Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
機械学習とセキュリティ
Search
setten-QB
July 07, 2020
Science
8
1.9k
機械学習とセキュリティ
機械学習モデルへの攻撃とその対策についての概要
setten-QB
July 07, 2020
Tweet
Share
More Decks by setten-QB
See All by setten-QB
第4回 確率・統計の基礎勉強会
settenqb
0
160
確率・統計の基礎勉強会3
settenqb
0
240
確率・統計勉強会2
settenqb
0
150
確率・統計の基礎勉強会1
settenqb
1
250
Other Decks in Science
See All in Science
Science of Scienceおよび科学計量学に関する研究論文の俯瞰可視化_ポスター版
hayataka88
0
130
As We May Interact: Challenges and Opportunities for Next-Generation Human-Information Interaction
signer
PRO
0
160
山形とさくらんぼに関するレクチャー(YG-900)
07jp27
1
220
【人工衛星開発】能見研究室紹介動画
02hattori11sat03
0
150
ほたるのひかり/RayTracingCamp10
kugimasa
0
210
多次元展開法を用いた 多値バイクラスタリング モデルの提案
kosugitti
0
190
MoveItを使った産業用ロボット向け動作作成方法の紹介 / Introduction to creating motion for industrial robots using MoveIt
ry0_ka
0
160
Sarcoptic Mange
uni_of_nomi
1
110
Презентация программы бакалавриата СПбГУ "Искусственный интеллект и наука о данных"
dscs
0
720
ABEMAの効果検証事例〜効果の異質性を考える〜
s1ok69oo
4
2.1k
JSol'Ex : traitement d'images solaires en Java
melix
0
110
WCS-LA-2024
lcolladotor
0
120
Featured
See All Featured
Faster Mobile Websites
deanohume
305
30k
"I'm Feeling Lucky" - Building Great Search Experiences for Today's Users (#IAC19)
danielanewman
226
22k
RailsConf & Balkan Ruby 2019: The Past, Present, and Future of Rails at GitHub
eileencodes
131
33k
Building Better People: How to give real-time feedback that sticks.
wjessup
364
19k
Building Applications with DynamoDB
mza
90
6.1k
Git: the NoSQL Database
bkeepers
PRO
427
64k
Docker and Python
trallard
40
3.1k
Why Our Code Smells
bkeepers
PRO
334
57k
Understanding Cognitive Biases in Performance Measurement
bluesmoon
26
1.4k
BBQ
matthewcrist
85
9.3k
A designer walks into a library…
pauljervisheath
204
24k
The MySQL Ecosystem @ GitHub 2015
samlambert
250
12k
Transcript
ػցֶशͱηΩϡϦςΟ ௨৴ࣄۀձࣾ ΄͛΄͛։ൃ෦ 2# !TFUUFO@2# %BUB4DJFODF$BGÉ!৽॓
ػցֶशºηΩϡϦςΟ Ø %PT߈ܸΛػցֶशͰݕ Ø ϚϧΣΞΛػցֶशͰݕ ػցֶशΛηΩϡϦςΟʹԠ༻ ػցֶशϞσϧࣗମͷηΩϡϦςΟ ػցֶशͰߏஙͨ͠ϞσϧʢػցֶशϞσϧʣΛΈࠐΜͩγεςϜͰ ैདྷͷγεςϜͱҟͳͬͨݻ༗ͷ߈ܸ͕ͳ͞ΕΔϦεΫ͕༗Δ ͦͷͨΊɼػցֶशϞσϧಛ༗ͷηΩϡϦςΟରࡦ͕ඞཁ
2
"EWFSTBSJBM"UUBDL ϞσϧΛὃ͢߈ܸ .PEFM&YUSBDUJPO ϞσϧΛ౪Ή߈ܸ .PEFM*OWFSTJPO ֶशσʔλʹؔ͢ΔใΛ෮ݩ͢Δ߈ܸ
None
"EWFSTBSJBM"UUBDL ܇࿅͞ΕͨػցֶशϞσϧΛὃ͢߈ܸ ݩͷը૾ ఢରతઁಈ "EWFSTBSJBM&YBNQMF ʢςφΨβϧʣ (PPEGFMMPX FUBM ΑΓҾ༻
5
ఢରతઁಈΛݟ͚ͭΔͨΊʹ argmin " , s.t. + ≠ argmin " ,
s.t. + = # ಛఆͷΫϥεʹޡྨͤ͞Δ͜ͱΛతͱͨ͠ "EWFSTBSJBM"UUBDL ޡྨͤ͞ΔΫϥεࢦఆͤͣ ͱʹ͔͘Ͳ͔͜ͷΫϥεʹޡྨͤ͞Δ͜ͱΛ తͱͨ͠"EWFSTBSJBM"UUBDL 6
දతͳ"EWFSTBSJBM"UUBDL (PPEGFMMPX FUBM !"# = + sign ∇ ℓ
, /PUBUJPO ɿઁಈڧʢͲΕ͙Β͍ઁಈΛڧ͘༩͑Δ͔Λද͢ʣ ℓɿଛࣦؔ 3FNBSL '(4.Ұͷޯ্ঢͰ࠷దԽΛऴྃ͢Δ͕ɼ͜ΕΛෳճʹ֦ுͨ͠ͷ͕#*.Ͱɼ CBMMʹऩ·ΔΑ͏ͳ੍ͷͱͰޯ্ঢΛ܁Γฦ͢ɽ '(4.#*.! ϊϧϜͰͷઁಈΛੜ͓ͯ͠Γɼ%FFQGPPM͜ͷϊϧϜΛ" ʹɼ $8# ʹͨ͠ͷͱݟΔ͜ͱ͕Ͱ͖Δɽ 7
8IJUF#PY4FUUJOHʹ͓͚Δఢରతઁಈͷݟ͚ͭํ '(4.BUUBDL (PPEGFMMPX FUBM #*. ,VSBLJO FUBM BUUBDL.*'(4.
