Model Selection and Parameter Estimation of Multi-dimensional Gaussian Mixture Model

Data-Driven Chance-Constrained Optimization based on Gaussian Mixture Models

Riemannian Gradient Descent for Gaussian Mixture Models with unknown diagonal covariances

This paper investigates the numerical resolution of the Beurling-LASSO (BLASSO), a convex optimization framework that promotes sparsity in the space of measures. We consider its application to the estimation of Gaussian mixture models (GMMs) with an unknown number of components and unknown diagonal covariance matrices....

Parameter Estimation in Multidimensional Diffusion Models with Low Regularity Coefficients

This paper studies parameter estimation for discretely observed multidimensional diffusion models with low-regularity coefficients. Since the transition density of such models is typically unavailable in closed form, likelihood-based inference becomes difficult, especially in multidimensional settings. To address this...

Improved Gaussian Mixture Models with Adaptive Toeplitz Inversion using FFT for High-Dimensional Clustering

Asymptotics for Model Selection in Probabilistic Principal Component Analysis

The probabilistic formulation of principal component analysis promises statistically grounded solutions to the problem of selecting the number of principal components. However, developing tractable model selection methods is complicated by the fact that the probabilistic principal component analysis (PPCA) model exhibi...

Gaussian Comparison Theorems for High-Dimensional Posterior Inference

We develop a Gaussian comparison theory for posterior inference in non-Gaussian high-dimensional models. The framework allows for model misspecification and does not require the posterior distribution itself to be approximately Gaussian. Working directly with likelihood processes on separable function spaces, we establ...