What is Linear Quiz Blending (Netflix Blending) ?

通称「Linear Quiz Blending」「Netflix Blending」の解説。

The BigChaos Solution to the Netflix Grand Prize
https://www.asc.ohio-state.edu/statistics/statgen/joul_aut2009/BigChaos.pdf

Transcript

1. -JOFBS
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   #MFOEJOH V
   !VQVSB .BZ
   
   
2. ίϯϖղ๏ͷ࿦จ IUUQTXXXBTDPIJP TUBUFFEVTUBUJTUJDTTUBUHFOKPVM@BVU#JH$IBPTQEG
3. -JOFBS
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   #MFOEJOH ͷ֓ཁ • QVCMJD
   -#ͷ৘ใΛ༻͍ͯɺ༏ΕͨFOTFNCMFͷ ॏΈΛۙࣅܭࢉ͢Δ • ධՁࢦඪ͕࠷খೋ৐ޡࠩͷ৔߹ʹར༻Ͱ͖Δ
4. ྑ͍༧ଌ஋ͷࠞͥํʁ Z@QSFE Z@QSFE Z@QSFE º  º 
5. ఆࣜԽ ྑ͍𝛽Λ஌Γ͍ͨ 𝑋 𝑦!"#$ º 𝛽 𝑦  ۙࣅ͍ͨ͠
6. ΋͠Z͕෼͔͍ͬͯͨΒʁ • 𝑋𝛽͕𝑦ʹ࠷΋ۙࣅ͢Δ𝛽Λ஌Γ͍ͨ • ! " 𝑋𝛽 − 𝑦 " ͕࠷খͱͳΔ𝛽Λܭࢉ͍ͨ͠ • 𝛽Ͱภඍ෼ͯ͠  ͱஔ͘͜ͱͰҎԼΛಘΔ ! 𝛽 = 𝑋!𝑋 "# 𝑋!𝑦
7. ࣮ࡍZ͸෼͔Βͳ͍ɺ͚ΕͲ ! 𝛽 = 𝑋!𝑋 "# 𝑋!𝑦 º 𝑦 𝑋% 𝑋%𝑦
8. 𝑋!𝑦ͷ𝑗൪໨ͷཁૉΛߟ͑Δ 𝑥#,% 𝑦% + 𝑥#,! 𝑦! + ⋯ + 𝑥#,&'! 𝑦&'! = ) ( 𝑥#( 𝑦( º 𝑦 𝑋% 𝑋%𝑦 𝑗 = 0 𝑗 = 1 𝑢 𝑢
9. ࣜมܗ ) ( 𝑥#( 𝑦( = 1 2 ) ( 𝑦( " + ) ( 𝑥#( " − ) ( 𝑦( − 𝑥#( "
10. ୈ߲ ) ( 𝑥#( 𝑦( = 1 2 ) ( 𝑦( " + ) ( 𝑥#( " − ) ( 𝑦( − 𝑥#( " • શͯͷ஋ΛͰఏग़ͨ͠ࡍͷ࠷খೋ৐ޡࠩ • QVCMJD
    -#ͷείΞͰۙࣅ
11. ୈ߲ ) ( 𝑥#( 𝑦( = 1 2 ) ( 𝑦( " + ) ( 𝑥#( " − ) ( 𝑦( − 𝑥#( " • 9͸ܭࢉՄೳ
12. ୈ߲ ) ( 𝑥#( 𝑦( = 1 2 ) ( 𝑦( " + ) ( 𝑥#( " − ) ( 𝑦( − 𝑥#( " • ࠷খೋ৐ޡࠩ • QVCMJD
    -#ͷείΞͰۙࣅ
13. ੔ཧ͢Δͱ • ∑( 𝑥#( 𝑦( = ! " ∑( 𝑦( " + ∑( 𝑥#( " − ∑( 𝑦( − 𝑥#( " ͸ ۙࣅܭࢉͰ͖Δ • Αͬͯ 𝑋)𝑦 ͕෼͔Δ • ͢ͳΘͪ - 𝛽 = 𝑋)𝑋 '! 𝑋)𝑦 ͕෼͔Δ
14. ·ͱΊ • -JOFBS
    2VJ[
    #MFOEJOH Λղઆͨ͠ • QVCMJD
    -#ͷ৘ใΛ༻͍ͯɺ༏ΕͨFOTFNCMFͷॏΈ Λۙࣅܭࢉ͢Δ • ධՁࢦඪ͕࠷খೋ৐ޡࠩͷ৔߹ʹར༻Ͱ͖Δ • ඞཁͳ৘ใ͸ 
    ෳ਺ͷ ༧ଌ஋
    QVCMJD
    -#ͷείΞ ͷϖΞ 
    શͯͰఏग़ͨ͠ࡍͷQVCMJD
    -#ͷείΞ