What if - Chapter 4
SO CHAPTER 4 IS HERE! Well, we are having a HUGE surprise in this chapter. Steve didn't show up, the memeber of the BRF who will visit the museum is revealed AND maybe we find out something else about the so-called Steve...😏
Enjoy yourselves!
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17th June 2005
Two weeks had passed since that day. Steve hadn’t shown up at the museum and Kate had an awful amount of work to do so at least she had her mind occupied. With the upcoming visit of a royal family member, the museum had to be at its finest and bests moments. The brunette didn’t know who was the visiting member yet, for some reason, her boss didn’t want to tell her.
Kate just carried on with work. It was Friday so she had lots of school groups. When she lead a group of teenagers in one of the biggest rooms, she instantly froze, recognizing a leather jacket walking to the following room.
-Miss?-One of the students called for her.- Excuse me, miss?
She came back from her shock to attend the young man who had a question about a painting. After going through the most important things in the exposition she let them wonder around.
-Now you can be on your own, this and the next room. I'll be there if you need anything.-She then let them walk alone through the rooms.
Kate went straight to the next one, trying to find him, she needed some answers. Once she got there the room was empty, no one was in there. She checked all over, stopping her eyes on the two pieces of Queen Victoria and Queen Alexandra, when she first met Steve. She got closer, looking at of the benches that were in the middle of the room, finding a white envelope. Catherine frowned her eyebrows, picking it up. It had her name on it. <<Steve…>>, was her first thought. A feeling of anger ran her body from head to toes, she was about to open the envelope but she was stopped by some voices.
-Mummy, mummy come see this, hurry.-A little girl.
-Dad, here, come on, look.-A little boy.
-Mo...Da…-A baby, trying to babble.
She immediately turned around, putting the envelope in a pocked, trying to find the source of the voices, not finding anyone. They were very familiar, like she had heard those children before but she wasn’t able to figure out when. Shaking her mind, she got back to the group, finishing the tour for the day.
Steve was hidden behind a door frame watching all her movements. God, he made a huge mistake. The young man also heard the voices, and moved his head around also trying to find where they came from but having the same result as Catherine. A hand touched his shoulder.
-Sorry Your Royal Highness, but I was informed to take you home.-His bodyguard informed him.
-Yes, of course Jack.-They started walking out when he realized.-You were behind me all the time, right?
-Yes, sir, I never left your side.
-Did you hear the voices?
-Voices? What voices?-Jack asked.
-I heard three voices: a little boy, a little girl and a baby.
-I’m sorry sir, I didn’t hear anything. There were just the lady from the museum, you and me in the room.-He opened the door for him, heading to the car.
-Oh...Well, maybe it was all in my mind…-But he had heard them so clearly, like they were even talking to them, to Kate and him. All the way home, he couldn’t stop thinking about the brunette and the voices. It had been such a strange moment.
He didn’t know what to do. On one hand he wanted to go back to the museum and talk to Catherine again, on the other hand he wanted to wait four more days to tell her the hole truth. Steve closed his bedroom door and screamed, how on earth did he get to this point.
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-Miss Middleton, do you have a minute?-The head of her department asked Kate when she had already finished.
-Yes, of course.-The brunette followed him to his office, closing the door after her and sitting on one of the chairs.
-Well, as you may remember, next Tuesday a member of the Royal Family will be visiting the Gallery and will be given the patronage. I never told you the name, only that you would be giving the tour through the exposition.-He smiled, the young woman was a very hard worker and proved she was very intelligent and resourceful. He could tell she wanted to know who was going to come.-Okay, I’m not going to delay it anymore, Prince William will be visiting us on his 23rd birthday next Tuesday.
-Wow…-Catherine face was a poem. She got up.-You won’t regret choosing me to tour him through the exposition.
-I know I won’t. You can go now, I know you don’t work this weekend so try not to tell too many people.-He laugh when she was leaving the office.
Kate got home that night with a big blur on her head, she could still hear the voices in her head tho she didn’t found any source. When she entered her room, she dropped dead on her bed mentally exhausted.
-Prince William...Wow...
Pippa had a birthday party that night so she wasn’t expecting her anytime soon. When the brunette started changing her clothes, she found the envelope she never got to open. Holding it between her hands was doubting whether to open it or not. She finally did.
“I feel I have not apologized enough, not for the awfully way I have treated you. I know you will not understand but I cross my heart when I say I did it to keep you safe. I am really sorry, Catherine. Yours, Steve.”
A tear ran down Kate’s cheek. She didn't want to think about him, about that rose she still had on her night table, about his scent. She shook her head, left the note in her jacket’s pocket and turned on the TV, trying to set her mind into something else.
