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What is Linear Quiz Blending (Netflix Blending) ?

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

Shotaro Ishihara

February 29, 2020
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  1. ΋͠Z͕෼͔͍ͬͯͨΒʁ • 𝑋𝛽͕𝑦ʹ࠷΋ۙࣅ͢Δ𝛽Λ஌Γ͍ͨ • ! " 𝑋𝛽 − 𝑦 "

    ͕࠷খͱͳΔ𝛽Λܭࢉ͍ͨ͠ • 𝛽Ͱภඍ෼ͯ͠  ͱஔ͘͜ͱͰҎԼΛಘΔ ! 𝛽 = 𝑋!𝑋 "# 𝑋!𝑦
  2. 𝑋!𝑦ͷ𝑗൪໨ͷཁૉΛߟ͑Δ 𝑥#,% 𝑦% + 𝑥#,! 𝑦! + ⋯ + 𝑥#,&'!

    𝑦&'! = ) ( 𝑥#( 𝑦( º 𝑦 𝑋% 𝑋%𝑦 𝑗 = 0 𝑗 = 1 𝑢 𝑢
  3. ࣜมܗ ) ( 𝑥#( 𝑦( = 1 2 ) (

    𝑦( " + ) ( 𝑥#( " − ) ( 𝑦( − 𝑥#( "
  4. ୈ߲ ) ( 𝑥#( 𝑦( = 1 2 ) (

    𝑦( " + ) ( 𝑥#( " − ) ( 𝑦( − 𝑥#( " • શͯͷ஋ΛͰఏग़ͨ͠ࡍͷ࠷খೋ৐ޡࠩ • QVCMJD-#ͷείΞͰۙࣅ
  5. ୈ߲ ) ( 𝑥#( 𝑦( = 1 2 ) (

    𝑦( " + ) ( 𝑥#( " − ) ( 𝑦( − 𝑥#( " • 9͸ܭࢉՄೳ
  6. ୈ߲ ) ( 𝑥#( 𝑦( = 1 2 ) (

    𝑦( " + ) ( 𝑥#( " − ) ( 𝑦( − 𝑥#( " • ࠷খೋ৐ޡࠩ • QVCMJD-#ͷείΞͰۙࣅ
  7. ੔ཧ͢Δͱ • ∑( 𝑥#( 𝑦( = ! " ∑( 𝑦(

    " + ∑( 𝑥#( " − ∑( 𝑦( − 𝑥#( " ͸ ۙࣅܭࢉͰ͖Δ • Αͬͯ 𝑋)𝑦 ͕෼͔Δ • ͢ͳΘͪ - 𝛽 = 𝑋)𝑋 '! 𝑋)𝑦 ͕෼͔Δ