跳转至

使用变分推断联合发现因果结构与聚类

文章背景与核心概要

在许多复杂的现实世界领域（如脑成像和气候建模）中，研究人员通常需要理解变量组之间的相互作用，而不是孤立的单个变量。然而，传统的因果发现方法往往假设变量的分组情况是先验已知的，这在实际应用中很难满足。实际上，变量的聚类群组以及它们之间的因果关系通常都是潜在且未知的。

为了解决这一难题，本文提出了一种基于变分推断（Variational Inference）的新颖方法，能够同时推断潜在的变量聚类和底层的因果结构。该方法分别利用分类分布（Categorical distribution）和伯努利分布（Bernoulli distribution）对聚类和图结构的近似后验进行建模，并推导出了用于学习变分参数和模型参数的变分下界与估计技术。在合成数据集和真实数据集上的实验表明，该方法在联合聚类与因果发现任务中展现出了强大的性能。

摘要 (Summary)

This paper introduces a novel variational inference approach to simultaneously discover latent groups (clusters) of variables and their underlying causal structures. Traditional methods usually assume that variable groupings are known a priori, which is rarely true in domains like brain imaging or climate modeling. By modeling the approximate posterior over clusters and graph structures using categorical and Bernoulli distributions respectively, the proposed method successfully infers both components and demonstrates strong performance on both synthetic and real-world datasets.

本文引入了一种新颖的变分推断方法，能够同时发现变量的潜在群组（聚类）及其底层因果结构。传统方法通常假设变量分组是先验已知的，但这在脑成像或气候建模等领域中几乎是不成立的。通过分别使用分类分布和伯努利分布对聚类和图结构的近似后验进行建模，该方法成功推断出了这两个组成部分，并在合成数据集和真实数据集上展示了出色的性能。

元数据 (Metadata)

作者 (Authors)

  • Avni Rajpal
  • Anubhav Kumar
  • Rishabh Karnad
  • Mohammad Emtiyaz Khan
  • P.K. Srijith

摘要详情 (Abstract)

Causal discovery aims to understand the relationships between individual random variables. In many applications, such as brain imaging and climate modeling, it is more meaningful to consider interactions among groups of variables. Existing methods assume that knowledge of such groups or clusters is explicitly available when modeling interactions. However, in practice, these clusters as well as the causal relationships among them, are latent.

因果发现旨在理解各个随机变量之间的关系。在许多应用中，例如脑成像和气候建模，考虑变量组之间的相互作用更有意义。现有方法在对相互作用进行建模时，通常假设这些群组或聚类的知识是显式可用的。然而在实践中，这些聚类以及它们之间的因果关系都是潜在的。

In this paper, we present a novel approach based on variational inference to simultaneously infer both the latent clusters and causal structures. We learn an approximate posterior over clusters and graph-structure by considering variational distributions based on categorical and Bernoulli models respectively. We derive variational lower bounds and estimation techniques to learn variational and model parameters. The effectiveness of our proposed methods for cluster and causal discovery are demonstrated on both synthetic and real data sets.

在本文中，我们提出了一种基于变分推断的新方法，用于同时推断潜在聚类和因果结构。通过分别考虑基于分类模型和伯努利模型的变分分布，我们学习了聚类和图结构的近似后验。我们推导了变分下界和估计技术，以学习变分参数和模型参数。我们在合成数据集和真实数据集上验证了我们提出的聚类和因果发现方法的有效性。