5 research outputs found
Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders
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.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty
in Artificial Intelligence (UAI2013
Nonparametric Estimation of Multi-View Latent Variable Models
Spectral methods have greatly advanced the estimation of latent variable
models, generating a sequence of novel and efficient algorithms with strong
theoretical guarantees. However, current spectral algorithms are largely
restricted to mixtures of discrete or Gaussian distributions. In this paper, we
propose a kernel method for learning multi-view latent variable models,
allowing each mixture component to be nonparametric. The key idea of the method
is to embed the joint distribution of a multi-view latent variable into a
reproducing kernel Hilbert space, and then the latent parameters are recovered
using a robust tensor power method. We establish that the sample complexity for
the proposed method is quadratic in the number of latent components and is a
low order polynomial in the other relevant parameters. Thus, our non-parametric
tensor approach to learning latent variable models enjoys good sample and
computational efficiencies. Moreover, the non-parametric tensor power method
compares favorably to EM algorithm and other existing spectral algorithms in
our experiments