Automatic Polynomial Expansions What? I vw can build polynomial decision surfaces: x 7→ 2 · 1[x1 x2 − 3x1 x4 x5 + 7x2 x4 x9 ≥ 0] − 1. What? I vw can build polynomial decision surfaces: x 7→ 2 · 1[x1 x2 − 3x1 x4 x5 + 7x2 x4 x9 ≥ 0] − 1. I Just add --stage poly to your command line. Why? I Polynomial features facilitate many problems (e.g., see kaggle forums). Why? I Polynomial features facilitate many problems (e.g., see kaggle forums). Why? I Polynomial features facilitate many problems (e.g., see kaggle forums). I vw already had (manual) polynomials of low degree: vw -q ff (..) vw --cubic fff (..) Why? I Polynomial features facilitate many problems (e.g., see kaggle forums). I vw already had (manual) polynomials of low degree: vw -q ff (..) vw --cubic fff (..) --stage poly vs. --ksvm: different bias. I Does it work? Theory. Loss minimization guarantee. Does it work? Theory. Loss minimization guarantee. Practice. . Relative error vs time tradeoff 1.0 linear quadratic cubic apple(0.125) apple(0.25) apple(0.5) apple(0.75) apple(1.0) relative error 0.8 0.6 0.4 0.2 0.0 −0.2 0 10 1 10 relative time 2 10 Does it work? Theory. Loss minimization guarantee. Practice. . Relative error vs time tradeoff 1.0 linear quadratic cubic apple(0.125) apple(0.25) apple(0.5) apple(0.75) apple(1.0) relative error 0.8 0.6 0.4 0.2 0.0 −0.2 0 10 1 10 relative time 2 10 More Info. NIPS 2014: Scalable Nonlinear Learning with Adaptive Polynomial Expansions. Alekh Agarwal, Alina Beygelzimer, Daniel Hsu, John Langford, Matus Telgarsky. Usage --stage poly Usage --stage poly --sched exponent arg1 Usage --stage poly --sched exponent arg1 --batch sz arg2 Usage --stage poly --sched exponent arg1 --batch sz arg2 --batch sz no doubling Hacking I Different types of features. Hacking I Different types of features. I Different support search. More info @ github wiki & NIPS paper. More info @ github wiki & NIPS paper.
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