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Pippa was drunk, very drunk. She said goodbye to her friends in front of Buckingham Palace once the party was over and all of them took different ways to go back home. The young Middleton was walking down the Mall to Trafalgar Square thinking whether to go home by taxi or underground. She was so drunk she didn’t see the young man she crashed into. They both ended up nearly falling, but he managed to grab Pippa by the waist to avoid the rough landing.
-Oh, god, I’m so, so, so, so sorry.-The brunette tried to talk and looked up, finding a leather jacket, a cap and a pair of sunglasses. <<Sunglasses at night…? How weird…>> She didn’t gave it too much importance, thinking he could be someone famous and didn’t want to be recognized.-Thank you, I...I was tying...trying to get hommmm.-Pippa started laughing due to the alcohol and stretched her arm to shook his hand.-I’m Pippa..
-Don’t worry, I’m W...I’m Steve. Are you okay to get home safely? Isn’t there anyone you could call to pick you up?-Steve had decided to go for a walk alone, without guards, and was already heading home. But after Pippa crashed into him, he wanted to make sure she got home safely.
-Well, I may call my s-sister she might be home…-She grabbed her phone from her purse and dialed Kate’s number, grabbing Steve’s arm trying not to fall.
Catherine was watching some random movie when her phone rang, strangely, it was her sister.
-Pips? Is everything okay?-She was worried because when her sister went out, she only called her when something was wrong.
-Everying is okaaaaay, I’m jssst a little drunk….-Pippa started laughing and could sense Kate’s eyes rolling.-Could you come pick me up, please? Or I can take a taxi If it’s too much bother…
-No, where are you? Are you alone?
-Uhm…-Pippa turned around with Steve’s help.-Right in front of Clarence Hus...Hose...h-o-u-s-e. Yep. And no, I’m with this night knight I crashed into some minutes ago. He’s staying until you arrive.
-Okay, I’ll be there in ten.
-Thank you Squeak…-She hang up and looked at Steve.-She will be here in about ten or fifteen minutes.-Pippa tried to relieve the pain her heels were causing her but it made her lose balance, falling again to the ground. Steve tried to grab her but this time they made more of a fuss. No one or nothing fell to the ground except for Steve’s sunglasses and cap.-God, I’m sorry really, gosh I’m embarrassing myself.
Pippa grabbed the glasses and the cap from the ground and went to give them to Steve who forgot to turn around. Pippa gasped realizing who he really was, still with the young man’s arm around her, feeling incredibly sleepy.
-You...You’re…-She fell asleep on Steve’s shoulder, not being able to finish the sentence. Steve put back his cap and sunglasses right before a car stopped in front of them and the woman who had been in his mind for weeks appeared.
-Catherine…?
-Steve...What..-Her heart skipped a bit and then she saw Pippa.-Is she okay?
-Yes, yes she just fell asleep. She is pretty drunk.-Kate got close with the intention to get her sister into the car.-Don’t worry, I’ll do it.
-Okay, I will open the door.
Neither of them said a thing about the previous weeks, using the situation to avoid the subject. Steve managed to put Pippa inside, leaving her head resting on the copilot’s seat. Once Kate closed the door and turned around she faced Steve, too close. They hadn’t realized how close they were until they both stared in each other’s eyes. Quickly, Kate managed to find some strength to move and walk away from him, just a little distance because all she wanted to do was pull his body closer. The same sensation that Steve was feeling, wanting to just close the air between them.
-Catherine, I…
-No, please, I have too much in my head right now.- She noticed the envelope in her jacked and pulled it out.-I...I can’t do this Steve…-Kate closed the distance between them and put the paper in his hands, taking them.
-I…-The young man looked through his sunglasses into the brunette’s eyes, realizing she was about to cry. She was beyond beautiful. They both had the feeling as if they had already hold their hands, maybe in a past life.-Kate, please…
She had no idea how but when she started to feel the urge to kiss him, she walked back and got into the car, driving away and letting her tears fell free. The man stood there, looking at the envelope. When he entered his home and got up the stairs, someone called for him.
-Hey you.-His little brother, with his pyjamas and a cup of tea.
-Hi you. What are you doing still awake? Babies and gingers need at least 9 hours of sleep.-The younger man laughed sarcastically, always teasing each other. They started to walk to their rooms.
-You know, at first I thought it was weird that you got out wearing a cap and sunglasses but…after witnessing what I just saw...there was quite a big tension between you and that woman, wasn’t it?.-The stood in their own doors, facing each other.
-Yes...Yes there were.
-Does she know your name?
-Yes.-His brother opened his eyes.
-What?!
-No, not my real name, I told her...I said my name is Steve.-Laugh, that was the response of the other man.-Of course I couldn’t tell her my real name.
-I know, I know. Look..-He leaned on the door frame.-all I’m saying is that there is something there, worth looking into.-The so-called Steve rose an eyebrow.- And no, it is NOT a sexual reference.
