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
不確実性と上手く付き合う意思決定の手法
Search
Takashi Nishibayashi
April 04, 2019
Technology
18
15k
不確実性と上手く付き合う意思決定の手法
予測モデルの不確実性を減らすActive Learning,
モデルの不確実性を予測結果に反映するThompson Sampling,
オンライン最適化など
Takashi Nishibayashi
April 04, 2019
Tweet
Share
More Decks by Takashi Nishibayashi
See All by Takashi Nishibayashi
論文紹介 Improving Medical Reasoning through Retrieval and Self-Reflection with Retrieval-Augmented Large Language Models
hagino3000
0
530
論文紹介 Audience Size Forecasting Fast and Smart Budget Planning for Media Buyers
hagino3000
0
210
論文紹介 Towards a Fair Marketplace: Counterfactual Evaluation of the trade-off between Relevance, Fairness & Satisfaction in Recommendation Systems
hagino3000
1
570
論文紹介 Budget Management Strategies in Repeated Auctions (公開版)
hagino3000
0
250
論文紹介 A Request-level Guaranteed Delivery Advertising Planning: Forecasting and Allocation
hagino3000
0
85
論文紹介 Online Experimentation with Surrogate Metrics Guidelines and a Case Study
hagino3000
0
180
論文紹介 Bidding Machine: Learning to Bid for Directly Optimizing Profits in Display Advertising
hagino3000
0
110
論文紹介 Balancing Relevance and Discovery to Inspire Customers in the IKEA App
hagino3000
0
690
インターネット広告の効果推定と因果推論 (2018)
hagino3000
8
3.8k
Other Decks in Technology
See All in Technology
難しいから面白い!医薬品×在庫管理ドメインの複雑性と向き合い、プロダクトの成長を支えるための取り組み / Initiatives to Support Product Growth
kakehashi
2
190
Evolving DevOps Teams and Flexible Organizational Culture
kakehashi
1
