Semi-definite approximation for Gaussian maximum likelihood function
Chi Bach Pham
A parser that help solve the maximum likelihood estimation with minimal amount of syntax
This project aims to develop a semi-definite approximation for the likelihood
function of multivariate Gaussian distribution. Previous studies on this topic use
specialized methods that are hard to replicate for people without some background
in the field. This project created a good approximation of the likelihood function so
that the Gaussian maximum likelihood estimation problem can be solved by a
conventional convex optimization solver. This project created a method for solving the Gaussian maximum likelihood
estimation problem using an off-the-shelf convex optimization solver. To do so,
we must devise a semi-definite programming approximation of the likelihood function. Several ways of approximating the likelihood function were devised during
the project and the result was a combination of two of these approaches. Then
numerical experimentation was done to balance the estimation parameters. The
outcome of this project is a parser that encapsulated all these complex approximation processes into a user-friendly python package for use concurrently with
CVXPY, a python-based solver.
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This project created a method for solving the Gaussian maximum likelihood estimation problem using an off-the-shelf convex optimization solver. To do so, we must devise a semi-definite programming approximation of the likelihood function. Several ways of approximating the likelihood function were devised during the project and the result was a combination of two of these approaches. Then numerical experimentation was done to balance the estimation parameters. The outcome of this project is a parser that encapsulated all these complex approximation processes into a user-friendly python package for use concurrently with CVXPY, a python-based solver.
