arXiv Statistics ML
Characterizing Heterogeneous Rates in Finite Mixture Estimation via Partial Optimal Transport
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arXiv Machine Learning
Oct 3
Polylogarithmic Sparsity of Randomly Reweighted NPMLEs for Gaussian Mixtures
arXiv:2610. 01088v1 Announce Type: cross Abstract: The nonparametric maximum likelihood estimator (NPMLE) of a Gaussian location mixture maximizes the likelihood over the infinite-dimensional space of mixing distributions.
arXiv Machine Learning
Jun 24
Mixtures Closest to a Given Measure: A Semidefinite Programming Approach
arXiv:2509. 22879v2 Announce Type: replace-cross Abstract: Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions.
arXiv Machine Learning
Jun 9
Dendrograms of Mixing Measures for Softmax-Gated Gaussian Mixture of Experts: Consistency Without Model Sweeps
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.
arXiv Machine Learning
Oct 22
Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance
The paper studies estimation of univariate Gaussian mixture densities using the nonparametric maximum likelihood estimator (NPMLE). It proves that the unconstrained NPMLE attains the minimax optimal rate ∑(n)/n in squared Hellinger distance when the true mixing measure is sub‑Gaussian, and that a compactly constrained NPMLE achieves a slightly faster rate ∑(n)/(n∑∑(n)). The analysis relies on sharp bounds for local Hellinger bracketing entropy and introduces new bounds on the L² bracketing entropy of bounded‑degree polynomial balls.
arXiv Machine Learning
Sep 1
Model Selection and Parameter Estimation for Multidimensional Gaussian Mixture Models with a Common Covariance Matrix
arXiv:2603.19657v2 Announce Type: replace-cross Abstract: We study model-order selection and component-mean estimation for multidimensional Gaussian mixture models with a known common covariance matr...
arXiv Machine Learning
Sep 1
Model Selection and Parameter Estimation of One-Dimensional Gaussian Mixture Models
arXiv:2404.12613v4 Announce Type: replace-cross Abstract: In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the m...