Learning Diagonal Gaussian Mixture Models and Incomplete Tensor Decompositions

Learning Negative Mixture Models by Tensor Decompositions

This work considers the problem of estimating the parameters of negative mixture models, i.e. mixture models that possibly involve negative weights. The contributions of this paper are as follows. (i) We show that every rational probability distributions on strings, a representation which occurs naturally in spectral learning, can be computed by a negative mixture of at most two probabilistic a...

Gaussian Mixtures and Tensor Decompositions

1 Tensors Tensors are the generalizations of vectors v ∈ R and matrices M ∈ Rm×n. These are respectively 1-tensors and 2-tensors, which we can represent using oneand two-dimensional arrays of real numbers. Although there are more general definitions, for our purposes, a p-th order tensor (or a p-tensor) is an object that can be represented using a p-dimensional array of real numbers. Technicall...

Tensor decompositions for learning latent variable models

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models—including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation—which exploits a certain tensor structure in their low-order observable moments (typically, of secondand third-order). Specifically, parameter estimation is reduced to the...

Efficient Greedy Learning of Gaussian Mixture Models

This article concerns the greedy learning of gaussian mixtures. In the greedy approach, mixture components are inserted into the mixture one after the other. We propose a heuristic for searching for the optimal component to insert. In a randomized manner, a set of candidate new components is generated. For each of these candidates, we find the locally optimal new component and insert it into th...

Efficient greedy learning of Gaussian mixture models