260
サプライチェーン攻撃に備える
ryunen344
0
160
20240912 JJUGナイトセミナー
mii1004
0
130
Agile in Automotive Industry, puzzles and lights.
hiranabe
2
580
ロボットアームを遠隔制御の話 & LLMをつかったIoTの話もしたい
soracom
PRO
1
270
Google CloudのLLM活用の選択肢を広げるVertex AIのパートナーモデル
nayuts
0
110
セキュリティ監視の内製化 効率とリスク
mixi_engineers
PRO
7
910
自社サービスのための独自リリース版Redmine「RedMica」の取り組み
vividtone
0
1.1k
突撃! 隣のAmazon Bedrockユーザー 〜YouはどうしてAWSで?〜
minorun365
PRO
3
330
LandingZoneAccelerator と学ぶ 「スケーラブルで安全なマルチアカウントAWS環境」と 私たちにもできるベストプラクティス
maimyyym
1
130
Oracle Autonomous Database:サービス概要のご紹介
oracle4engineer
PRO
1
7k
Featured
See All Featured
Web Components: a chance to create the future
zenorocha
308
42k
How STYLIGHT went responsive
nonsquared
93
5.1k
The Art of Programming - Codeland 2020
erikaheidi
48
13k
Visualizing Your Data: Incorporating Mongo into Loggly Infrastructure
mongodb
38
9.2k
Documentation Writing (for coders)
carmenintech
65
4.3k
Learning to Love Humans: Emotional Interface Design
aarron
270
40k
Dealing with People You Can't Stand - Big Design 2015
cassininazir
363
22k
The Success of Rails: Ensuring Growth for the Next 100 Years
eileencodes
41
6.5k
Bootstrapping a Software Product
garrettdimon
PRO
304
110k
How GitHub Uses GitHub to Build GitHub
holman
472
290k
Visualization
eitanlees
142
15k
Thoughts on Productivity
jonyablonski
66
4.2k
Transcript
༧ଌͷෆ࣮֬ੑͱ্ख͖͘߹͏ ҙࢥܾఆͷख๏ ެ։൛ 5BLBTIJ/JTIJCBZBTIJ 3FQSP5FDI
͓લͩΕΑ Name: Takashi Nishibayashi twitter.com/@hagino3000 Job: Software Engineer VOYAGE GROUPͰωοτࠂ৴αʔϏε࡞ͬͯ
