Lecture 1 : Tensor Methods in Machine Learning

Figure 1.1: Visualization of Tensors of different orders. gained popularity in parameter estimation for a variety of problems. In this lecture, the focus is on how they may be used in estimating the parameters of Gaussian Mixture Models and Hidden Markov Models. In a Gaussian mixture model, there are k unknown n-dimensional multivariate Gaussian distributions. Samples are generated by first picking one of the k Gaussians, then drawing a sample from that Gaussian distribution. Given samples from the mixture distribution, our goal is to estimate the means and covariance matrices of these underlying Gaussian distributions [GHK15]. That is, given x = (x1, x2, ..., xN ) FX(x) = r ∑