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: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.
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: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:2504.05161v2 Announce Type: replace-cross Abstract: Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key...
arXiv:2411. 12438v2 Announce Type: replace-cross Abstract: We develop a new approach for clustering non-spherical (i.
arXiv:2609.16622v1 Announce Type: cross Abstract: Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated sub...
arXiv:2607. 14304v1 Announce Type: cross Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold.
arXiv:2609.00773v1 Announce Type: cross Abstract: High-dimensional clustering is challenging when component distributions are both heavy-tailed and directionally asymmetric. We propose a deep skew-$t...
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...