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: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: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.
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: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: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...
arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.
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: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: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:2606. 02515v1 Announce Type: new Abstract: Optimal transport (OT) provides a principled framework for mapping between probability distributions.
arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.