·͢ɻओʹ৴ϩδοΫ͔Βσʔλੳج൫·Ͱɻ ࠷ۙͷڵຯΦϯϥΠϯҙࢥܾఆͱϝΧχζϜσβ Πϯɻ
࠷ۙͷ׆ಈ ਓೳֶձࢽ Vol. 32 No. 4 (2017/07) ͷʮࠂͱ AI ಛूʯʹʮΞυωοτϫʔΫʹ͓͚Δࠂ৴ܭ
ըͷ࠷దԽʯ͕ܝࡌ͞Ε·ͨ͠ɻ ΦϥΠϦʔ͔ΒʮࣄͰ͡ΊΔػցֶशʯ͕ग़· ͨ͠ɻ @chezou, @tokorotenͱڞஶ ࢴ൛ɾిࢠॻ੶྆ํ͋Γ·͢
ࠓͷ w ༧ଌγεςϜͱҙࢥܾఆ w Ϗδωεʹ͓͚Δ࠷దԽ w ϥϕϧແ͠σʔλͷ୳ࠪ w ༧ଌϞσϧͷෆ͔֬͞Λߦಈʹө͢Δ w
ΦϯϥΠϯ࠷దԽ ػցֶशͰಘͨ༧ଌΛͲͷΑ͏ʹͯ͠͏͔ɺ༧ଌͷ࣍ͷҙࢥܾ ఆͷϑΣʔζʹ͠·͢ɻ࣮ࡍͷΞϓϦέʔγϣϯհͭͭ͠ ΛਐΊ·͢ɻ
༧ଌγεςϜͱҙࢥܾఆ
༧ଌͱҙࢥܾఆͷྫ ༧ଌλεΫ ҙࢥܾఆ ԿͷͨΊʹ धཁ༧ଌ ੜ࢈ܭը ҆શࡏݿ֬อɾࡏݿίετݮ ނোՕॴͷ༧ଌ ϝϯςφϯεܭը ϝϯςφϯεඅ༻ݮ
Ձͷ༧ଌ ചΓങ͍ͷܾఆ औҾ͕ੜΉརӹͷ࠷େԽ ࠂޮՌͷਪఆ ࠂΛද͖͔ࣔ͢Ͳ͏͔ ༧ࢉͰͷࠂޮՌ࠷େԽ Ͱ͖ΕࣗಈͰܾΊ͍ͨɺͰͲ͏͢Ε Ή͠ΖΞϓϦέʔγϣϯΤϯδχΞͷࣄࣗಈԽ͕ϝΠϯ
ཧ࠷దԽ ͋Δ੍ͷݩͰతؔΛ࠷େ ࠷খ Խ͢ΔύϥϝʔλΛٻΊΔ ෆ࣮֬ੑͷແ͍ͱ
*1"ಠཱߦ๏ਓใॲཧਪਐػߏɿࢠɾׂ߹ɾղྫɾ࠾ߨධʢɺฏʣ IUUQTXXXKJUFDJQBHPKQ@IBOOJ@TVLJSVNPOEBJ@LBJUPV@IIUNMBLJ ͋ΔͰදʹࣔ͢Λ͍ͯ͠Δɻ࣮ݱՄೳͳ࠷େརӹԿԁ͔ɻ͜͜Ͱɺ ֤ͷ݄ؒधཁྔʹ্ݶ͕͋Γɺ·ͨɺఔʹ͑Δͷ݄࣌ؒؒ࣌ ؒ·ͰͰɺෳछྨͷΛಉ࣌ʹฒߦͯ͢͠Δ͜ͱͰ͖ͳ͍ͷͱ͢Δɻ جຊใॲཧٕज़ऀࢼݧ)ळقΑΓ 9 : ; ݸͨΓͷརӹ
ԁ ݸ͋ͨΓͷॴ༻࣌ؒ ݄ؒधཁ࠷্ݶ ྫੜ࢈ܭը ֬ఆͨ͠
ެ։൛ࢿྉʹ͖ͭิ ҎԼͷ௨Γܭըͱͯ͠ఆࣜԽͯ͠ղ͚ Yݸ Zݸ [ݸΛ࡞Εརӹ͕࠷େʹͳΔͷ͕Θ͔Δɻ࣮Ͱखܭࢉ͠ͳ͍
༧ଌΛར༻ͨ͠࠷దԽ 9 : ; ݸͨΓͷརӹ ԁ ʙ ݸ͋ͨΓͷॴ༻࣌ؒ
ʙ ݄ؒधཁ࠷্ݶ ࣮ࡍʹ࡞ͬͨΓചͬͯΈΔ·ͰΘ͔Βͳ͍෦ ༧ଌΛར༻͍ͯ͠Δ࣌ͰɺԿΒ͔ͷෆ࣮֬ੑΛแ͍ͯ͠Δ ͦΕͳΓʹ༧ଌͰ͖Δ෦ ͜Μͳঢ়ଶ͔Βελʔτ͢ΔʹͲ͏ͨ͠Β͍͍͔
ࠓհ͢Δओͳํࡦ wҎԼͷ܁Γฦ͠ ༧ଌ ҙࢥܾఆɾߦಈ ݁Ռͷ؍ଌ ༧ଌثͷߋ৽
༨ஊ࠷దͱԿ͔ w ඇࣗ໌Ͱ͋Δࣄ͕ଟ͍ͱײ͡Δ w ࠗ׆ϚονϯάΞϓϦ w Ϛονϯά͕͗͢Δͱࢢ͕ബ͘ͳΔδϨϯϚ w ೖΕՁ֨ w
ʮೖΕՁ֨Λ্͍͛ͨʯʮརӹ૬Ͱ ʯ w ೖΕʹϚʔδϯ Λͤͯച͍ͬͯͨˠೖΕ্͕͕Δͱૈར૿ w ͚ϧʔϧΛม͑Δॴ͔Βͬͨ w ۀͦͷͷΛม͑ΒΕΔ༨͕ͲΕ͚ͩ͋Δ͔
'MJOUࢢͷਫಓަࣄۀ
5IF4FBSDIGPS-FBE1JQFT JO'MJOU .JDIJHBO<> w Ԗڅਫ -FBE1JQFT ͷަΛ͢ΔͨΊʹػցֶश༧ଌϞσϧΛར༻ͨ͠ࣄྫ w ,%%ʹ࠾͞Εͨจʹख๏͕ࡌ͍ͬͯΔ w
എܠ w ԖڅਫԖ༹͕ग़͠ͳ͍Α͏ʹද໘͕ίʔςΟϯά͞Ε͍ͯΔ w 'MJOUࢢʹ͓͍ͯਫݯΛม͑ͨ࣌ʹਫ࣭͕มΘͬͯίʔςΟϯά͕ണ͛ͨ w ਫಓਫͷԖͷ༹ग़ʹΑΔ݈߁ඃ͕ൃੜ w ߦͷهෆਖ਼֬
5IF4FBSDIGPS-FBE1JQFT JO'MJOU .JDIJHBO ଓ͖ w w ͲͷՈʹԖڅਫ͕ΘΕ͍ͯͯɺͦΕͲ͜ʹ͋Δͷ͔ w ݶΒΕͨ༧ࢉΛͲͷΑ͏ʹͯ͠ԖڅਫͷަʹׂΓͯΕ͍͍ͷ͔
