Recent Development in Selective Inference II

Explore recent developments in selective inference through this tutorial from the Adaptive Data Analysis Workshop. Delve into advanced topics including Gaussian randomization schemes, randomized conditional approaches, and the Polyhedral Lemma. Examine computational challenges in randomized inference, full model and target concepts, and the randomized selective law. Learn about approximate reference techniques, confidence intervals, and selective maximum likelihood estimation. Investigate marginal screening of eGenes, validity of inference, power analysis, and point estimation comparisons. Conclude by revisiting LASSO and its data generative scheme. Gain insights from Snigdha Panigrahi's expertise in this comprehensive exploration of cutting-edge selective inference methodologies.

Intro
A natural Gaussian randomization scheme
Randomized conditional approach
Can Polyhedral Lemma come to our rescue?
Breakdown of Polyhedral Lemma
Randomized inference is computationally challenging
Full model and target
Randomized selective law
Approximate reference - MCMC free approach
Basis of approximation
Approximate density: simple problem
Confidence intervals
Selective MLE - Point Estimate
Marginal screening of eGenes
Validity of inference - Coverage of intervals
Power - Lengths of intervals
Point Estimation - Comparison of risks
Revisit LASSO: Data generative scheme