English
Related papers

Related papers: Learning Poisson Binomial Distributions

200 papers

The sum of $n$ {non-independent} Bernoulli random variables could be modeled in several different ways. One of these is the Multiplicative Binomial Distribution (MBD), introduced by Altham (1978) and revised by Lovison (1998). In this work,…

Statistics Theory · Mathematics 2018-02-26 Francesca Fortunato

Supervised learning aims to train a classifier under the assumption that training and test data are from the same distribution. To ease the above assumption, researchers have studied a more realistic setting: out-of-distribution (OOD)…

Machine Learning · Computer Science 2023-02-28 Zhen Fang , Yixuan Li , Jie Lu , Jiahua Dong , Bo Han , Feng Liu

We give the first almost optimal polynomial-time proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. For $s$-sparse polynomial over $n$ variables and $\epsilon=1/s^\beta$, $\beta>1$, our…

Machine Learning · Computer Science 2022-02-08 Nader H. Bshouty

We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of…

Probability · Mathematics 2010-04-02 Vydas Čekanavičius , Erol A. Peköz , Adrian Röllin , Michael Shwartz

A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…

Data Structures and Algorithms · Computer Science 2020-02-11 Ronitt Rubinfeld , Arsen Vasilyan

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…

Mathematical Physics · Physics 2015-05-28 E. M. F. Curado , J. P. Gazeau , Ligia M. C. S. Rodrigues

Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…

Machine Learning · Computer Science 2025-10-09 Binchuan Qi , Wei Gong , Li Li

We study the {\em robust proper learning} of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis…

Data Structures and Algorithms · Computer Science 2016-06-10 Ilias Diakonikolas , Daniel M. Kane , Alistair Stewart

We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…

Data Structures and Algorithms · Computer Science 2014-05-20 Constantinos Daskalakis , Gautam Kamath

We give a $2^{\tilde{O}(\sqrt{n}/\epsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Our algorithm is robust to adversarial label noise and has a running time nearly…

Data Structures and Algorithms · Computer Science 2023-03-29 Jane Lange , Ronitt Rubinfeld , Arsen Vasilyan

We consider the problem of learning a discrete distribution in the presence of an $\epsilon$ fraction of malicious data sources. Specifically, we consider the setting where there is some underlying distribution, $p$, and each data source…

Machine Learning · Computer Science 2017-11-23 Mingda Qiao , Gregory Valiant

In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…

Methodology · Statistics 2018-05-22 Debasis Kundu

The problem of learning a computational model from examples has been receiving growing attention. For the particularly challenging problem of learning models of distributed systems, existing results are restricted to models with a fixed…

Formal Languages and Automata Theory · Computer Science 2023-12-13 Dana Fisman , Noa Izsak , Swen Jacobs

We define a novel, basic, unsupervised learning problem - learning the lowest density homogeneous hyperplane separator of an unknown probability distribution. This task is relevant to several problems in machine learning, such as…

Machine Learning · Computer Science 2009-01-22 Shai Ben-David , Tyler Lu , David Pal , Miroslava Sotakova

In this work, we continue the line of research on the complexity of distributions (Viola, Journal of Computing 2012), and study samplers defined by low degree polynomials. An $n$-tuple $P = (P_1,\dots, P_n)$ of functions $P_i \colon…

Computational Complexity · Computer Science 2026-05-05 Mohammad Mahdi Khodabandeh , Igor Shinkar

Supervised learning aims to train a classifier under the assumption that training and test data are from the same distribution. To ease the above assumption, researchers have studied a more realistic setting: out-of-distribution (OOD)…

Machine Learning · Computer Science 2024-04-09 Zhen Fang , Yixuan Li , Feng Liu , Bo Han , Jie Lu

Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal…

Machine Learning · Statistics 2017-06-23 Christopher Beckham , Christopher Pal

Neural networks have revolutionized the field of machine learning with increased predictive capability. In addition to improving the predictions of neural networks, there is a simultaneous demand for reliable uncertainty quantification on…

Machine Learning · Computer Science 2023-08-10 Ethan Ancell , Christopher Bennett , Bert Debusschere , Sapan Agarwal , Park Hays , T. Patrick Xiao

A key element in transfer learning is representation learning; if representations can be developed that expose the relevant factors underlying the data, then new tasks and domains can be learned readily based on mappings of these salient…

Machine Learning · Computer Science 2014-12-18 Yujia Li , Kevin Swersky , Richard Zemel

We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…

Data Structures and Algorithms · Computer Science 2016-01-22 Clément L. Canonne , Ilias Diakonikolas , Themis Gouleakis , Ronitt Rubinfeld