Efficient Conditionally Invariant Representation Learning

• URL: http://arxiv.org/abs/2212.08645v2
• Date: Tue, 19 Dec 2023 18:46:19 GMT
• Title: Efficient Conditionally Invariant Representation Learning
• Authors: Roman Pogodin, Namrata Deka, Yazhe Li, Danica J. Sutherland, Victor Veitch, Arthur Gretton
• Abstract summary: Conditional Independence Regression CovariancE (CIRCE) Measures of conditional feature dependence require multiple regressions for each step of feature learning. In experiments, we show superior performance to previous methods on challenging benchmarks.
• Score: 41.320360597120604
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the Conditional Independence Regression CovariancE (CIRCE), a measure of conditional independence for multivariate continuous-valued variables. CIRCE applies as a regularizer in settings where we wish to learn neural features $\varphi(X)$ of data $X$ to estimate a target $Y$, while being conditionally independent of a distractor $Z$ given $Y$. Both $Z$ and $Y$ are assumed to be continuous-valued but relatively low dimensional, whereas $X$ and its features may be complex and high dimensional. Relevant settings include domain-invariant learning, fairness, and causal learning. The procedure requires just a single ridge regression from $Y$ to kernelized features of $Z$, which can be done in advance. It is then only necessary to enforce independence of $\varphi(X)$ from residuals of this regression, which is possible with attractive estimation properties and consistency guarantees. By contrast, earlier measures of conditional feature dependence require multiple regressions for each step of feature learning, resulting in more severe bias and variance, and greater computational cost. When sufficiently rich features are used, we establish that CIRCE is zero if and only if $\varphi(X) \perp \!\!\! \perp Z \mid Y$. In experiments, we show superior performance to previous methods on challenging benchmarks, including learning conditionally invariant image features.

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