%POHFUBM %FFQGPPM .PPTBWJ%F[GPPMJ FUBM /FXUPO'PPM +BOHFUBM +4." 1BQFSOPU FUBM (SBEJFOU #BTFE 0CKFDUJWF 'VODUJPO #BTFE $8 $BSMJOJ FUBM &"% $IFOFUBM 0QU.BSHJO 8BSSFOFUBM ˞8IJUF#PY4FUUJOHɿଛࣦؔͷޯ͕ܭࢉͰ͖ͨΓɼϞσϧͷDPOGJEFODFTDPSFΛΔ͜ͱ͕Ͱ͖Δઃఆ 8
"EWFSTBSJBM"UUBDLͷରࡦɿ"EWFSTBSJBM5SBJOJOH Ϟσϧͷֶश࣌ʹBEWFSTBSJBMFYBNQMFTͰl༧छz͓͚ͯ͠ BEWFSTBSJBMFYBNQMFTʹର͢Δϩόετੑ্͕ΔΜ͡Όͳ͍͔ʁ 9 ℓ!"# , () ≔ ℓ !"#,
!"# + 1 − ℓ , *EFB 3FTVMU n ࣮ࡍʹBEWFSTBSJBMFYBNQMFTʹର͢Δϩόετੑ্͢Δ ҰํͰʜ n ֶशʹཁ͢Δ͕࣌ؒ૿͑Δ n "EWFSTBSJBMFYBNQMFTͷϩόετੑBEWFSTBSJBMFYBNQMFTͷ࡞Γํʹґଘ͢Δ n ѱҙͷͳ͍ϊΠζ͕ͬͨը૾Λ͏·͘ྨͰ͖ͳ͘ͳΔ ͱ͍ͬͨൃੜ͢Δ
"EWFSTBSJBM"UUBDL ϞσϧΛὃ͢߈ܸ .PEFM&YUSBDUJPO ϞσϧΛ౪Ή߈ܸ .PEFM*OWFSTJPO ֶशσʔλʹؔ͢ΔใΛ෮ݩ͢Δ߈ܸ
.PEFM&YUSBDUJPOɿϞσϧΛ౪Ή & "SDIJUFDUVSF %FDJTJPO#PVOEBSZ 'VODUJPOBMJUZ ϨΠϠʔͷχϡʔϩϯͷ ͞Βʹ׆ੑԽؔͳͲͷ ϞσϧͷߏΛ౪ΉλΠϓ ϞσϧͷܾఆڥքΛ ౪ΉλΠϓ
ϞσϧʹΑΔ ೖྗͱग़ྗͷରԠؔΛ ౪ΉλΠϓ 11
.PEFM&YUSBDUJPOͷओཁͳΞϓϩʔν $ , $ $%& ' : ℝ( → ֶश
), ) )%& * +: ℝ( → ֶश 0SJHJOBM.PEFM 4VCTUJUVUF.PEFM "1*ʹΑͬͯฦ͞ΕΔ Λతมͱͯ͠ར༻͢Δ͜ͱͰཧϞσϧΛߏங͢Δɽ දతͳݚڀͱͯ͠$PSSFJB4JMWBFUBM 0SFLPOEZ FUBM ͕ڍ͛ΒΕΔɽ 12
4VCTUJUVUF.PEFMʹؔ͢Δ߈ %FGFODF 0GGFODF "1*ୟ͚ΔճΛ੍ݶ গͳ͍ԠճͰ 4VCTUJUVUF.PEFMΛߏங͢Δํ๏͕ఏҊ͞ΕΔ 0SFLPOEZ FUBM 3PTFOCFSHFUBM
13
"EWFSTBSJBM"UUBDL ϞσϧΛὃ͢߈ܸ .PEFM&YUSBDUJPO ϞσϧΛ౪Ή߈ܸ .PEFM*OWFSTJPO ֶशσʔλʹؔ͢ΔใΛ෮ݩ͢Δ߈ܸ
