Selective inference
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Selective inference is a statistical framework that accounts for selection bias when using feature selection methods like Lasso. When features are selected from a larger set for inclusion in a model, directly interpreting p-values from fitting that model can be misleading without correcting for the selection process. Selective inference provides adjusted confidence intervals to correctly assess whether selected features have statistically significant effects while controlling for the selection bias introduced by the feature selection method.
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Selective inference
- 1. What is Selective Inference? • When you use a feature selection method (e.g. Lasso), there exists selection bias. • There are features : 𝑥1, 𝑥2, … 𝑥100, and 𝑥2, 𝑥21, 𝑥30 are chosen. • Then you make the model : y = 𝑤2 𝑥2 + 𝑤21 𝑥21 + 𝑤30 𝑥30 • Fit it, and get the parameters : 𝑤2 = +3.8, 𝑤21 = −4.5, 𝑤30 = +6.2 • p-values of 𝑤2, w21, w30 are beyond 𝛼 = 0.05. • However, you cannot directly say that : “𝑤2 and w30 have positive effects and 𝑤21 has negative effect.” • Hypothesis selected by some algorithm has selection bias and we have to correct the bias. To do that, we get following 𝑙 𝑎𝑛𝑑 𝑢. Ρ 𝑤𝑖 ∉ 𝑙, 𝑢 𝑖 ∈ 𝑆, 𝑆 ← 𝐿𝑎𝑠𝑠𝑜) < 𝛼 • このような条件付分布に基づく統計的推論の枠組をSelective Inference と呼ぶようです