The paper introduces a new variational inference framework that uses tangent transformations to handle strongly super‑Gaussian likelihoods across a wide range of probability models. By constructing tangent minorants of the log‑likelihood through convex duality, the method achieves conjugacy with Gaussian priors, enabling tractable inference where traditional approaches struggle. The authors provide algorithmic convergence guarantees and near‑parametric risk bounds, and demonstrate superior scalability and accuracy on both simulated and real‑world datasets compared to existing variational algorithms.
By Somjit Roy, Pritam Dey, Debdeep Pati, Bani K. Mallick
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.
By Yicheng Li, Huifu Xu
arXiv:2604. 07635v2 Announce Type: replace-cross Abstract: This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures.
By Debjoy Thakur
arXiv:2610.07786v1 Announce Type: new
Abstract: Pathwise gradients are preferred for continuous random variables because they are unbiased, low variance, and work with a single sample. For discrete v...
By Donghan He, Luhuan Wu
The paper investigates Double Machine Learning (DML) estimators under structure‑agnostic (SA) models, which assume the data‑generating law lies within a neighborhood of fixed machine‑learning estimates. It shows that for two of three studied functionals—the quadratic functional in the Gaussian sequence model and the quadratic density integral functional—the DML estimators are asymptotically inadmissible, being dominated by second‑order empirical higher‑order influence function (HOIF) estimators. For the third functional, the expected conditional covariance, both DML and HOIF estimators remain minimax but neither dominates the other.
By Lin Liu, Rajarshi Mukherjee, James M Robins
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.
By Abhishake Rastogi, Tatiana A. Bubba, Tapio Helin, Luca Ratti
arXiv:2607. 03871v1 Announce Type: new Abstract: Minimum maximum mean discrepancy (MMD) estimation has emerged as a robust and likelihood-free alternative to maximum likelihood estimation for parameter estimation.
By Sophia Seulkee Kang, Louis Sharrock, Xiaoyuan Cheng, Fran\c{c}ois-Xavier Briol, Zonghao Chen
The paper introduces a generalized score matching objective for parameter estimation on convex subsets of ρ^d, derived from Minimum Probability Flow learning. It shows that this objective is a proper local scoring rule of second order, ensuring recovery of the true density when minimized, and proves convexity and consistency for exponential family models under standard conditions. Experiments demonstrate the method’s effectiveness on constrained domains where the partition function is intractable, including a generative modeling use‑case.
By Nishanth Shetty, Saisuchith Mahajan, Chandra Sekhar Seelamantula
The paper develops a rigorous framework for computing the Normalized Maximum Likelihood (NML) codelength for regular path‑differentiable Lipschitz (PDL) estimators, which include non‑smooth models such as Lasso and Sparse SVMs. By leveraging geometric measure theory and a novel Propose‑and‑Project Metropolis‑Hastings sampler, the authors provide a method to exactly evaluate the stochastic complexity for these non‑smooth estimators and demonstrate its scalability to high‑dimensional settings. The study shows that the exact NML criterion can match cross‑validation performance while being more data‑efficient, offering a theoretically grounded alternative for model selection in modern machine learning.
By Trenton Lau, Gary P. T. Choi
arXiv:2605.07107v4 Announce Type: replace-cross
Abstract: It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and con...
By Leighton P. Barnes, Alex Dytso
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.
By Stefano Favaro, Sandra Fortini, Soham Jana
The paper introduces a method to incorporate linear inequality constraints—such as nonnegativity, monotonicity, and no‑arbitrage—into Gaussian process solvers for linear partial differential equations. By proving that conditioning a Gaussian process jointly on equality observations and a finite‑dimensional inequality event is equivalent to sequential conditioning, the authors obtain a non‑Gaussian but computable posterior that respects both PDE physics and inequality constraints. Experiments on Poisson problems, option‑price surfaces, and air‑quality data show substantial error reductions and improved adherence to constraints when the new method is applied.
By Boyuan Deng, Kshitiz Upadhyay, Michael Shields