arXiv Statistics ML
Beyond Maximum Likelihood: Variational Inequality Estimation for Generalized Linear Models
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arXiv Machine Learning
Sep 14
A Generalized Tangent Approximation based Variational Inference Framework for Strongly Super-Gaussian Likelihoods
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.
arXiv Machine Learning
Sep 23
Error Bounds for Statistical Estimators in BTL Model with Parametric Multivariate Utility Functions
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 Machine Learning
Aug 5
Variational Approximated Restricted Maximum Likelihood Estimation for Spatial Data
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.
arXiv Machine Learning
Oct 7
Extending Pathwise Gradients to Discrete Random Variables via Finite-Order Relaxation
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...
arXiv Statistics ML
Sep 7
On the Asymptotic Inadmissibility of Double Machine Learning Estimators Under Structure-Agnostic Models
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.
arXiv Machine Learning
Jul 9
Statistical inverse learning and $\ell^1$-regularization
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.