Linear Non-Gaussian Component Analysis Via Maximum Likelihood

Maximum Likelihood Principal Component Analysis

PETER D. WENTZELL, DARREN T. ANDREWS, DAVID C. HAMILTON, KLAAS FABER AND BRUCE R. KOWALSKI 1 Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4J3, Canada 2 Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada 3 Center for Process Analytical Chemistry, University of Washingto...

Independent Component Analysis via Nonparametric Maximum Likelihood Estimation By

Independent Component Analysis (ICA) models are very popular semiparametric models in which we observe independent copies of a random vector X =AS, where A is a non-singular matrix and S has independent components. We propose a new way of estimating the unmixing matrix W = A−1 and the marginal distributions of the components of S using nonparametric maximum likelihood. Specifically, we study th...

Parameter Estimation via Gaussian Processes and Maximum Likelihood Estimation

Computer models usually have a variety of parameters that can (and need to) be tuned so that the model better reflects reality. This problem is called calibration and is an inverse problem. We assume that we have a set of observed responses to given inputs in a physical system and a computer model that depends on parameters that models the physical system being studied. It is often the case tha...

Fast Spatial Gaussian Process Maximum Likelihood Estimation via Skeletonization Factorizations

Maximum likelihood estimation for parameter-fitting given observations from a Gaussian process in space is a computationally-demanding task that restricts the use of such methods to moderately-sized datasets. We present a framework for unstructured observations in two spatial dimensions that allows for evaluation of the log-likelihood and its gradient (i.e., the score equations) in Õpn3{2q time...

Maximum-likelihood blind deconvolution: non-white Bernoulli-Gaussian case