Learning generative models for valid knockoffs using novel multivariate-rank based statistics

10/29/2021
by   Shoaib Bin Masud, et al.
0

We consider the problem of generating valid knockoffs for knockoff filtering which is a statistical method that provides provable false discovery rate guarantees for any model selection procedure. To this end, we are motivated by recent advances in multivariate distribution-free goodness-of-fit tests namely, the rank energy (RE), that is derived using theoretical results characterizing the optimal maps in the Monge's Optimal Transport (OT) problem. However, direct use of use RE for learning generative models is not feasible because of its high computational and sample complexity, saturation under large support discrepancy between distributions, and non-differentiability in generative parameters. To alleviate these, we begin by proposing a variant of the RE, dubbed as soft rank energy (sRE), and its kernel variant called as soft rank maximum mean discrepancy (sRMMD) using entropic regularization of Monge's OT problem. We then use sRMMD to generate deep knockoffs and show via extensive evaluation that it is a novel and effective method to produce valid knockoffs, achieving comparable, or in some cases improved tradeoffs between detection power Vs false discoveries.

READ FULL TEXT
research
02/15/2023

On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detection

This paper considers the use of recently proposed optimal transport-base...
research
10/29/2021

Robust and efficient change point detection using novel multivariate rank-energy GoF test

In this paper, we use and further develop upon a recently proposed multi...
research
03/16/2021

Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport

In this paper, we extend the recently proposed multivariate rank energy ...
research
10/26/2021

On the Optimization Landscape of Maximum Mean Discrepancy

Generative models have been successfully used for generating realistic s...
research
07/29/2020

Generalization Properties of Optimal Transport GANs with Latent Distribution Learning

The Generative Adversarial Networks (GAN) framework is a well-establishe...
research
06/01/2017

Learning Generative Models with Sinkhorn Divergences

The ability to compare two degenerate probability distributions (i.e. tw...
research
02/10/2015

Generative Moment Matching Networks

We consider the problem of learning deep generative models from data. We...

Please sign up or login with your details

Forgot password? Click here to reset