ together with their multiplicities. If $r_m (u |W) \neq r_m(v|W)$ for every pair of distinct vertices $u$ and $v$, then $W$ is called a resolving set of $G$. If $G$ has a resolving set, then the cardinality of a smallest resolving set is called the multiset dimension of $G$, denoted by $md(G)$. If $G$ does not contain a resolving set, we write $md(G) = \infty$. We present basic results on the multiset dimension. We also study graphs of given diameter and give some sufficient conditions for a graph to have an infinite multiset dimension. … Empirical Bayes Geometric Mean (EBGM) Adjusted estimate for the relative reporting ratio. Example: if EBGM=3.9 for acetaminophen-hepatic failure, then this drug-event combination occurred in the data 3.9 times more frequently than expected under the assumption of no association between the drug and the event. … Jack the Reader (Jack) Many Machine Reading and Natural Language Understanding tasks require reading supporting text in order to answer questions. For example, in Question Answering, the supporting text can be newswire or Wikipedia articles; in Natural Language Inference, premises can be seen as the supporting text and hypotheses as questions. Providing a set of useful primitives operating in a single framework of related tasks would allow for expressive modelling, and easier model comparison and replication. To that end, we present Jack the Reader (Jack), a framework for Machine Reading that allows for quick model prototyping by component reuse, evaluation of new models on existing datasets as well as integrating new datasets and applying them on a growing set of implemented baseline models. Jack is currently supporting (but not limited to) three tasks: Question Answering, Natural Language Inference, and Link Prediction. It is developed with the aim of increasing research efficiency and code reuse. … Jaya Optimisation Algorithm An Efficient Multi-core Implementation of the Jaya Optimisation Algorithm … https://bit.ly/33NdQMJ
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Multiset Dimension We introduce a variation of the metric dimension, called the multiset dimension. The representation multiset of a vertex $v$ with respect to $W$ (which is a subset of the vertex set of a graph $G$), $r_m (v|W)$, is defined as a multiset of distances between $v$ and the vertices in $W$ together with their multiplicities. If $r_m (u |W) \neq r_m(v|W)$ for every pair of distinct vertices $u$ and $v$, then $W$ is called a resolving set of $G$. If $G$ has a resolving set, then the cardinality of a smallest resolving set is called the multiset dimension of $G$, denoted by $md(G)$. If $G$ does not contain a resolving set, we write $md(G) = \infty$. We present basic results on the multiset dimension. We also study graphs of given diameter and give some sufficient conditions for a graph to have an infinite multiset dimension. … Empirical Bayes Geometric Mean (EBGM) Adjusted estimate for the relative reporting ratio. Example: if EBGM=3.9 for acetaminophen-hepatic failure, then this drug-event combination occurred in the data 3.9 times more frequently than expected under the assumption of no association between the drug and the event. … Jack the Reader (Jack) Many Machine Reading and Natural Language Understanding tasks require reading supporting text in order to answer questions. For example, in Question Answering, the supporting text can be newswire or Wikipedia articles; in Natural Language Inference, premises can be seen as the supporting text and hypotheses as questions. Providing a set of useful primitives operating in a single framework of related tasks would allow for expressive modelling, and easier model comparison and replication. To that end, we present Jack the Reader (Jack), a framework for Machine Reading that allows for quick model prototyping by component reuse, evaluation of new models on existing datasets as well as integrating new datasets and applying them on a growing set of implemented baseline models. Jack is currently supporting (but not limited to) three tasks: Question Answering, Natural Language Inference, and Link Prediction. It is developed with the aim of increasing research efficiency and code reuse. … Jaya Optimisation Algorithm An Efficient Multi-core Implementation of the Jaya Optimisation Algorithm … https://bit.ly/2Wz64V7
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SSC CGL Tier 2 Syllabus
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SSC CGL Tier 2 Syllabus
SSC CGL Exam Syllabus 2017 along with exam pattern 2017 is available here to download. Candidates can check the SSC CGL Tier 2 Syllabus 2017 from our web page. SSC CGL syllabus for the recruitment of Group B Group C Posts in various locations in India. SSC has released employment notification earlier and the suitable candidates have effectively completed the procedure of application which completed recently. Participant’s candidates are preparing for online examination through SSC CGL exam.
SSC CGL Tier 2 Syllabus 2017
For such candidates who are really preparing for SSC, posts should take look at this blog post which very clearly explains regarding SSC CGL Exam syllabus to get maximum score in this examination which will be held in an upcoming month. To get the knowledge about SSC CGL Tier 2 Exam syllabus you need to download the complete pdf file from the below-given link and start preparation in well manner.
