Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions

Shunsuke Horii
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:955-963, 2021.

Abstract

In estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the goal is to estimate the causal effect, it is not necessary to fix a single causal structure or probability distributions. In this paper, we first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating a single model. This idea is also known as Bayesian model averaging. Although the Bayesian model averaging is optimal, as the number of candidate models increases, the weighting calculations become computationally hard. We develop an approximation to the Bayes optimal estimator by using Gaussian scale mixture distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-horii21a, title = { Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions }, author = {Horii, Shunsuke}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {955--963}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/horii21a/horii21a.pdf}, url = {https://proceedings.mlr.press/v130/horii21a.html}, abstract = { In estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the goal is to estimate the causal effect, it is not necessary to fix a single causal structure or probability distributions. In this paper, we first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating a single model. This idea is also known as Bayesian model averaging. Although the Bayesian model averaging is optimal, as the number of candidate models increases, the weighting calculations become computationally hard. We develop an approximation to the Bayes optimal estimator by using Gaussian scale mixture distributions. } }
Endnote
%0 Conference Paper %T Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions %A Shunsuke Horii %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-horii21a %I PMLR %P 955--963 %U https://proceedings.mlr.press/v130/horii21a.html %V 130 %X In estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the goal is to estimate the causal effect, it is not necessary to fix a single causal structure or probability distributions. In this paper, we first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating a single model. This idea is also known as Bayesian model averaging. Although the Bayesian model averaging is optimal, as the number of candidate models increases, the weighting calculations become computationally hard. We develop an approximation to the Bayes optimal estimator by using Gaussian scale mixture distributions.
APA
Horii, S.. (2021). Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:955-963 Available from https://proceedings.mlr.press/v130/horii21a.html.

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