Generalized Balancing Weights via Deep Neural Networks

TL;DR

This paper introduces Neural Balancing Weights (NBW), a deep learning method for estimating causal effects by balancing covariate distributions through density ratio estimation using variational $f$-divergences, applicable to complex interventions.

Contribution

It proposes a novel deep neural network approach for estimating balancing weights via variational $f$-divergences, handling multidimensional data and arbitrary interventions.

Findings

Effective estimation of causal effects with complex interventions.

Improved generalization and balance checking methods for weights.

Discussion on sample size requirements and curse of dimensionality.

Abstract

Estimating causal effects from observational data is a central problem in many domains. A general approach is to balance covariates with weights such that the distribution of the data mimics randomization. We present generalized balancing weights, Neural Balancing Weights (NBW), to estimate the causal effects of an arbitrary mixture of discrete and continuous interventions. The weights were obtained through direct estimation of the density ratio between the source and balanced distributions by optimizing the variational representation of $f$-divergence. For this, we selected $\alpha$-divergence as it presents efficient optimization because it has an estimator whose sample complexity is independent of its ground truth value and unbiased mini-batch gradients; moreover, it is advantageous for the vanishing-gradient problem. In addition, we provide the following two methods for estimating the balancing weights: improving the generalization performance of the balancing weights and checking the balance of the distribution changed by the weights. Finally, we discuss the sample size requirements for the weights as a general problem of a curse of dimensionality when balancing multidimensional data. Our study provides a basic approach for estimating the balancing weights of multidimensional data using variational $f$-divergences.