Adaptiveなウィンドウを求めて 〜 サーベイと実装 Go言語編 〜/fukuokago15-adwin-exphist

Fukuoka.go#15 + 鹿児島Gophers(オンライン開催)
https://fukuokago.connpass.com/event/164350/

Transcript

1. ࡾ୐༔հ / Pepabo R&D Institute, GMO Pepabo, Inc.
   2020.03.02 Fukuoka.go#15+ࣛࣇౡGophers
   Adaptiveͳ΢Οϯυ΢ΛٻΊͯ
   ʙ αʔϕΠͱ࣮૷ Goݴޠฤ ʙ
   

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2. 1SJODJQBMFOHJOFFS
   :VTVLF.*:",&!NPOPDISPNFHBOF
   1FQBCP3%*OTUJUVUF (.01FQBCP *OD
   IUUQTCMPHNPOPDISPNFHBOFDPN
   

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3. ΤϯδχΞϑϨϯυϦʔγςΟ෱ԬΞϫʔυड৆
   3
   < Thank you!!
   

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4. 1. ͸͡Ίʹ
   2. Adwin in Go
   3. Exponential Histograms in Go
   4. ·ͱΊ
   4
   ໨࣍
   

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5. 1.
   ͸͡Ίʹ
   

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6. • λΠϜεςοϓ t͝ͱʹ஋͕؍ଌ͞ΕΔ࣌ܥྻσʔλ
   • 1෼͝ͱͷαʔό΁ͷΞΫηεස౓ͷਪҠɺ1࣌ؒ͝ͱͷΫϦοΫ཰ͷਪҠ etc…
   6
   Time series data and Windowing
   1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0 ?, ?, ?, ?, ?, ?,?, …
   աڈ ະདྷ
   ݱࡏ
   

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7. • ແݶʹଓ࣌͘ܥྻσʔλͷશظؒσʔλΛอ࣋ɾ෼ੳ͢Δͷ͸ݱ࣮తͰ͸ͳ͍
   • ௚ۙ nεςοϓͷσʔλΛؚΉ΢Οϯυ΢Λର৅ͱͯ͠อ࣋ɾ෼ੳ͢Δ
   7
   Time series data and Windowing
   1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0 ?, ?, ?, ?, ?, ?,?, …
   n=7
   աڈ ະདྷ
   t=15
   t=9
   t=15
   

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8. • ແݶʹଓ࣌͘ܥྻσʔλͷશظؒσʔλΛอ࣋ɾ෼ੳ͢Δͷ͸ݱ࣮తͰ͸ͳ͍
   • ௚ۙ nεςοϓͷσʔλΛؚΉ΢Οϯυ΢Λର৅ͱͯ͠อ࣋ɾ෼ੳ͢Δ
   8
   Time series data and Windowing
   1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0 ?, ?, ?, ?, ?, ?,?, …
   n=7
   t=15
   t=9
   t=15
   1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0 ?, ?, ?, ?, ?, ?,?, …
   t=16
   t=10
   t=16
   

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9. • ΢Οϯυ΢αΠζܾఆͷδϨϯϚ
   • ྫ͑͹ɺ΢Οϯυ΢ʹؚ·ΕΔ஋ͷฏۉΛར༻͢ΔͳΒ͹
   • αΠζ͕গͳ͚Ε͹ɺաڈͷ৘ใΛऔΓ͜΅͢
   • αΠζ͕ଟ͚Ε͹ɺ௚ۙͷ৘ใͷॏཁੑ͕ബΕΔ
   9
   How many is the optimal window size?
   

