# gaussian mixture models

• Christopher Tosh and Sanjoy Dasgupta

### Lower Bounds for the Gibbs Sampler over Mixtures of Gaussians (pdf)

The mixing time of a Markov chain is the minimum time $t$ necessary for the total variation distance between the distribution of the Markov chain's current state $X_t$ and its stationary distribution to fall below some $\epsilon > 0$. In this paper, we present lower bounds for the mixing time of the Gibbs sampler over Gaussian mixture models with Dirichlet priors.

• Uri Shalit and Gal Chechik

### Coordinate-descent for learning orthogonal matrices through Givens rotations (pdf)

Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we propose a framework for optimizing orthogonal matrices, that is the parallel of coordinate-descent in Euclidean spaces. It is based on {\em Givens-rotations

2013-2014 ICML | International Conference on Machine Learning