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In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the approximation results in total variation…

Probability · Mathematics 2020-07-07 Pratima Eknath Kadu

Instance discriminative self-supervised representation learning has been attracted attention thanks to its unsupervised nature and informative feature representation for downstream tasks. In practice, it commonly uses a larger number of…

Machine Learning · Computer Science 2022-01-17 Kento Nozawa , Issei Sato

In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…

Probability · Mathematics 2026-04-10 Fraser Daly

Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like the…

Machine Learning · Statistics 2017-10-17 Philemon Brakel , Yoshua Bengio

Sparse additive models have attracted much attention in high-dimensional data analysis due to their flexible representation and strong interpretability. However, most existing models are limited to single-level learning under the…

Machine Learning · Computer Science 2026-04-23 Xuelin Zhang , Xinyue Liu , Lingjuan Wu , Hong Chen

Well-spread samples are desirable in many disciplines because they improve estimation when target variables exhibit spatial structure. This paper introduces an integrated methodological framework for spreading samples over the population's…

Methodology · Statistics 2025-10-29 Bardia Panahbehagh , Mehdi Mohebbi , Amir Mohammad HosseiniNasab

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…

Machine Learning · Computer Science 2017-11-07 Rebecca E. Morrison , Ricardo Baptista , Youssef Marzouk

In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn $x=(x_1,\ldots,x_n) \in \{0,1\}^n$ from a stream of random linear equations over $\mathrm{F}_2$ that are correct with…

Machine Learning · Computer Science 2021-07-07 Sumegha Garg , Pravesh K. Kothari , Pengda Liu , Ran Raz

Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…

Logic in Computer Science · Computer Science 2025-03-19 Olivier Zeyen , Maxime Cordy , Martin Gubri , Gilles Perrouin , Mathieu Acher

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…

Statistical Mechanics · Physics 2015-05-14 Attilio L. Stella , Fulvio Baldovin

One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently…

Statistics Theory · Mathematics 2019-04-02 Jaakko Lehtomaa , Sidney Resnick

Reinforcement learning algorithms are typically limited to learning a single solution for a specified task, even though diverse solutions often exist. Recent studies showed that learning a set of diverse solutions is beneficial because…

Machine Learning · Statistics 2022-04-14 Takayuki Osa , Voot Tangkaratt , Masashi Sugiyama

The independent component model is a latent variable model where the components of the observed random vector are linear combinations of latent independent variables. The aim is to find an estimate for a transformation matrix back to…

Statistics Theory · Mathematics 2015-05-12 Joni Virta , Klaus Nordhausen , Hannu Oja

Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…

Machine Learning · Computer Science 2017-06-01 Linus Hamilton , Frederic Koehler , Ankur Moitra

Let $X,X_1,...,X_n$ be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable $\sum_{k=1}^{n}a_k X_k$ according to the arithmetic…

Probability · Mathematics 2014-01-07 Yu. S. Eliseeva , A. Yu. Zaitsev

Active statistical inference is a new method for inference with AI-assisted data collection. Given a budget on the number of labeled data points that can be collected and assuming access to an AI predictive model, the basic idea is to…

Machine Learning · Statistics 2025-11-13 Puheng Li , Tijana Zrnic , Emmanuel Candès

This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined…

Econometrics · Economics 2023-12-05 Florian Huber

For zero-error function computation over directed acyclic networks, existing upper and lower bounds on the computation capacity are known to be loose. In this work we consider the problem of computing the arithmetic sum over a specific…

Information Theory · Computer Science 2016-01-28 Ardhendu Tripathy , Aditya Ramamoorthy

In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution…

Data Structures and Algorithms · Computer Science 2014-02-18 Clément Canonne , Ronitt Rubinfeld

A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…

Information Theory · Computer Science 2007-07-13 Joseph DeStefano , Erik Learned-Miller