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10. 10
    Kaburaya autoscaler
    • ఏҊ͢ΔΦʔτεέʔϦϯά੍ޚܥ[1]ʹ͓͍ͯαʔό͋ͨΓͷϨεϙϯελΠ
    ϜΛੑೳࢦඪͱͯ͠ར༻
    • ͲΕ͙Β͍ͷظؒͷฏۉϨεϙϯελΠϜΛऔಘ͢Ε͹Α͍ͷ͔ = ΢Οϯ
    υ΢αΠζͷܾఆ
    • Ҡಈฏۉʁ
    • ՃॏҠಈฏۉʁ
    • ࢦ਺Ҡಈฏۉʁ
    <>ࡾ୐༔հ ܀ྛ݈ଠ࿠ ,BCVSBZB"VUP4DBMFSଟ؀ڥͰͷӡ༻ੑΛߟྀͨࣗ͠཯దԠܕΦʔτεέʔϦϯά੍ޚܥ Πϯλʔωοτͱӡ༻ٕज़γϯϙδ΢Ϝ
    ࿦จू QQ /PW
    

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11. • ΢Οϯυ΢αΠζܾఆͷδϨϯϚ
    • αΠζ͕গͳ͚Ε͹ɺաڈͷ৘ใΛऔΓ͜΅͢
    • αΠζ͕ଟ͚Ε͹ɺ௚ۙͷ৘ใͷॏཁੑ͕ബΕΔ
    11
    Adaptive windowing
    • มԽ͕ͳ͍ظؒ͸ͳΔ΂͘௕͍ظؒͷ৘ใΛอ࣋͢Δ
    • มԽ͕͋ͬͨ࣌͸ɺաڈͷ৘ใΛ੾Γࣺͯɺ௚ۙͷ৘ใΛ༏ઌ͢Δ
    ࠓ೔ͷΞϓϩʔν"EBQUJWF8JOEPXJOH దԠతͳ΢Οϯυ΢
    
    

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12. • ࿦จͷΞϧΰϦζϜ͸ಡΜ͚ͩͩͩͱΘ͔Βͳ͍ʢ๻͸ʣ
    • ଞͷݴޠͷ࣮૷΋࠷ऴతʹ͸࿦จͱಥ͖߹ΘͤͯಡΉͷͰࣗ෼Ͱ࣮૷͢Δఔ౓
    ʹ͸͕͔͔࣌ؒΔ
    • ࣗ෼Ͱ࣮૷͢Δ͜ͱͰ࿦จʹର͢Δཧղ͕֨ஈʹ޿͕Δ
    • Ұ౓࣮૷͓͚ͯ͠͹αʔϏεͰར༻͢Δࡍʹ࠷దͳݴޠ΁ͷίϯόʔτ͸ָ
    • GoͰ࣮૷͢Δͱɺཚ਺Λ൐͏γϛϡϨʔγϣϯ݁ՌͷฏۉԽͳͲʹର͢Δฒ
    ྻγϛϡϨʔλͷ࣮૷͕ൺֱత༰қ
    12
    Why Go?
    

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13. 2.
    ADWIN in Go
    

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14. • “Learning from time-changing data with adaptive windowing”, Bifet, Albert,
    and Ricard Gavalda; Proceedings of the 2007 SIAM international conference
    on data mining. Society for Industrial and Applied Mathematics, 2007
    • ࣌ܥྻσʔλͷ෼෍͕࣌ؒܦաʹΑͬͯมԽ͢Δ͜ͱΛલఏʹ࠷దͳ΢Οϯυ
    ΢αΠζΛಈతʹܾఆ͢ΔΞϧΰϦζϜ (ADWIN)
    • ΢Οϯυ΢αΠζ͕େ͖͘ͳͬͨ৔߹ʹ΋ܭࢉྔ΍ϝϞϦ࢖༻ྔΛ཈͑ΔͨΊ
    ʹExponential histogramsͱ͍͏σʔλߏ଄Λಋೖ (ADWIN2)
    14
    ADWIN: Adaptive Windowing Algorithm
    

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15. 15
    ADWIN in Go
    https://github.com/monochromegane/adwin
    • ADWINΛGoͰ࣮૷
    

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16. 16
    ADWIN: Adaptive Windowing Algorithm
    • ฏۉ0.8ɺඪ४ภࠩ0.01ͷཚ਺
    Λ࣌ܥྻσʔλͱͯ͠ੜ੒
    • ్த͔ΒฏۉΛ0.4ʹมߋ
    • ΢Οϯυ΢αΠζͷมԽʹ஫໨
    ᶃ҆ఆظؒ΢Οϯυ΢αΠζ૿Ճ
    ᶄมԽ఺΢Οϯυ΢αΠζ࡟ݮ
    ᶅ҆ఆظؒ΢Οϯυ΢αΠζ૿Ճ
    