w ঢ়گɾ੍ w ਫಓΛ۷Γىͯ֬͠ೝ͢Δίετ͕ߴ͍ ϥϕϧ͚ίετ w ܇࿅σʔλݶΒΕ͓ͯΓɺภ͍ͬͯΔ
'MJOUMFBEQJQFSFQMBDFNFOUQSPHSBNUPTXJUDIIBOETJONMJWFDPN IUUQTXXXNMJWFDPNOFXTqJOUqJOU@MFBE@QJQF@SFQMBDFNFOU@QSIUNM
"CFSOFUIZ +BDPC FUBM"DUJWF3FNFEJBUJPO5IF4FBSDIGPS-FBE1JQFTJO'MJOU .JDIJHBO1SPDFFEJOHTPGUIFUI "$.4*(,%%*OUFSOBUJPOBM$POGFSFODFPO,OPXMFEHF%JTDPWFSZ%BUB.JOJOH"$. ༧ଌ݁ՌΛݩʹௐࠪϙΠϯτΛܾΊΔϧʔϧ ༧ଌ݁ՌΛݩʹύΠϓަϙΠϯτΛܾΊΔϧʔϧ ༧ଌϞσϧ
5IF4FBSDIGPS-FBE1JQFT JO'MJOU .JDIJHBO ଓ͖ w ௐࠪϙΠϯτܾఆϧʔϧ w ใΛऔಘͯ͠༧ଌੑೳΛ্͛Δͷ͕త w ೳಈֶश
"DUJWF-FBSOJOH w ύΠϓަϙΠϯτܾఆϧʔϧ w ޡ۷ίετΛ࠷খԽ͍ͨ͠ w ࠷֬ͷߴ͍ϙΠϯτΛબͿɺᩦཉ๏ (SFFEZ"MHPSJUIN
ೳಈֶश "DUJWF-FBSOJOH w എܠ w ڭࢣ͋Γֶश܇࿅σʔλ͕ଟ͍ఔਫ਼্͕͕Δ w ͨͩ͠ϥϕϧ͚ Ξϊςʔγϣϯ ʹίετ͕͔͔Δ
w Ξϓϩʔν w ༧ଌثͷਫ਼্ʹد༩͢ΔσʔλΛબͿ w ํࡦͷྫ࠷ෆ͔֬ͳσʔλΛબ͢Δ w 'MJOUͰ*NQPSUBODF8FJHIUFE"DUJWF-FBOJOHΛ࠾༻
ᩦཉ๏ (SFFEZ"MHPSJUIN w ࢼߦຖʹͦͷ࣌Ͱ࠷ظใु͕େ͖ͳߦಈΛऔΔํࡦ w FHμΠΫετϥ๏ w ۙࣅղ͕ಘΒΕΔ w ʹΑͬͯϫʔετέʔεͷۙࣅʹཧอূ͕͋Δ
w FHφοϓαοΫ w େମ্ख͍࣮͕͘͘͠༰қͳͷͰΑ͘ΘΕΔ
͞ΒͳΔࠔ w ࢪࡦͷධՁύΠϓަ݅͋ͨΓͷίετݮྔ w ˠ w .ͷઅ w
Ռग़ͨͷͷࢢຽ͕ൃ w ਓؒͷ໋Λٹ͏ͣͩͬͨ"*͕࣏ͱແʹΑͬͯແࢹ͞Εͯ͠·ͬͨ IUUQTOPUFNVEBUBTDJFODFOOEFCEEBGF w ΞϧΰϦζϜΛݟΕΘ͔Δ௨Γɺेͳ༧ࢉ͕͋ΕશॅΛ۷Γฦ͠ ͯݕࠪ͢ΔࣄʹͳΔɻௐࠪ͢Δॱ൪͕ૣ͍͔͍͔ͷҧ͍ɻ w ࠷దͱҰମԿͳͷ͔
༧ଌϞσϧͷෆ͔֬͞Λ өͨ͠ߦಈ
ྦྷੵใुΛ࠷େԽ͍ͨ͠ ࢼߦճ ͋ͨΓճ Q ㅟ εϩοτϚγϯ" εϩοτϚγϯ#
֬QͰͨΓ͕ग़ΔϕϧψʔΠࢼߦΛߟ͑Δɺ͜ͷޙͲ͏͖͔͢ ෳ͋ΔબࢶͦΕͧΕ͔Β֬త JJE ʹใु͕ಘΒΕΔઃఆͰγʔέϯγϟϧʹ ߦಈΛܾΊͯྦྷੵใु࠷େԽΛࢦ͢Λʮ֬తόϯσΟοτʯɺ͜ͷ࣌ ͷબࢶΛʮΞʔϜʯͱݺͿɻ
QͷࣄޙΛݟΔ ύϥϝʔλQͷ #FUB ޭճ ࣦഊճ #͕"ΑΓྑ͍ͱஅ͢Δʹ·ͩϦεΫ͕͋Δ
QͷࣄޙΛݟΔ ύϥϝʔλQͷ #FUB ޭճ ࣦഊճ ͍ͯͨ͠Β#ͷΈΛબྑ͍
֬తόϯσΟοτͷํࡦ w ֬Ұக๏ w ΞʔϜa ͷظ͕࠷େͰ͋Δ֬ͰaΛબ͢Δ w ͲͷΑ͏ʹ w
ϥϯυຖʹ w ΞʔϜͦΕͧΕͷظͷࣄޙ͔ΒЖaΛੜ ㅟ w Жa ͕࠷େͷΞʔϜΛબ͢Δ ㅟ w ݁Ռͷ؍ଌΛͯ͠બͨ͠ΞʔϜͷهΛߋ৽ w 㱺5IPNQTPO4BNQMJOH
ઢܗϞσϧͷ߹ ύϥϝʔλͷਪఆͦΕͧΕҟͳΔޡࠩΛ࣋ͭ සओٛͰ࠷ਪఆྔwΛݻఆͨ͠ύϥϝʔλͱͯ͠͏͕
