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Poster
Model-Powered Conditional Independence Test
Rajat Sen · Ananda Theertha Suresh · Karthikeyan Shanmugam · Alex Dimakis · Sanjay Shakkottai

Mon Dec 04 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #190
in Posters Mon »
We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we determine whether $X \independent Y \vert Z$. We approach this by converting the conditional independence test into a classification problem. This allows us to harness very powerful classifiers like gradient-boosted trees and deep neural networks. These models can handle complex probability distributions and allow us to perform significantly better compared to the prior state of the art, for high-dimensional CI testing. The main technical challenge in the classification problem is the need for samples from the conditional product distribution $f^{CI}(x,y,z) = f(x|z)f(y|z)f(z)$ -- the joint distribution if and only if $X \independent Y \vert Z.$ -- when given access only to i.i.d. samples from the true joint distribution $f(x,y,z)$. To tackle this problem we propose a novel nearest neighbor bootstrap procedure and theoretically show that our generated samples are indeed close to $f^{CI}$ in terms of total variational distance. We then develop theoretical results regarding the generalization bounds for classification for our problem, which translate into error bounds for CI testing. We provide a novel analysis of Rademacher type classification bounds in the presence of non-i.i.d \textit{near-independent} samples. We empirically validate the performance of our algorithm on simulated and real datasets and show performance gains over previous methods.
Keywords: Learning Theory · Causal Inference

Author Information

Rajat Sen (University of Texas at Austin)
Ananda Theertha Suresh (Google)
Karthikeyan Shanmugam (IBM Research, NY)
Alex Dimakis (University of Texas, Austin)
Sanjay Shakkottai (The University of Texas at Austin)

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