Brian Manzo | Searcharxiv

arXiv2023

Scalable Causal Structure Learning via Amortized Conditional Independence Testing

Controlling false positives (Type I errors) through statistical hypothesis testing is a foundation of modern scientific data analysis. Existing causal structure discovery algorithms either do not provide Type I error control or cannot scale to the size of modern scientific datasets. We consider a variant of the causal discovery problem with two sets of nodes, where the only edges of interest form a bipartite causal subgraph between the sets. We develop Scalable Causal Structure Learning (SCSL), a method for causal structure discovery on bipartite subgraphs that provides Type I error control. SCSL recasts the discovery problem as a simultaneous hypothesis testing problem and uses discrete optimization over the set of possible confounders to obtain an upper bound on the test statistic for each edge. Semi-synthetic simulations demonstrate that SCSL scales to handle graphs with hundreds of nodes while maintaining error control and good power. We demonstrate the practical applicability of the method by applying it to a cancer dataset to reveal connections between somatic gene mutations and metastases to different tissues.

stat.ME↗

arXiv2021

Normalizing Flows for Knockoff-free Controlled Feature Selection

Controlled feature selection aims to discover the features a response depends on while limiting the false discovery rate (FDR) to a predefined level. Recently, multiple deep-learning-based methods have been proposed to perform controlled feature selection through the Model-X knockoff framework. We demonstrate, however, that these methods often fail to control the FDR for two reasons. First, these methods often learn inaccurate models of features. Second, the "swap" property, which is required for knockoffs to be valid, is often not well enforced. We propose a new procedure called FlowSelect to perform controlled feature selection that does not suffer from either of these two problems. To more accurately model the features, FlowSelect uses normalizing flows, the state-of-the-art method for density estimation. Instead of enforcing the "swap" property, FlowSelect uses a novel MCMC-based procedure to calculate p-values for each feature directly. Asymptotically, FlowSelect computes valid p-values. Empirically, FlowSelect consistently controls the FDR on both synthetic and semi-synthetic benchmarks, whereas competing knockoff-based approaches do not. FlowSelect also demonstrates greater power on these benchmarks. Additionally, FlowSelect correctly infers the genetic variants associated with specific soybean traits from GWAS data.

stat.ML↗