ʢٛͷʣ.PEFM*OWFSTJPO"UUBDL ֶशσʔλʹؔ͢ΔใΛ෮ݩ͢Δ߈ܸ 1SPQFSUZ*OGFSFODF"UUBDL .PEFM*OWFSTJPO"UUBDL దͳ ͕Ϟσϧͷֶशσʔληοτʹؚ·Ε͍ͯΔ͔ʁ Λ໌Β͔ʹ͢Δ߈ܸ ֶशσʔληοτʹؔ͢Δੑ࣭Λਪଌ͢Δ߈ܸ FH͕͍ਓυϨεΛண͍ͯΔਓ͕ ੑผྨͷϞσϧͷֶशσʔλʹؚ·Ε͍ͯΔ͔ʁ
ֶशσʔλΛ෮ݩ͢Δ߈ܸ ˞.PEFM*OWFSTJPO"UUBDLʹ.FNCFSTIJQ*OGFSFODF1SPQFSUZ*OGFSFODFΛؚΊΔ͔ʹॾઆ͋Γ 15
("/Λ༻͍ͨ.PEFM*OWFSTJPO ,VTBOP FUBM ิॿσʔληοτ ) , )%& * ,
, ∼$$( ℱ′ ֶशσʔληοτ $ , $ $%& ' , ∼$$( ℱ ΫΤϦ & ,, … * , Ԡ (& ,), … * , (FOFSBUPS Ͱ ℱ ʢͬΆ͍ͷʣΛۙࣅ αϯϓϦϯά (FOFSBUPS͔Β ֶशσʔλͬΆ͍ͷΛੜ 16
σʔλͷҰ෦͔ΒΓͷ෦Λ෮ݩ ֶशσʔλ ∈ ℝ( ͔ΒҰ෦ͷಛྔ͚ͩΛൈ͖ग़ͯ͠ ࡞ͨ͠ϕΫτϧ " ∈ ℝ-, <
͔Β ΓͷಛྔΛ෮ݩ͢Δ จͰ " ࿙Ӯͯ͠ͳ͍ηϯγςΟϒͰͳ͍ಛྔͰ ΓͷಛྔηϯγςΟϒͳಛྔͩͱఆ͍ͯ͠Δ ("/Λ༻͍ͨ.PEFM*OWFSTJPO ;IBOFUBM 17
͍ɼϜζ͘Ͷʜʁ ./*45Λֶशσʔλͱͨ͠ྨϞσϧʹରͯ͠.PEFM *OWFSTJPO"UUBDLΛߦͬͨ݁Ռ ิॿσʔλखॻ͖จࣈͷࣈͱΞϧϑΝϕοτ ࣮ࡍʹ෮ݩͯ͠Έͨ݁Ռ 18
None
ػցֶशϞσϧͷ߈ܸʹؔ͢Δݚڀ ͬͺΓ"EWFSTBSJBM"UUBDL͕μϯτπͳײ͡ ݚڀ͞ΕͯΔײ ֶशσʔλΛͯ͢෮ݩ͢ΔλΠϓͷ.PEFM*OWFSTJPO"UUBDL͕Ұ൪ͦ͠͏ ʢ࣮ࡍʹ͔ͬͨ͠ʣ ߈ܸͷ͠͞ n "EWFSTBSJBM"UUBDLσʔλ͕ߴ࣍ݩʹͳΔͱෆՄආతʹੜ͡ΔͨΊ ຊ࣭తʹରࡦ͕ࠔʁ n
.PEFM&YUSBDUJPO"UUBDLΫΤϦ੍ݶ͕༗ޮʹࢥ͑Δ͕ ΫΤϦ੍ݶͷͱͰ͋ΔఔͷϞσϧෳ͕ग़དྷ͓ͯΓ ࠓޙͷಈʹ ରࡦͷ͠͞ 20
3FGFSFODF (PPEGFMMPX *+ 4IMFOT + 4[FHFEZ $ &YQMBJOJOHBOEIBSOFTTJOHBEWFSTBSJBMFYBNQMFT BS9JW
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
3FGFSFODF 8BSSFO ) #P - %BXO 4 %FDJTJPO#PVOEBSZ"OBMZTJTPG"EWFSTBSJBM&YBNQMFT*OUFSOBUJPOBM $POGFSFODFPG-FBSOJOH3FQSFTFOUBUJPOT
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