arXiv:2409. 09903v3 Announce Type: replace-cross Abstract: Softmax Mixture Models (SMMs) are discrete $K$-component mixture models for the probabilities of selecting one of $p$ candidate feature vectors $X_1,\ldots,X_p\in\mathbb{R}^L$ in heterogeneous populations and are widely used in econometrics and scientific applications.
arXiv:2610. 07551v1 Announce Type: cross Abstract: Learning Gaussian mixture models (GMMs) using the Expectation-Maximization (EM) algorithm and its gradient-based variants is a fundamental problem in machine learning.
arXiv:2506. 06584v2 Announce Type: replace Abstract: Learning Gaussian Mixture Models (GMMs) is a fundamental problem in statistics and machine learning, with the Expectation-Maximization (EM) algorithm and its popular variant gradient EM being arguably the most widely used algorithms in practice.
Learning Gaussian mixture models (GMMs) using the Expectation-Maximization (EM) algorithm and its gradient-based variants is a fundamental problem in machine learning. It is known that randomly initia...
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.
The paper develops a nonparametric empirical Bayes approach for estimating sums of functions of observable and unobservable variables in Poisson mixture models, using regular and coarsened minimum‑distance estimation of the mixing distribution. It proves large‑sample guarantees that the plug‑in estimates converge to the oracle Bayes estimate, achieving nearly parametric rates when the mixing distribution has finite support. Finite‑sample analyses are provided for two specific sums—total intensity below a threshold and the number of units exceeding latent intensity—along with minimax regret bounds and conditions for bounded regret.
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: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:2507.20459v2 Announce Type: replace-cross Abstract: With direct computation of moments through order $L$ in $d$ dimensions, standard method of moments (MM) incurs $\Omega(d^L)$ computation and...
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:2607. 22889v1 Announce Type: new Abstract: Learning the natural parameters $z \in \mathbb{R}^n$ of discrete distributions $\mu_z$ from independent samples constrained to a subset $S \subseteq \{0,1\}^n$ is a foundational challenge in high-dimensional statistics.
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
arXiv:2610.27265v1 Announce Type: new Abstract: Over-fitted Gaussian mixtures can contain many parameter configurations with nearly the same density, making the order of density cancellation central...