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17. ᶃ มԽ఺ͷݕ஌
    • ΢Οϯυ΢Λաڈͱݱࡏʹೋ෼ͯ͠஋ͷ܏޲ʹมԽ͕͋ͬͨՕॴΛݟ͚ͭΔ
    • > Whenever two “large enough” sub windows of W exhibit “distinct
    enough” average,
    • ౷ܭͷݕఆతͳΞϓϩʔν
    17
    How to achieve adaptive windowing?
    1, 1, 0, 1
    1
    1, 0, 1
    1, 1
    0, 1
    1, 1, 1
    

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18. ᶃ มԽ఺ͷݕ஌
    • ྫ͑͹ೋ෼ͨ͠΢Οϯυ΢ಉ࢜ΛʮରԠͷͳ͍tݕఆʯͰߟ͑Δʢ࣮ࡍ͸΋ͬ
    ͱෳࡶɻ࿦จͷAppendix A ࢀরʣ
    18
    How to achieve adaptive windowing?
    11.01, 12.02, 11.01, 12.02, 11.01
    11.00, 12.01, 11.02, 12.01, 11.02
    t = 0.0057
    9.92, 9.01, 9.82, 9.01, 9.12
    t = 6.4083
    ˎࣗ༝౓ͷU஋͸
    

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19. ᶄ ΢Οϯυ΢ͷॖখ
    • มԽ఺Λݕ஌ͨ͠Βɺ࠷΋ݹ͍ํͷ΢Οϯυ΢ΛҰͭ࡟ݮ
    • มԽ͕ͳ͘ͳΔ·Ͱ܁Γฦ͢
    19
    How to achieve adaptive windowing?
    11.00, 12.01, 11.02, 12.01, 11.02 9.92, 9.01, 9.82, 9.01, 9.12
    

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20. 20
    ADWIN: Adaptive Windowing Algorithm
    • มԽ͕ͳ͚Ε͹΢Οϯυ΢αΠ
    ζ͸ͲΜͲΜେ͖͘ͳΔ
    • ΢Οϯυ΢αΠζʹൺྫͯ͠
    • ϝϞϦ࢖༻ྔ͕૿Ճ
    • ܭࢉྔ͕૿Ճ
    • ΢Οϯυ΢ͷ෼ׂճ਺
    • ݕఆճ਺
    

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21. 3.
    Exponential Histograms in Go
    

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22. • “Maintaining Stream Statistics over Sliding Windows”, M.Datar, A.Gionis,
    P.Indyk, R.Motwani; ACM-SIAM, 2002
    • େ͖ͳαΠζͷ΢Οϯυ΢޲͚ͷσʔλߏ଄
    • աڈσʔλΛόέοτʹαϚϥΠζͯ͠ϝϞϦ༰ྔͱܭࢉྔΛ࡟ݮ
    • ͨͩ͠஋ͷूܭ͸ۙࣅ஋ͱͳΔ
    • ७ਮͳExponential histograms͸Bits(0or1)͔Positive Integers(ਖ਼ͷ੔਺)ͷ࣌
    ܥྻσʔλͷΈѻ͏ʢADWIN2Ͱ͸࣮਺΋ѻ͑ΔΑ͏ʹ͍ͯ͠Δʣ
    22
    Exponential histograms: data structure for sliding windows
    

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23. 23
    Exponential histograms: data structure for sliding windows
    1
    1
    1
    2 1 1
    2
    3 1 1
    2
    3
    2
    3
    NFSHF
    4 1 2
    3
    4
    5 0 2
    3
    4
    6 1 2
    3
    4
    6
    2
    4
    6
    NFSHF
    *HOPSF
    7 1 2
    4
    6
    7
    8 1 2
    4
    6
    7
    8
    2
    4
    7
    8
    4
    7
    8
    NFSHFY
    Time Bit Bucket Time Bit Bucket
    .FSHFTJ[F
    .FSHFTJ[F
    
