Causal mediation analysis (CMA) is a powerful method to dissect the total
effect of a treatment into direct and mediated effects within the potential
outcome framework. This is important in many scientific applications to
identify the underlying mechanisms of a treatment effect. However, in many
scientific applications the mediator is unobserved, but there may exist related
measurements. For example, we may want to identify how changes in brain
activity or structure mediate an antidepressant's effect on behavior, but we
may only have access to electrophysiological or imaging brain measurements. To
date, most CMA methods assume that the mediator is one-dimensional and
observable, which oversimplifies such real-world scenarios. To overcome this
limitation, we introduce a CMA framework that can handle complex and indirectly
observed mediators based on the identifiable variational autoencoder (iVAE)
architecture. We prove that the true joint distribution over observed and
latent variables is identifiable with the proposed method. Additionally, our
framework captures a disentangled representation of the indirectly observed
mediator and yields accurate estimation of the direct and mediated effects in
synthetic and semi-synthetic experiments, providing evidence of its potential
utility in real-world applications.

提出了一种基于可识别 VAE 体系结构的 CMA 框架，可以处理复杂的和间接观测到的中介变量，并在合成和半合成实验中提供准确的效应估计，为实际应用提供证据。

多维和间接观察中介变量的因果中介分析

Causal Mediation Analysis with Multi-dimensional and Indirectly Observed  Mediators

The recently proposed identifiable variational autoencoder (iVAE) framework
provides a promising approach for learning latent independent components (ICs).
iVAEs use auxiliary covariates to build an identifiable generation structure
from covariates to ICs to observations, and the posterior network approximates
ICs given observations and covariates. Though the identifiability is appealing,
we show that iVAEs could have local minimum solution where observations and the
approximated ICs are independent given covariates.-a phenomenon we referred to
as the posterior collapse problem of iVAEs. To overcome this problem, we
develop a new approach, covariate-informed iVAE (CI-iVAE) by considering a
mixture of encoder and posterior distributions in the objective function. In
doing so, the objective function prevents the posterior collapse, resulting
latent representations that contain more information of the observations.
Furthermore, CI-iVAEs extend the original iVAE objective function to a larger
class and finds the optimal one among them, thus having tighter evidence lower
bounds than the original iVAE. Experiments on simulation datasets, EMNIST,
Fashion-MNIST, and a large-scale brain imaging dataset demonstrate the
effectiveness of our new method.

研究了可识别变分自编码器，在生成结构中使用辅助协变量来从协变量到观测值和独立组件（IC）中学习潜在的独立组件，并开发了一种称为 CI-iVAE 的新方法来解决后退化坍塌问题。