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We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…

Econometrics · Economics 2024-11-18 Matteo Mogliani , Anna Simoni

We construct a classifier which attains the rate of convergence $\log n/n$ under sparsity and margin assumptions. An approach close to the one met in approximation theory for the estimation of function is used to obtain this result. The…

Statistics Theory · Mathematics 2016-08-16 Guillaume Lecué

We propose a unified probabilistic framework for sparse count tensors with excess zeros, motivated by single-cell Hi-C data. The observed data are naturally represented as a three-way tensor indexed by genomic loci pairs and cells,…

Methodology · Statistics 2026-04-27 Elena Tuzhilina , Yaoming Zhen

We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…

Machine Learning · Statistics 2016-11-17 Mohammad Hossein Rohban , Prakash Ishwar , Birant Orten , William C. Karl , Venkatesh Saligrama

Training neural network models with discrete (categorical or structured) latent variables can be computationally challenging, due to the need for marginalization over large or combinatorial sets. To circumvent this issue, one typically…

Machine Learning · Computer Science 2020-12-29 Gonçalo M. Correia , Vlad Niculae , Wilker Aziz , André F. T. Martins

Performing signal processing tasks on compressive measurements of data has received great attention in recent years. In this paper, we extend previous work on compressive dictionary learning by showing that more general random projections…

Machine Learning · Statistics 2015-04-07 Farhad Pourkamali-Anaraki , Stephen Becker , Shannon M. Hughes

We study frequentist properties of Bayesian and $L_0$ model selection, with a focus on (potentially non-linear) high-dimensional regression. We propose a construction to study how posterior probabilities and normalized $L_0$ criteria…

Statistics Theory · Mathematics 2021-10-07 David Rossell

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…

Machine Learning · Computer Science 2025-08-25 Sebastian Sanokowski , Sepp Hochreiter , Sebastian Lehner

Expand-and-sparsify representations are a class of theoretical models that capture sparse representation phenomena observed in the sensory systems of many animals. At a high level, these representations map an input $x \in \mathbb{R}^d$ to…

Statistics Theory · Mathematics 2026-03-20 Kaushik Sinha , Christopher Tosh

We consider model selection in generalized linear models (GLM) for high-dimensional data and propose a wide class of model selection criteria based on penalized maximum likelihood with a complexity penalty on the model size. We derive a…

Statistics Theory · Mathematics 2016-03-31 Felix Abramovich , Vadim Grinshtein

In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where…

Methodology · Statistics 2023-11-08 Yasuyuki Hamura , Takahiro Onizuka , Shintaro Hashimoto , Shonosuke Sugasawa

This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signal-independent…

Information Theory · Computer Science 2009-04-30 Rebecca M. Willett , Maxim Raginsky

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

Statistics Theory · Mathematics 2015-10-15 Ismaël Castillo , Johannes Schmidt-Hieber , Aad van der Vaart

Multi-dimensional distributions whose marginal distributions are uniform are called copulas. Among them, the one that satisfies given constraints on expectation and is closest to the independent distribution in the sense of Kullback-Leibler…

Methodology · Statistics 2022-04-11 Yici Chen , Tomonari Sei

The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…

Statistics Theory · Mathematics 2015-03-19 Michel Broniatowski , Aida Toma , Igor Vajda

We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…

Statistics Theory · Mathematics 2010-09-20 Sebastian Schmutzhard , Alexander Jung , Franz Hlawatsch , Zvika Ben-Haim , Yonina C. Eldar

We present a structured additive regression approach to model conditional densities given scalar covariates, where only samples of the conditional distributions are observed. This links our approach to distributional regression models for…

Methodology · Statistics 2025-10-17 Eva-Maria Maier , Alexander Fottner , Sonja Greven , Almond Stöcker

Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria…

Statistics Theory · Mathematics 2018-03-19 B. J. K. Kleijn , Y. Y. Zhao

An unbiased $m$-sparsification of a vector $p\in \mathbb{R}^n$ is a random vector $Q\in \mathbb{R}^n$ with mean $p$ that has at most $m<n$ nonzero coordinates. Unbiased sparsification compresses the original vector without introducing bias;…

We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood,…

Machine Learning · Statistics 2015-08-19 Changwei Hu , Piyush Rai , Lawrence Carin