    

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24. • όέοτͷ࣋ͭλΠϜελϯϓ͸Ұͭલͷόέοτ·ͰͷλΠϜελϯϓͷؒ
    ʹόέοταΠζ෼ͷ1ؚ͕·ΕΔ͜ͱΛࣔ͢
    • όέοτͷλΠϜελϯϓ͕΢Οϯυ΢αΠζΛ௒͑Δ৔߹ʢظݶ੾Εͷόέο
    τʣ͸࡟আ͞ΕΔ
    • ࣮ࡍ͸TOTALʢظݶ಺ͷόέοτͷ஋ͷ߹ܭʣͱLASTʢظݶ಺ͷόέοτͷ
    ࠷େαΠζ (2^i)ʣͱ͍͏ม਺Λߋ৽͢Δ
    • Χ΢ϯτ͸ TOTAL - LAST/2 ͰۙࣅͰ͖Δʢabsolute error͸LAST/2ʣ
    • ޡࠩΛͲͷఔ౓ڐ༰Ͱ͖Δ͔ΛύϥϝλEpsilonͰ੍ޚ 24
    Exponential histograms: data structure for sliding windows
    

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25. • ࿦จͰ͸Positive Integers΋঺հ͞Ε͍ͯΔ
    • ୯७ʹ஋͕Nͷ৔߹ɺNճͷσʔλૠೖ͕ߦΘΕΔ
    • ܭࢉྔ͸ͱΓ͏Δ੔਺ͷ࠷େ஋·Ͱ૿Ճ
    25
    Exponential histograms: data structure for sliding windows
    

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26. 26
    Exponential Histograms in Go
    https://github.com/monochromegane/exponential-histograms
    • Exponential Histograms (Bits, Positive Integers)ΛGoͰ࣮૷
    

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27. 27
    ADWIN2: Adaptive Windowing using ExpHist
    • ΢Οϯυ΢Λ഑ྻ͔ΒExpHistʢͷѥछʣʹมߋ
    • ࣮਺Λ֨ೲ͠ɺόέοτ͸߹ܭ஋Λอ࣋͢Δ
    • αϒ΢Οϯυ΢ͷࠩͷݕఆΛ࠷΋աڈʢ=௕͍ظؒʣͷόέοτͱͦΕҎ֎Λ
    ൺֱ͢Δ͚ͩʹมߋ
    • มߋΛݕ஌ͨ͠৔߹͸ɺͦͷ࠷΋աڈόέοτΛ࡟আͯ͠ऴΘΓ
    

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28. 28
    ADWIN2 in Go
    https://github.com/monochromegane/adwin
    • ADWIN2ΛGoͰ࣮૷
    

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29. 29
    ADWIN2: Adaptive Windowing using ExpHist
    &YQ)JTUͷಋೖʹΑͬͯ΢Οϯυ΢ͷ࡟আ͕
    όονతʹͳΔ͕͜ͷྫͰ͸໰୊ͳͦ͞͏
    

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30. 4.
    ·ͱΊ
    

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31. • ࿦จͷΞϧΰϦζϜͷཧղͷͨΊʹADWINͱExponential HistogramsΛGoݴ
    ޠͰ࣮૷ͨ͠
    • Adaptiveͳ΢Οϯυ΢ͷ࣮ݱ͢ΔɺADWINΛ঺հͨ͠
    • େ͖ͳαΠζͷεϥΠσΟϯά΢Οϯυ΢ΛলϝϞϦͰ࣮ݱ͢ΔExponential
    HistogramsΛ঺հͨ͠
    • ͜ΕΒΛ૊Έ߹ΘͤͨADWIN2Λ঺հͨ͠
    • GoͰ࣮૷͢Δ͜ͱͰΞϧΰϦζϜͷཧղͰ͖Δ૚Λ޿͛Δ͜ͱʹߩݙʢଟ෼ʣ
    31
    ·ͱΊ
    

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