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SSC CGL Tier 2 Exam Pattern 2017
CGL Tier 2 comprises of four papers, with each paper has the duration of 2 hours. Out of these four papers, paper 1 & paper 2 are compulsory for everyone, while papers 3 and paper 4 are for those who apply for specialized posts like the statistical investigator and assistant audit officer. To check the more information you must read the official advertisement.
Section name
Questions Marks Weigh
Time limit
Paper I: Quantitative Ability (for ALL POSTS) 100 Ques. 200 Marks
2 Hours
(2 Hours 40 Min for VH & Candidates suffering from Cerebral Palsy)
Paper II: English Language (for ALL POSTS) 200 Ques. 200 Marks
2 Hours
(2 Hours 40 Min for VH & Candidates suffering from Cerebral Palsy)
TOTAL 300 Ques. 400 Marks
4 Hours
5 Hrs 20 Min for VH & Candidates suffering from Cerebral Palsy
Paper III: Statistics (for Statistical Investigator Grade II & Compiler posts only) 100 Ques. 200 Marks
40 minutes
(2 Hrs 40 Min for VH & Candidates suffering from Cerebral Palsy)
Paper IV: General Studies (Finance & Economics) (for Assistant Audit Officer Gazetted Group “B” posts only) 100 Ques. 200 Marks
40 minutes
(2 Hrs 40 Min for VH & Candidates suffering from Cerebral Palsy)
Choosing process of the candidates will be completely basis of marks scored in selection rounds. To check the more information regarding SSC CGL Tier II syllabus, pattern, sample paper, previous year papers, model test papers etc get in touch with SSC official website and also bookmark our web page for latest news. Syllabus of any exam is very important to prepare well. Those aspirants who qualify the tier 1 exam will be allowed to attend the Tier 2 exam.
SSC CGL Tier 2 Quantitative aptitude syllabus
Subject Name
Questions
Difficulty Level
Simplification 3-6 Questions Easy Number Series 0-2 Questions Moderate Number System 6-8 Questions Tricky Algebra 5-9 Questions Easy Averages 5-6 Questions Easy Percentage 1-4 Questions Easy Ratio & Proportions 1-6 Questions Moderate Interest 4-5 Questions Moderate Profit & Loss 9-14 Questions Moderate Time & Work 6-7 Questions Moderate Time & Speed 4-6 Questions Easy-Moderate Mensuration 10-13 Questions Easy-Moderate Geometry 12-18 Questions Easy-Difficult Trigonometry 7-10 Questions Easy-Difficult Data Interpretation 5-7 Questions Easy-Difficult Mixtures & Allegations 1-4 Questions Tricks
Below we are providing SSC CGL Tier 2 exam syllabus in pdf file. Just click on the given link and download the pdf file to check the SSC CGL Tier 2 syllabus. The exact date of SSC CGL Tier 2 exam is not announced yet but as per the information was given by SSC in its notification that will be released in November.
SSC CGL Tier 2 english syllabus
Subject Name
Questions
Difficulty Level
Reading Comprehension 30 Tougher than Tier-I Verbal Ability 20 Moderate Grammar 35-40 Moderate Vocabulary 40-50 Moderate Active-Passive 20 Moderate Direct-Indirect 27-30 Moderate
SSC CGL Tier 2 Statics syllabus
Subject
Important Topics
Collection and Representation of Data
Methods of data collection
Frequency distributions
Measures of Central Tendency
Mean
Median and mode
Partition Values – quartiles
Deciles & percentiles
Measures of Dispersion
Range
Quartile deviations
Standard deviation
Mean deviation
Moments, Skewness and Kurtosis
Skewness and kurtosis
Moments and their relationship.
