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

ArXi:2603.19657v1 Announce Type: cross In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower bound on the critical sample complexity required for reliable model selection. specifically, we show that distinguishing a $k$-component mixture from a simpler model necessitates a sample size scaling of $\Omega(\Delta^{-(4k-4.