3 papers
stat.ML2025
Learning Overspecified Gaussian Mixtures Exponentially Fast with the EM Algorithm
Zhenisbek Assylbekov, Alan Legg, Artur Pak
We investigate the convergence properties of the EM algorithm when applied to overspecified Gaussian mixture models -- that is, when the number of components in the fitted model ex…
math.CV2023
Ellipses and Polynomial-to-Polynomial Mapping of Weighted Szego Projections
Alan R. Legg
We take a look at weighted Szego projections on ellipses and ellipsoids in light of some known results of real and complex potential theory. We show that on planar ellipses there i…
math.CV2016
Mapping Properties of Quadrature Domains in Several Complex Variables
Alan R. Legg
We make use of the Bergman kernel function to study quadrature domains for square-integrable holomorphic functions of several variables. Emphasis is given to generalizing biholomor…