English
Related papers

Related papers: Quantifying the information lost in optimal covari…

200 papers

This letter provides an adaptive resampling method. It determines the number of particles to resample so that the Kullback-Leibler distance (KLD) between distribution of particles before resampling and after resampling does not exceed a…

Applications · Statistics 2017-07-31 Tiancheng Li , Shudong Sun , Tariq Pervez Sattar

Group sequential designs enable interim analyses and potential early stopping for efficacy or futility. While these adaptations improve trial efficiency and ethical considerations, they also introduce bias into the adapted analyses. We…

Methodology · Statistics 2025-10-07 G. Caruso , W. F. Rosenberger , P. Mozgunov , N. Flournoy

Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank at most k. This problem has already been solved when…

Quantum Physics · Physics 2026-01-26 Nathaniel Johnston , Chi-Kwong Li

Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational…

Statistics Theory · Mathematics 2023-11-23 Yanjun Han , Philippe Rigollet , George Stepaniants

Generative Flow Networks (GFlowNets) are amortized inference models designed to sample from unnormalized distributions over composable objects, with applications in generative modeling for tasks in fields such as causal discovery, NLP, and…

Machine Learning · Computer Science 2026-04-13 Tiago da Silva , Eliezer de Souza da Silva , Diego Mesquita

This paper addresses the challenge of Toeplitz covariance matrix estimation from partial entries of random quantized samples. To balance trade-offs among the number of samples, the number of entries observed per sample, and the data…

Signal Processing · Electrical Eng. & Systems 2025-09-18 Hongwei Xu , Zai Yang

Many statistical studies are concerned with the analysis of observations organized in a matrix form whose elements are count data. When these observations are assumed to follow a Poisson or a multinomial distribution, it is of interest to…

Statistics Theory · Mathematics 2022-01-04 Jérémie Bigot , Charles Deledalle

This study tackles the efficient estimation of Kullback-Leibler (KL) Divergence in Dirichlet Mixture Models (DMM), crucial for clustering compositional data. Despite the significance of DMMs, obtaining an analytically tractable solution for…

Machine Learning · Statistics 2024-03-20 Samyajoy Pal , Christian Heumann

We prove optimal sparsity oracle inequalities for the estimation of covariance matrix under the Frobenius norm. In particular we explore various sparsity structures on the underlying matrix.

Statistics Theory · Mathematics 2012-05-08 Philippe Rigollet , Alexandre Tsybakov

Many of the recent trajectory optimization algorithms alternate between linear approximation of the system dynamics around the mean trajectory and conservative policy update. One way of constraining the policy change is by bounding the…

Machine Learning · Computer Science 2018-07-03 Riad Akrour , Abbas Abdolmaleki , Hany Abdulsamad , Jan Peters , Gerhard Neumann

We derive a deterministic, non-asymptotic upper bound on the Kullback-Leibler (KL) divergence of the flow-matching distribution approximation. In particular, if the $L_2$ flow-matching loss is bounded by $\epsilon^2 > 0$, then the KL…

Machine Learning · Computer Science 2025-11-10 Maojiang Su , Jerry Yao-Chieh Hu , Sophia Pi , Han Liu

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…

Image and Video Processing · Electrical Eng. & Systems 2022-07-27 Jonathan Monsalve , Juan Ramirez , Iñaki Esnaola , Henry Arguello

Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…

Information Theory · Computer Science 2015-03-13 François Bavaud

Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the…

Statistics Theory · Mathematics 2016-06-30 Andrew J. Majda , Xin T. Tong

Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

Methodology · Statistics 2023-01-25 Anupam Kundu , Mohsen Pourahmadi

The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…

Statistics Theory · Mathematics 2021-06-08 Rohit Agrawal , Thibaut Horel

Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…

Statistics Theory · Mathematics 2018-02-13 Loïc Giraldi , Olivier P. Le Maître , Ibrahim Hoteit , Omar M. Knio

A loss function measures the discrepancy between the true values (observations) and their estimated fits, for a given instance of data. A loss function is said to be proper (unbiased, Fisher consistent) if the fits are defined over a unit…

Information Theory · Computer Science 2018-05-11 Amichai Painsky , Gregory W. Wornell

We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating…

Statistics Theory · Mathematics 2015-02-03 Olga Klopp , Stéphane Gaiffas

As the popularity of hierarchical point forecast reconciliation methods increases, there is a growing interest in probabilistic forecast reconciliation. Many studies have utilized machine learning or deep learning techniques to implement…

Artificial Intelligence · Computer Science 2023-11-22 Guanyu Zhang , Feng Li , Yanfei Kang