-It may be too late...Good night.-With that he turned around.
-Good night William.
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Pippa woke up the next morning feeling her worse self. With a groan she stepped into the kitchen just to find her sister making breakfast. She had the tv on, watching the news.
-God, the light is killing me. And the noise. And life.
-Well, you were pretty drunk last night sweetie.-Kate placed an orange juice in front of her.
-I don’t remember anything.
-Not...not a single thing?-Pippa looked at her after listening the tone in which she was speaking.
-Don’t tell me I did something really stupid. I just remember walking down the Mall and nothing else.
-Well you crashed into Steve actually, the guy from the museum I talked about and the one who didn’t showed up to our date, so I…-Kate was interrupted by the the tone of breaking news from the TV. Both sisters centered their attention to the screen.
-Next Tuesday, Prince William will visit the National Portrait Gallery and will be named patron for his 23rd birthday.- Kate smiled at Pippa.
-I found out yesterday. And guess who will be giving the tour that day.
-No way! Way to go Squeak!-The news then showed some footage of the last speech the Prince made and Kate’s smile fade away. PIppa looked at her.-Hey, something’s wrong?
-That’s…-The elder sister realized as soon as she heard the Prince speak, that voice had been stuck in her days for weeks now.-Steve…-Kate pointed the TV.-That’s Steve.
-What do you mean…?
-Steve, the man you crashed into yesterday, very, very drunk? The guy with the cap and the sunglasses from the museum? The jerk that didn't show up to our date?
-But...That is not Steve, that is…-Pippa opened her mouth in surprise, remembering the previous night and...-Prince…
-William.
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Chapter 3 | Chapter 5
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機械学習におけるDifferential Privacyについて
Ideinの先崎です。
最近Tensorflowが実装を公開するなど注目を集めている、機械学習+Differential Privacyという研究分野があります。これはDifferential Privacyと呼ばれる技術を使って、機械学習におけるトレーニングデータのプライバシを保護しようというものです。 本記事では、この研究分野でどのようなことが行われているのかについて書きたいと思います。
概念・定義
まずはじめに、Differential Privacyの概念と定義について簡単に説明したいと思います。 より詳しい説明は、[1]や[2]などがわかりやすいです。
Differential Privacy(DP)はDworkによって考案された[3]概念で、あるデータセットに対する解析結果を公開する場合にそのデータのプライバシはどの程度保護されているのか、という問題を取り扱います。 Dworkはこれをパラメータεを用いて以下のように定義しました。
ここでDはデータセット、Mはこれに対する操作、SはMにより出力されうる値の集合の任意のサブセットです。 またD'はDと1レコードだけ違う、すなわちDに隣接したデータセットです。 Mがあるεに対し上式を満たす時Mはε-Differential Privacyを満たすといいます。 なんとなく式だけでは理解しにくいですが、直感的には「DとD'は1レコード分異なるはずであるがこれらに対する出力には差がない、すなわちこの1レコードのプライバシは保護されている」ということを言いたいのだと理解するとよさそうです[1]。このとき、εの値が小さければ小さいほど制限が強くなり、より強くプライバシが保護されるということになります。 このようなことを実現するためには、一般的にLaplacian NoiseやGaussian Noiseなどを解析結果に加えるということが行われます。 これにより出力が確定的に決まることを避けつつ、ノイズを加えた結果が本来のデータセットに対する操作の結果とかけ離れすぎないようにすることで、プライバシを保護しながらデータセットを解析できることが期待されます。
Deep Learningの文脈でのDP
Deep Learningでは多くの場合学習に大量のデータを必要とします。もしこれが個人情報などのセンシティブなデータを含んでいる場合には、当然それらのプライバシが問題となってきます。このような背景のもと、生成されたモデルがDPを満たすように訓練する手法が活発に研究されています。例えば、[4]では確率的勾配降下法(Stochastic Gradient Descent, SGD)をDPを満たすように改変したDifferentially Private SGD(DPSGD)を用いる手法が提案されています。 (DPSGDの概要。([5]のFigure 2.))
図からもわかる通り、通常のSGDと異なる点は勾配を用いてパラメータを更新する前に勾配を一定のノルムでclipすることと、さらにそこにGaussian Noiseを加えることです。ε-Differential Privacyを満たすためにはこのノイズの強度などのパラメータをどのように設定すればいいかなどが論文中で議論されています。
また直接勾配にノイズを加えて学習するのではなく、Knowledge Transferを利用し教師モデルのアンサンブルによってDPを満たすPrivate Aggregation of Teacher Ensembles(PATE)という手法も提案されています[6]。 (PATEの概要。([6]のFigure 1.))
