Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders
This work addresses the problem of mixture identification and confounder inference for researchers in statistics and causal inference, presenting a novel kernel-based approach.
The authors tackled the problem of identifying finite mixtures of nonparametric product distributions by proposing a kernel method based on Hilbert space embeddings, which allows recovery of mixture components through data clustering. This method was applied to identify finite confounders in causal inference.
We propose a kernel method to identify finite mixtures of nonparametric product distributions. It is based on a Hilbert space embedding of the joint distribution. The rank of the constructed tensor is equal to the number of mixture components. We present an algorithm to recover the components by partitioning the data points into clusters such that the variables are jointly conditionally independent given the cluster. This method can be used to identify finite confounders.