Causal Regularization: On the trade-off between in-sample risk and out-of-sample risk guarantees

Fuente: arXiv
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Auteurs principaux: Kania, Lucas, Wit, Ernst
Format: Preprint
Publié: 2022
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author Kania, Lucas
Wit, Ernst
author_facet Kania, Lucas
Wit, Ernst
contents Invariant prediction uses the prediction stability of causal relationships across different environments to identify causal variables. Conversely, using causal variables gives prediction guarantees even in out-of-sample data settings. In this paper, we investigate the identification of causal-like models from in-sample data that ensure out-of-sample risk guarantees when predicting a target variable from an arbitrary set of covariates. Ordinary least squares minimizes in-sample risk but offers limited out-of-sample guarantees, while causal models optimize out-of-sample guarantees at the expense of in-sample performance. We introduce a form of \textit{causal regularization} to balance these properties. In the population setting, higher regularization yields estimators with greater risk stability, albeit with increased in-sample risk. Empirically, however, there is a further trade-off to consider, as finite in-sample data reduced the ability to correctly identify models with high out-of-sample risk guarantees. We show how in such empirical settings the optimal causal regularizer can be found via cross-validation.
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id arxiv_https___arxiv_org_abs_2205_01593
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publishDate 2022
record_format arxiv
spellingShingle Causal Regularization: On the trade-off between in-sample risk and out-of-sample risk guarantees
Kania, Lucas
Wit, Ernst
Methodology
Invariant prediction uses the prediction stability of causal relationships across different environments to identify causal variables. Conversely, using causal variables gives prediction guarantees even in out-of-sample data settings. In this paper, we investigate the identification of causal-like models from in-sample data that ensure out-of-sample risk guarantees when predicting a target variable from an arbitrary set of covariates. Ordinary least squares minimizes in-sample risk but offers limited out-of-sample guarantees, while causal models optimize out-of-sample guarantees at the expense of in-sample performance. We introduce a form of \textit{causal regularization} to balance these properties. In the population setting, higher regularization yields estimators with greater risk stability, albeit with increased in-sample risk. Empirically, however, there is a further trade-off to consider, as finite in-sample data reduced the ability to correctly identify models with high out-of-sample risk guarantees. We show how in such empirical settings the optimal causal regularizer can be found via cross-validation.
title Causal Regularization: On the trade-off between in-sample risk and out-of-sample risk guarantees
topic Methodology
url https://arxiv.org/abs/2205.01593