この手法ではセンシティブなデータとそうでないデータがあるという仮定の元、まずセンシティブデータを分割しそれぞれでモデルを訓練します。 次にこれらのモデルの多数決にノイズを加えたものを教師モデルとして、センシティブでないデータを用いて生徒モデルを訓練します。 これにより、生徒モデルの学習にセンシティブデータは直接利用されておらず、ノイズが加えられているためDPも満たしているということになるようです。(εの値に関しての議論もなされています)
学習データプライバシの侵害
ここまでご紹介してきたように学習データのプライバシを保護するためにDPを応用する手法が研究されていますが、逆にDeep Learningにおいて学習データのプライバシはどのように侵害されうるのか?についても研究が進められています。(もし仮に誰もプライバシを侵害できないなら、プライバシ保護にコストをかける理由は薄れるでしょう。) このようなものとしては、モデルから学習データを復元するModel Inversion [7]、あるデータが学習用データセットに含まれていたかどうかを推測するMembership Inference [8]、学習データに特定のプロパティを持つものが含まれていたかどうかを推測するProperty Inference [9]などが提案されています。 (顔画像の分類を行うモデルから学習データを復元したもの(左)と元の学習データ(右)([7]のFigure 1.))
データを直接復元することは最もイメージしやすいプライバシの侵害ですが、これ以外の攻撃も脅威となりえます。例えば、ある病気の患者のデータからなんらかのモデルを構築した場合、そのデータセットに自分のデータが含まれていることが明らかになることにより自分がその病気であることが明らかになってしまう、といったシナリオが考えられます。
精度とプライバシ保護のトレードオフ
上で述べたような攻撃に対し、モデルがε-DPを満たしていればその防御策になるといったことは考えられますが、実際にどの程度のεであればどの程度攻撃を緩和できるのか、といった評価についての報告は(私の知る限り)あまり多くはありません。 DPの定義より、よりεが小さくなるようにすればより攻撃を防げるようになるはずですが、本来のタスクに対する精度も低下すると考えられます。
[6]では[4]で提案されたDPSGDによってDPを満たしたモデルに対しMembership Inference攻撃を行うという設定で、εの値が攻撃成功率にどの程度影響を与えるか、またそのときテスト精度にはどの程度影響を与えるかという評価実験の結果が報告されています。 (CIFAR-10で学習したモデルに対するMembership Inferenceの成功率([6]のfigure 4(a)))
確かにεを小さくするとMembership Inferenceの成功率が下がっていることがわかります(Membership Inferenceはあるデータが学習データに含まれるか否かの2値分類なので、ベースラインが50%)。 しかし一方で、CIFAR-10のテストセットの認識精度はDPを適用しないモデル、ε=8、ε=1でそれぞれ94%、68%、24%となったことも報告されており(Table 3)、εを小さくしすぎると著しく本来の機能が損なわれるということがわかります。
このように、現状ではプライバシの保護を優先すれば精度が損なわれてしまう(逆もしかり)という状態のようです。 これらの技術を実際のアプリケーション等に使うためには、εと精度のよりよいトレードオフを追求する必要がありそうです。
参考文献
[1] 注目のプライバシー Differential Privacy https://www.jstage.jst.go.jp/article/jssst/29/4/29_4_40/_pdf
[2] 差分プライバシーとは何か? (定義 & 解釈編) https://www.slideshare.net/kentarominami39/ss-64088396
[3] C. Dwork. Differential Privacy. In ICALP 2006, 2006.
[4] M. Abadi, A. Chu, I. Goodfellow, B. McMahan, I. Mironov, K. Talwar, and L. Zhang. Deep learning with differential privacy. In 23rd ACM Conference on Computer and Communications Security(ACM CCS), pp. 308–318, 2016.
[5] M. A. Rahman, T. Rahman, R. Laganiere, N. Mohammed, and Y. Wang. Membership inference attack against differentially private deep learning model. Transactions on Data Privacy, 11, 2018.
[6] N. Papernot, M. Abadi, Ú. Erlingsson, I. Goodfellow, and K. Talwar. Semi-supervised knowledge transfer for deep learning from private training data. In Proceedings of the International Conference on Learning Representations, 2017.
[7] M. Fredrikson, S. Jha, and T. Ristenpart. Model inversion attacks that exploit confidence information and basic countermeasures. In Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security. ACM, 2015.
[8] R. Shokri, M. Stronati, C. Song, V. Shmatikov. Membership inference attacks against machine learning models. 2017 IEEE Symposium on Security and Privacy (SP). IEEE, 2017.
[9] K. Ganju, Q. Wang, W. Yang, C. A. Gunter, N. Borisov. Property Inference Attacks on Fully Connected Neural Networks using Permutation Invariant Representations, Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security. ACM, 2018.
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