Conditional Independence Testing using Adversarial Neural Networks - PowerPoint PPT Presentation

Conditional Independence Testing using Adversarial Neural Networks Alexis Bellot Mihaela van der Schaar

From two-sample testing to independence testing X ~ 𝑸 Y ~ 𝑹 Two sample problem: Can we say whether 𝑸 = 𝑹 ? Independence problem: Can we say whether 𝒀, 𝒁 ⊥ (𝟏, 𝟐) ?

From independence to conditional independence X ~ 𝑸 Y ~ 𝑹 Two sample problem: Can we say whether 𝑸 = 𝑹 ? Can we say whether 𝒀 ⊥ 𝒁 ? Independence problem: Can we say whether 𝒀 ⊥ 𝒁 | 𝒂 ? Conditional Independence problem:

Can we find genes directly associated with disease? Other observed gene mutations ? Genes of Disease interest

Many questions fit into this formalism Important concepts of statistics (sufficiency, What data should I collect for my ancillarity …) can be regarded as expressions prediction problem ? Z of conditional independence Is our prediction rule invariant to Is it likely that interventions will affect changes in the environment ? the variable of interest ? ? Y X How do we learn a Bayesian network over our data ? Is our prediction rule fair ? Are sensitive attributes influential ?

𝒀 ⊥ 𝒁 | 𝒂 iff 𝒒 𝒁 𝒀, 𝒂 = 𝒒 𝒁 𝒂) The intuition Z • If we had access to 𝒒 𝒁 𝒂) • Samples from this distribution breaks the direct dependency 𝒀 − 𝒁 • A comparison of the dependencies between synthetic and observed data ? should not reveal any differences under Y X the null.

Why you should come see our poster • • We develop a modified GAN to sample Provably valid testing from 𝒒 𝒁 𝒂) with high power ➢ No assumptions on data ➢ Better performance in high distribution. ➢ Non-asymptotic error bounds. dimensions

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