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
460
論文紹介 Audience Size Forecasting Fast and Smart Budget Planning for Media Buyers
hagino3000
0
200
論文紹介 Towards a Fair Marketplace: Counterfactual Evaluation of the trade-off between Relevance, Fairness & Satisfaction in Recommendation Systems
hagino3000
1
560
論文紹介 Budget Management Strategies in Repeated Auctions (公開版)
hagino3000
0
240
論文紹介 A Request-level Guaranteed Delivery Advertising Planning: Forecasting and Allocation
hagino3000
0
80
論文紹介 Online Experimentation with Surrogate Metrics Guidelines and a Case Study
hagino3000
0
170
論文紹介 Bidding Machine: Learning to Bid for Directly Optimizing Profits in Display Advertising
hagino3000
0
100
論文紹介 Balancing Relevance and Discovery to Inspire Customers in the IKEA App
hagino3000
0
680
インターネット広告の効果推定と因果推論 (2018)
hagino3000
8
3.7k
Other Decks in Technology
See All in Technology
エンジニア向け会社紹介資料
caddi_eng
14
230k
技術広報経験0のEMがエンジニアブランディングを始めてみた
coconala_engineer
2
120
Distributed Tracing in LINE Taiwan — 大規模分散式追蹤的實踐與挑戰
johnlin
1
270
Datadog APM による 性能改善から始める技術的負債解消
recruitengineers
PRO
6
210
モデリング実践で見えた 分析モデルと業務モデルの特性
leveragestech
1
210
アンドパッドのマルチプロダクト戦略を支えるSRE / SRE NEXT 2024
cassius7
1
1.7k
事業価値と Engineering 2024年版
recruitengineers
PRO
14
2.1k
プロダクト全体で取り組むSREing イシューから始める信頼性・生産性向上の実践/SRE NEXT 2024
visional_engineering_and_design
3
1.3k
Oracle Base Database Service 技術詳細
oracle4engineer
PRO
5
43k
Kaggleで賞金200万円ゲットした話 〜 Machine Unlearning と Google AI Assistants 〜
toshi_k_datasci
2
920
次の20年をどう生きるのか? ― IT 20年の歴史から学ぶ「変わる事・変わらない事」
soracom
PRO
1
170
2024年における生成AIエンジニアとは何者か
yyo616
5
2.3k
Featured
See All Featured
Java REST API Framework Comparison - PWX 2021
mraible
PRO
24
7.2k
実際に使うSQLの書き方 徹底解説 / pgcon21j-tutorial
soudai
158
46k
Designing for humans not robots
tammielis
247
25k
Practical Orchestrator
shlominoach
185
10k
The Invisible Customer
myddelton
117
13k
Intergalactic Javascript Robots from Outer Space
tanoku
267
26k
Helping Users Find Their Own Way: Creating Modern Search Experiences
danielanewman
26
2.1k
個人開発の失敗を避けるイケてる考え方 / tips for indie hackers
panda_program
85
15k
Music & Morning Musume
bryan
43
5.9k
Design by the Numbers
sachag
277
19k
VelocityConf: Rendering Performance Case Studies
addyosmani
321
23k
Gamification - CAS2011
davidbonilla
79
4.9k
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