Results: Ordinary least squares ================================================================== Model: OLS Adj. R-squared: 0.946
Dependent Variable: y AIC: 3196.9303 Date: 2019-04-04 00:32 BIC: 3230.7426 No. Observations: 506 Log-Likelihood: -1590.5 Df Model: 8 F-statistic: 1110. Df Residuals: 498 Prob (F-statistic): 8.68e-312 R-squared: 0.947 Scale: 31.960 -------------------------------------------------------------------- Coef. Std.Err. t P>|t| [0.025 0.975] -------------------------------------------------------------------- CRIM -0.1858 0.0380 -4.8884 0.0000 -0.2605 -0.1111 ZN 0.0833 0.0146 5.7100 0.0000 0.0546 0.1119 CHAS 3.8725 1.0130 3.8227 0.0001 1.8821 5.8629 NOX -18.5928 3.0070 -6.1833 0.0000 -24.5007 -12.6849 RM 6.8287 0.2539 26.8931 0.0000 6.3298 7.3276 DIS -1.3713 0.1736 -7.8985 0.0000 -1.7124 -1.0302 RAD 0.2022 0.0711 2.8420 0.0047 0.0624 0.3420 TAX -0.0180 0.0038 -4.7172 0.0000 -0.0255 -0.0105 ------------------------------------------------------------------ ྫ#PTUPOෆಈ࢈Ձ֨σʔλͷઢܗճؼ #PTUPOIPVTFQSJDFTEBUBTFUΛલॲཧແ͠Ͱ0-4ͨ݁͠Ռ
ਪఆʹ༧ଌͷෆ͔֬͞Λө͢Δ w wͷࣄޙ͔Βੜͨ͠wΛͬͯਪఆΛٻΊΔ ㅟ w ใु͕ઢܗϞσϧ͔Βੜ͞ΕΔઃఆͷόϯσΟοτͷղ๏<> w 5IPNQTPO4BNQMJOHGPS$POUFYUVBM#BOEJUTXJUI-JOFBS1BZP⒎T<> w ϕΠδΞϯϒʔτετϥοϓͰࣄޙΛੜ͢ΔҊ<>
w ิ$POUFYUVBM#BOEJU w ϥϯυຖʹίϯςΩετใ͕༩͑ΒΕΔઃఆ w ࠂ৴ΞʔϜ͚ͩͰใु͕JJEʹੜ͞ΕΔͱݴ͑ͳ͍ͷͰίϯςΩ ετΛ͏
"HSBXBM 4IJQSB BOE/BWJO(PZBM5IPNQTPOTBNQMJOHGPSDPOUFYUVBMCBOEJUTXJUIMJOFBSQBZP⒎T *OUFSOBUJPOBM$POGFSFODFPO.BDIJOF-FBSOJOH ଟมྔਖ਼ن͔Βαϯϓϧ͍ͯ͠Δ ޡ͕ࠩਖ਼نΛԾఆ
5IPNQTPO4BNQMJOH w ࣄޙ͔֬ΒͷαϯϓϧΛར༻͢Δ w ଟόϯσΟοτͷ༷ͳ׆༻ͱ୳ࡧ͕ඞཁͳ࣌ʹڧ͍ w ใुͷ৴པ্ݶʹجͮ͘બΛߦͳ͏ख๏ 6$# ΑΓੑೳ͕ྑ͍ w
