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Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

Systems and Control · Electrical Eng. & Systems 2024-09-09 Kristian Løvland , Bjarne Grimstad , Lars Struen Imsland

In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…

Optimization and Control · Mathematics 2021-09-21 Lam M. Nguyen , Quoc Tran-Dinh , Dzung T. Phan , Phuong Ha Nguyen , Marten van Dijk

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate…

Machine Learning · Computer Science 2025-11-03 Yuchen Liang , Renxiang Huang , Lifeng Lai , Ness Shroff , Yingbin Liang

This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation…

Statistics Theory · Mathematics 2011-12-25 Winston Wei Dou , David Pollard , Harrison H. Zhou

Learning discrete distributions from i.i.d. samples is a well-understood problem. However, advances in generative machine learning prompt an interesting new, non-i.i.d. setting: after receiving a certain number of samples, an estimated…

Information Theory · Computer Science 2026-01-06 Millen Kanabar , Michael Gastpar

In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…

Statistics Theory · Mathematics 2025-10-07 Henrik Kaiser

We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…

Statistics Theory · Mathematics 2025-09-03 Max Berger , Hajo Holzmann

We study the problem of asymptotic consensus as it occurs in a wide range of applications in both man-made and natural systems. In particular, we study systems with directed communication graphs that may change over time. We recently…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-11-09 Bernadette Charron-Bost , Matthias Függer , Thomas Nowak

We study convergence rates of the classic proximal bundle method for a variety of nonsmooth convex optimization problems. We show that, without any modification, this algorithm adapts to converge faster in the presence of smoothness or a…

Optimization and Control · Mathematics 2023-05-03 Mateo Díaz , Benjamin Grimmer

We analyze the convergence rates of stochastic gradient algorithms for smooth finite-sum minimax optimization and show that, for many such algorithms, sampling the data points without replacement leads to faster convergence compared to…

Optimization and Control · Mathematics 2022-10-11 Aniket Das , Bernhard Schölkopf , Michael Muehlebach

A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…

Statistics Theory · Mathematics 2017-12-21 Ben Berckmoes , Geert Molenberghs

We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…

Machine Learning · Computer Science 2018-07-10 Alkis Gotovos , Hamed Hassani , Andreas Krause , Stefanie Jegelka

This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…

Machine Learning · Statistics 2025-06-25 Galen Reeves , Henry D. Pfister

Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. Previous known results show that for any $N$-dimensional subspace of the space of continuous functions it is…

Functional Analysis · Mathematics 2024-05-08 E. D. Kosov , V. N. Temlyakov

In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed smoothness parameter not larger than $1/2$. Our focus will…

Functional Analysis · Mathematics 2021-11-01 Vladimir Temlyakov , Tino Ullrich

Stochastic variance reduced methods have gained a lot of interest recently for empirical risk minimization due to its appealing run time complexity. When the data size is large and disjointly stored on different machines, it becomes…

Machine Learning · Computer Science 2020-08-26 Shicong Cen , Huishuai Zhang , Yuejie Chi , Wei Chen , Tie-Yan Liu

We extend the Approximate-Proximal Point (aProx) family of model-based methods for solving stochastic convex optimization problems, including stochastic subgradient, proximal point, and bundle methods, to the minibatch and accelerated…

Optimization and Control · Mathematics 2021-01-08 Karan Chadha , Gary Cheng , John C. Duchi

Consider a number of workers running SGD independently on the same pool of data and averaging the models every once in a while -- a common but not well understood practice. We study model averaging as a variance-reducing mechanism and…

Machine Learning · Statistics 2016-06-24 Jian Zhang , Christopher De Sa , Ioannis Mitliagkas , Christopher Ré

This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models…

Probability · Mathematics 2015-03-05 Ester Mariucci