Empirical Bayes (EB) estimators can match the first-order asymptotic risk of maximum likelihood (ML) while behaving very differently at second order: recent excess mean squared error (XMSE) analysis shows that kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter. This paper turns that diagnostic into a design principle.
arXiv:2606. 26975v1 Announce Type: cross Abstract: Empirical Bayes (EB) estimators can match the first-order asymptotic risk of maximum likelihood (ML) while behaving very differently at second order: recent excess mean squared error (XMSE) analysis shows that kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter.
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.
arXiv:2601. 07094v2 Announce Type: replace-cross Abstract: Bayesian optimization (BO) iteratively fits a Gaussian process (GP) surrogate to accumulated evaluations and selects new queries via an acquisition function.
The paper introduces a neighboring early‑stopping rule for adaptive regularization in kernel ridge regression with random features (KRR‑RF). By using a uniform grid in inverse regularization and comparing only adjacent estimators, the method reduces discrepancy checks and can be computed directly in the random‑feature space without forming the full kernel Gram matrix. Under standard source and capacity assumptions, the selected estimator achieves the oracle polynomial learning rate up to logarithmic factors, enabling regularization selection without prior knowledge of smoothness or capacity exponents.
arXiv:2609.06873v1 Announce Type: cross Abstract: We study how a limited labeling budget should be allocated to minimize multiclass zero-one classification risk. We consider parametric classification...
arXiv:2602. 13362v2 Announce Type: replace-cross Abstract: A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty.
arXiv:2606. 25169v1 Announce Type: cross Abstract: Sampling from an unnormalized target by reversing an Ornstein--Uhlenbeck diffusion requires the score of each noise-perturbed marginal.
arXiv:2609.26843v1 Announce Type: cross Abstract: Residual-based adaptive GMsFEM for high-contrast elliptic problems repeatedly evaluates local weighted $H^{-1}$ indicators on every coarse neighborho...
arXiv:2609.15785v1 Announce Type: cross Abstract: We study density ratio estimation and importance-weighted regression under target shift with continuous outputs. Under target shift, the conditional...
The paper investigates preference elicitation under the Bradley‑Terry‑Luce model, focusing on estimating an unknown partworth vector from pairwise queries that satisfy a joint identifiability condition. It derives minimax lower bounds and shows that the canonical maximum likelihood estimator (MLE) exists, is unique, and achieves near‑optimal error rates once the sample size exceeds a design‑dependent threshold, without requiring compactness constraints or external regularizers. The analysis decomposes the estimation error into a linear stochastic term, a second‑order bias, and a higher‑order remainder, providing a unified non‑asymptotic theory for parametric utility elicitation.
arXiv:2606. 25169v2 Announce Type: replace-cross Abstract: Sampling from an unnormalized target by reversing an Ornstein-Uhlenbeck diffusion requires the score of each noise-perturbed marginal.
arXiv:2607. 06879v1 Announce Type: new Abstract: Best-arm identification is a canonical model for data-driven decision-making, but in many applications each reward observation is costly.