Guy Blanc Neha Gupta Jane Lange Li-Yang Tan ! x f(x) 000010101 - - PowerPoint PPT Presentation

Guy Blanc Neha Gupta Jane Lange Li-Yang Tan

x f(x) 000010101

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011011010 1 100100111 1 101001000 1 001010010

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𝑦! 𝑦" 𝑦#

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1 1 𝑦" 1 −1 ID3, C4.5, CART

𝑦$

1) Choose a good root 𝐶𝑣𝑗𝑚𝑒(𝑔 𝑦$ < 0 ) 𝐶𝑣𝑗𝑚𝑒(𝑔 𝑦$ ≥ 0 ) 2) Recurse on subtrees “Good” root = relevant, important, influential [variable influence, information gain, Gini impurity]

Noise-stable functions

[new in BGLT20]

Heuristics do poorly

[already well-known]

Monotone functions

[new in BLT20]

Heuristics do well New algorithm: provable guarantees for all functions [BGLT20]

𝑦!

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1 1 𝒚𝟐 𝒚𝟑 𝒚𝟒 𝒚𝟓 𝒚𝟔 $2 $0 $5 $1200 $45 Query cost vector Randomized DT Stochastic node