Marginal independence enables identifiability of components and mixing matrix in unlabeled mixtures, with a PM-MMD estimator shown to converge uniformly under approximate independence.
Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders
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abstract
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.
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2026 1verdicts
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Identifiability and Estimation for Unlabeled Finite Mixtures under Marginal Independence
Marginal independence enables identifiability of components and mixing matrix in unlabeled mixtures, with a PM-MMD estimator shown to converge uniformly under approximate independence.