Correlation and Regression
Scatter diagram
Simple correlation coefficient
Simple regression lines
Spearman’s rank correlation
Measures of association of attributes
Multiple regression
Multiple and partial correlation
Probability Theory
Probability
Compound Probability
Conditional Probability
Independent events
Bayes’ Theorem
Random Variable and Probability Distributions
Random variables
Probability functions
Expectation and Variance of a random variable
Higher moments of a random variable
Binomial
Poisson
Normal and Exponential distributions
Joint distribution of two random variable
Sampling Theory
Concept of population and sample
Parameter and statistics
Sampling and non-sampling errors
Probability and non-probability sampling techniques (simple random sampling
Stratified sampling
Multistage sampling
Multiphase sampling
Cluster sampling
Systematic sampling
Purposive sampling
Convenience sampling and quota sampling)
Sampling distribution (statement only)
Sample size decisions
Statistical Inference
Point estimation and interval estimation
Properties of a good estimator
Methods of estimation (Moments method
Maximum likelihood method, Least squares method)
Testing of hypothesis
Basic concept of testing
Small sample and large sample tests
Tests based on Z, t, Chi-square and F statistic
Confidence intervals
Analysis of Variance
–
Time Series Analysis
Components of time series
Determinations of trend component by different methods
Measurement of seasonal variation by different methods
Index Numbers
Meaning of Index Numbers
Problems in the construction of index numbers
Types of index number
Different formulae
Base shifting and splicing of index numbers
Cost of living Index Numbers
Uses of Index Numbers
SSC CGL Tier 2 Financial & Accounting syllabus
Subject
Important Topics
Fundamental principles and basic concept of Accounting
Basics
Financial Accounting
Nature and scope
Limitations of Financial Accounting
Basic concepts and Conventions
Generally Accepted Accounting Principles
Basic concepts of accounting
Single and double entry
Bank Reconciliation, ledgers
Journal, Books of original Entry
Rectification of Errors
Trial Balance
Trading
Profit & loss Appropriation Accounts
Manufacturing
Balance Sheet Distinction between Capital and Revenue Expenditure
Depreciation Accounting
Valuation of Inventories
Receipts and Payments and Income & Expenditure Accounts
Non-profit organizations Accounts
Bills of Exchange
Self Balancing Ledgers
SSC CGL Tier 2 Economics and Governance Syllabus
Comptroller & Auditor General of India- Constitutional provisions, Roles and responsibilities. Finance Commission-Role and functions. Basic Concept of Economics and introduction to Micro Economics Central problems of an economy and Production possibilities curve and Methods of economic study. Theory of Demand and Supply Elasticity Price Income and cross elasticity Theory of consumer’s behaviour-Marshallian approach and Indifference curve approach meaning and determinants of supply Law of supply and Elasticity of Supply. Theory of Production and cost Meaning and Factors of production Laws of production – Law of variable proportions 22 and Laws of returns to scale. Forms of Market and price determination in different markets. Indian Economy Population Poverty Unemployment Growth Infrastructure Liberalisation Privatisation Globalisation Disinvestment. Money and Banking. Role of Information Technology in Governance
The only Tier 1 qualified candidates will be eligible to attend the Tier 2 exam. To give their best in these examination candidates must know the SSC CGL Tier 2 Syllabus 2017. Below we have posted a direct link to download SSC CGL Syllabus 2017 along with exam pattern. To check the more information you must read the official advertisement.
SSC exams 2017
SSC CGL Exam 2017
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CSIR UGC NET Application 2017
COMMON SYLLABUS FOR PART ‘B’ PLUS ‘C’ MATHEMATICAL SCIENCES DEVICE - 1 Analysis: Primary set theory, finite, countable and uncountable sets, True number system as the complete ordered field, Archimedean property, supremum, infimum. admission.scholarshipbag.com Sequences and series, convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, differentiability, indicate value theorem. Sequences plus a number of functions, homogeneous convergence. Riemann sums plus Riemann integral, Improper Integrals. Monotonic functions, types associated with discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral. Functions of various variables, directional derivative, partially derivative, derivative as being a geradlinig transformation, inverse and implied function theorems. Metric areas, compactness, connectedness. Normed geradlinig Spaces. Spaces of constant functions as examples. Geradlinig Algebra: Vector spaces, subspaces, linear dependence, basis, aspect, algebra of linear changes. Algebra of matrices, position and determinant of matrices, linear equations. Eigenvalues plus eigenvectors, Cayley-Hamilton theorem. Matrix representation of linear changes. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms. Internal product spaces, orthonormal base. Quadratic forms, reduction plus classification of quadratic types UNIT - two Complicated Analysis: Algebra of complicated numbers, the complex aircraft, polynomials, power series, transcendental functions such as rapid, trigonometric and hyperbolic features. Analytic functions, Cauchy-Riemann equations. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum modulus rule, Schwarz lemma, Open umschlüsselung theorem. Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius changes. Algebra: Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements. Fundamental theorem of math, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive origins. Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, class equations, Sylow theorems. Rings, ideals, excellent and maximal ideals, quotient rings, unique factorization site, principal ideal domain, Euclidean domain. Polynomial rings plus irreducibility criteria. Fields, limited fields, field extensions, Galois Theory. Topology: basis, thick sets, subspace and item topology, separation axioms, connectedness and compactness. UNIT -- 3 Ordinary Differential Equations (ODEs): Existence and originality of solutions of preliminary value problems for initial order ordinary differential equations, singular solutions of initial order ODEs, a system associated with first order ODEs. The common theory of homogenous plus nonhomogeneous linear ODEs, deviation of parameters, Sturm-Liouville border value problem, Green’s functionality. Partial Differential Equations (PDEs): Lagrange and Charpit strategies for solving first purchase PDEs, Cauchy problem intended for first order PDEs. Category of second order PDEs, General solution of increased order PDEs with continuous coefficients, Method of splitting up of variables for Laplace, Heat and Wave equations. Numerical Analysis: Numerical options of algebraic equations, Technique of iteration and Newton-Raphson method, Rate of convergence, Solution of systems associated with linear algebraic equations making use of Gauss elimination and Gauss-Seidel methods, Finite differences, Lagrange, Hermite and spline interpolation, Numerical differentiation and incorporation, Numerical solutions of ODEs using Picard, Euler, customised Euler andRunge-Kutta methods. Calculus of Variations: A variety associated with a functional, Euler-Lagrange formula, Necessary and sufficient situations for extreme. Variational strategies for boundary value troubles in ordinary and partially differential equations. Linear Essential Equations: The Linear integral formula of the first plus second kind of Fredholm and Volterra type, Options with separable kernels. Feature numbers and eigenfunctions, resolvent kernel. Classical Mechanics: General coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s rule and the principle of minimum action, Two-dimensional motion associated with rigid bodies, Euler’s dynamical equations for the movement of the rigid entire body about an axis, the concept of small oscillations. DEVICE - four Descriptive figures, exploratory data analysis Example space, discrete probability, 3rd party events, Bayes theorem. Unique variables and distribution features (univariate and multivariate); requirement and moments. Independent unique variables, marginal and conditional distributions. Characteristic functions. Possibility inequalities (Tchebyshef, Markov, Jensen). Modes of convergence weakened and strong laws associated with large numbers, Central Restrict theorems (i. i. g. case). Markov chains along with finite and countable condition space, classification of claims, limiting behaviour of n-step transition probabilities, stationary submission, Poisson and birth-and-death procedures. Standard discrete and constant univariate distributions. sampling distributions, standard errors and asymptotic distributions, distribution of purchase statistics and range. Strategies of estimation, properties associated with estimators, confidence intervals. Testing of hypotheses: most effective and uniformly most effective tests, likelihood ratio testing. Analysis of discrete information and chi-square test associated with goodness of fit. Big sample tests. Simple non-parametric tests for just one particular and two sample troubles, rank correlation and check for independence. Elementary Bayesian inference. Gauss-Markov models, estimability of parameters, best geradlinig unbiased estimators, confidence times, tests for linear ideas. Analysis of variance plus covariance. Fixed, random plus mixed effects models. Assured multiple linear regression. Primary regression diagnostics. Logistic regression. Multivariate normal distribution, Wishart distribution and their qualities. Distribution of quadratic types. Inference for parameters, partially and multiple correlation coefficients and related tests. Information reduction techniques: Principle element analysis, Discriminant analysis, Bunch analysis, Canonical correlation. Easy random sampling, stratified sample and systematic sampling. Possibility proportional to size sample. Ratio and regression strategies. Completely randomised designs, randomised block designs and Latin-square designs. Connectedness and orthogonality of block designs, BIBD. 2K factorial experiments: confounding and construction. Hazard functionality and failure rates, censoring and life testing, collection and parallel systems. Geradlinig programming problem, simple strategies, duality. Elementary queuing plus inventory models. Steady-state options of Markovian queuing versions: M/M/1, M/M/1 with restricted waiting space, M/M/C, M/M/C with the limited waiting area, M/G/1. All students are usually required to answer queries from Unit I. College students in mathematics are anticipated to answer an additional query from Unit II plus III. Students with within statistics are required in order to answer the additional question through Unit IV.
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In the former purpose (that of approximating a posterior probability), variational Bayes is an alternative to Monte Carlo sampling methods — particularly, Markov chain Monte Carlo methods such as Gibbs sampling — for taking a fully Bayesian approach to statistical inference over complex distributions that are difficult to directly evaluate or sample from. In particular, whereas Monte Carlo techniques provide a numerical approximation to the exact posterior using a set of samples, Variational Bayes provides a locally-optimal, exact analytical solution to an approximation of the posterior.
Variational Bayesian methods - Wikipedia
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