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We examine the last-iterate convergence rate of Bregman proximal methods - from mirror descent to mirror-prox and its optimistic variants - as a function of the local geometry induced by the prox-mapping defining the method. For generality,…

Optimization and Control · Mathematics 2024-12-13 Waïss Azizian , Franck Iutzeler , Jérôme Malick , Panayotis Mertikopoulos

Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably…

Statistics Theory · Mathematics 2007-06-13 James O. Berger , William Strawderman , Dejun Tang

It is a relatively well-known fact that in problems of Bayesian model selection improper priors should, in general, be avoided. In this paper we derive a proper and parsimonious uniform prior for regression coefficients. We then use this…

Methodology · Statistics 2013-08-07 H. R. N. van Erp , R. O. Linger , P. H. A. J. M. van Gelder

Attributing an observed outcome to its root cause is a central task in domains ranging from medical diagnosis to engineering fault diagnosis. Existing approaches either equate the root cause with a root node of the causal graph, as in…

Methodology · Statistics 2026-05-13 Zitong Lu , Zhi Geng , Wei Li , Min Xie

We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…

Probability · Mathematics 2026-03-03 Kun Yin

Most work in algorithmic fairness to date has focused on discrete outcomes, such as deciding whether to grant someone a loan or not. In these classification settings, group fairness criteria such as independence, separation and sufficiency…

Machine Learning · Computer Science 2020-02-18 Daniel Steinberg , Alistair Reid , Simon O'Callaghan , Finnian Lattimore , Lachlan McCalman , Tiberio Caetano

In this article, we study the rate of convergence of prices when a model is approximated by some simplified model. We also provide a method how explicit error formula for more general options can be obtained if such formula is available for…

Probability · Mathematics 2013-01-08 Lauri Viitasaari

Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty…

Methodology · Statistics 2022-02-18 Tommaso Rigon , Emanuele Aliverti

Reward modelling from preference data is a crucial step in aligning large language models (LLMs) with human values, requiring robust generalisation to novel prompt-response pairs. In this work, we propose to frame this problem in a causal…

Artificial Intelligence · Computer Science 2026-05-12 Katarzyna Kobalczyk , Mihaela van der Schaar

A fundamental challenge in causal inference with observational data is correct specification of a causal model. When there is model uncertainty, analysts may seek to use estimates from multiple candidate models that rely on distinct, and…

Methodology · Statistics 2026-03-03 Rohit Bhattacharya , Ina Ocelli , Ted Westling

We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The a posteriori error estimates are…

Numerical Analysis · Mathematics 2022-04-25 Sören Bartels , Alex Kaltenbach

We consider reinforcement learning in an environment modeled by an episodic, finite, stage-dependent Markov decision process of horizon $H$ with $S$ states, and $A$ actions. The performance of an agent is measured by the regret after…

Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into…

Computer Vision and Pattern Recognition · Computer Science 2023-08-30 Berthy T. Feng , Jamie Smith , Michael Rubinstein , Huiwen Chang , Katherine L. Bouman , William T. Freeman

Nowadays model uncertainty has become one of the most important problems in both academia and industry. In this paper, we mainly consider the scenario in which we have a common model set used for model averaging instead of selecting a…

Machine Learning · Computer Science 2023-01-26 Yimin Huang , Weiran Huang , Liang Li , Zhenguo Li

We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…

Optimization and Control · Mathematics 2017-10-19 Achintya Kundu , Francis Bach , Chiranjib Bhattacharyya

A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…

Numerical Analysis · Mathematics 2024-06-12 Sören Bartels , Alex Kaltenbach

Inference-time reward alignment asks how to turn a pre-trained diffusion model with base law $p$ into a sampler that favors a reward $r$ while remaining close to $p$. Since there is no canonical distributional distance for this closeness…

Machine Learning · Computer Science 2026-05-13 Ankur Moitra , Andrej Risteski , Dhruv Rohatgi

Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…

Econometrics · Economics 2020-08-04 Jushan Bai , Serena Ng

In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.

Statistics Theory · Mathematics 2019-09-24 Emanuele Dolera , Edoardo Mainini

The penalized profile sampler for semiparametric inference is an extension of the profile sampler method (Lee, Kosorok and Fine, 2005) obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior…

Statistics Theory · Mathematics 2007-06-13 Guang Cheng , Michael R. Kosorok