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.
By Hansheng Jiang
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.
By Shayan Hundrieser, Tudor Manole
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...
By Sinho Chewi, Alkis Kalavasis, Anay Mehrotra, Omar Montasser
arXiv:2608. 11162v1 Announce Type: new Abstract: The Naive Bayes (NB) classifier remains a standard choice for categorical data, yet its widely used smoothing rules, such as Laplace, Lidstone, Krichevsky-Trofimov, and the $m$-estimate, all prescribe a fixed smoothing strength that ignores feature cardinality, sample size, and class imbalance, inducing a non-vanishing bias on modern high-cardinality tabular data.
By Nguyen Thai Anh, Truong Viet Vu, Tran Thien Thanh, Vo Nguyen Quoc Bao, Ngo Hoang Tu
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.
By Rohan Chauhan, Ioannis Panageas
The paper introduces a leave‑a‑window‑out estimator for next‑token functionals, such as the surprise probability and test error, in sequences of random variables. By deleting a window of length τ after each index, the estimator generalizes leave‑one‑out and achieves parametric error decay for stationary β‑mixing processes that admit a Marton coupling. The authors provide both upper bounds and a minimax lower bound for the surprise probability, and demonstrate through simulations that their method outperforms traditional baselines on Markov, moving‑average, and autoregressive processes.
By Milind Nakul, Vidya Muthukumar, Ashwin Pananjady