όϯσΟοτʹద༻͢Δͱڧ͍ࣄΒΕ͍͕ͯͨɺੑೳͷཧղੳ͕ ͞Εͨͷ
*ODSFNFOUBMJUZ#JEEJOH"UUSJCVUJPO<> w /FUqJYͷਓͷ35#ೖࡳઓུ w 35#ࠂදࣔݖརͷϦΞϧλΠϜΦʔΫγϣϯ w ࠂͷҼՌޮՌ͕࠷େʹͳΔೖࡳΛ͍ͨ͠ w ༧ଌೖࡳϦΫΤετຖ ԯճEBZ
w ༧ଌͷෆ͔֬͞Λදݱ͢ΔͷʹύϥϝʔλΛࣄޙ͔Βੜ w ༰ΓΓͷ8PSLJOH1BQFSͰݟॴ͕ଟ͍ w ࠂͷϥϯμϜԽൺֱࢼݧ (IPTU"ET ɺޮՌͷݮਰϞσϧ
ΦϯϥΠϯ࠷దԽ
ΦϯϥΠϯ࠷దԽ w Γ͕͠Ͱ͖ͳ͍ઃఆͰతؔͷ࠷େԽΛૂ͏ w ࠓ੍͖ΦϯϥΠϯತ࠷దԽͷհ w ·ͣΦϑϥΠϯઃఆ͔Β
ತ࠷దԽ w ੍ɾత͍ؔͣΕತؔ w ղ͕ತू߹Ͱ͋Δඞཁ w ྫ͑ࠂબํ๏ΛٻΊΔͩͱ /ݸ͋ΔࠂͷͲΕΛબ͢Δ͔x㱨\ ^/ͷΘΓʹ ͦΕͧΕͷࠂΛબ͢Δ֬x㱨<
>/ΛٻΊΔ
ΦϯϥΠϯͰΓ͍ͨ w ੍ΛͲΕ͚ͩҧ͢Δ͔ɺͬͯΈͳ͍ͱΘ͔Βͳ͍ w ੍Λҧͯͨͩͪ͠ʹఀࢭ͢ΔͷࠔΔ ؇੍͍ w 0OMJOF$POWFY0QUJNJ[BUJPOXJUI4UPDIBTUJD$POTUSBJOUT<> w
G Y H Y ͦΕͧΕඍͰ͖Εྑ͍ w ࣮ݧσʔληϯλʔͷফඅిྗΛ࠷খԽ͢ΔόονδϣϒͷׂΓ͋ͯ
·ͱΊ w "DUJWF-FBSOJOH w ᩦཉ๏ w ༧ଌͷෆ࣮֬ੑΛߦಈʹө͢Δͱڧ͍ w ΦϯϥΠϯͰ࠷దԽͰ͖Δ w
Կ͕࠷ద͔ܾΊΔͷ͕͍͠
ࢀߟจݙ <>"CFSOFUIZ +BDPC FUBM"DUJWF3FNFEJBUJPO5IF4FBSDIGPS-FBE 1JQFTJO'MJOU .JDIJHBO1SPDFFEJOHTPGUIFUI"$.4*(,%% *OUFSOBUJPOBM$POGFSFODFPO,OPXMFEHF%JTDPWFSZ%BUB.JOJOH"$. <>"HSBXBM
4IJQSB BOE/BWJO(PZBM'VSUIFSPQUJNBMSFHSFUCPVOETGPS UIPNQTPOTBNQMJOH"SUJpDJBMJOUFMMJHFODFBOETUBUJTUJDT <>ຊଟ३ BOEதଜಞόϯσΟοτͷཧͱΞϧΰϦζϜߨஊࣾ <>"HSBXBM 4IJQSB BOE/BWJO(PZBM5IPNQTPOTBNQMJOHGPSDPOUFYUVBM CBOEJUTXJUIMJOFBSQBZP⒎T*OUFSOBUJPOBM$POGFSFODFPO.BDIJOF -FBSOJOH
ࢀߟจݙ <>-FXJT 3BOEBMM" BOE+F⒎SFZ8POH*ODSFNFOUBMJUZ#JEEJOH "UUSJCVUJPO <>$.Ϗγϣοϓʢஶʣݩాߒɼ܀ాଟتɼṤޱ೭ɼদຊ༟࣏ɼଜాঢ ʢ༁ʣύλʔϯೝࣝͱػցֶशʢ্ʣɿϕΠζཧʹΑΔ౷ܭత༧ଌ <>ଜాঢใཧͷجૅใͱֶशͷ؍తཧղͷͨΊʹαΠΤϯεࣾ
<>)B[BO &MBE*OUSPEVDUJPOUPPOMJOFDPOWFYPQUJNJ[BUJPO'PVOEBUJPOT BOE5SFOETJO0QUJNJ[BUJPO <>:V )BP .JDIBFM/FFMZ BOE9JBPIBO8FJ0OMJOFDPOWFYPQUJNJ[BUJPO XJUITUPDIBTUJDDPOTUSBJOUT"EWBODFTJO/FVSBM*OGPSNBUJPO1SPDFTTJOH 4ZTUFNT