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For all $n, \epsilon >0$, we show that the set of Poisson Binomial distributions on $n$ variables admits a proper $\epsilon$-cover in total variation distance of size $n^2+n \cdot (1/\epsilon)^{O(\log^2 (1/\epsilon))}$, which can also be…

Computation · Statistics 2014-10-03 Constantinos Daskalakis , Christos Papadimitriou

A Bayesian network is a directed acyclic graph that represents statistical dependencies between variables of a joint probability distribution. A fundamental task in data science is to learn a Bayesian network from observed data.…

Data Structures and Algorithms · Computer Science 2021-05-21 Niels Grüttemeier , Christian Komusiewicz , Nils Morawietz

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

We study the problem, introduced by Qiao and Valiant, of learning from untrusted batches. Here, we assume $m$ users, all of whom have samples from some underlying distribution $p$ over $1, \ldots, n$. Each user sends a batch of $k$ i.i.d.…

Data Structures and Algorithms · Computer Science 2019-11-07 Sitan Chen , Jerry Li , Ankur Moitra

Partially Observable Markov Decision Processes (POMDPs) are a natural and general model in reinforcement learning that take into account the agent's uncertainty about its current state. In the literature on POMDPs, it is customary to assume…

Machine Learning · Computer Science 2022-03-24 Noah Golowich , Ankur Moitra , Dhruv Rohatgi

The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or…

Data Analysis, Statistics and Probability · Physics 2015-06-17 G. Bohm , G. Zech

Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…

Methodology · Statistics 2021-07-06 Jun Yu , HaiYing Wang , Mingyao Ai , Huiming Zhang

Bayesian Networks (BNs) are useful tools giving a natural and compact representation of joint probability distributions. In many applications one needs to learn a Bayesian Network (BN) from data. In this context, it is important to…

Machine Learning · Computer Science 2012-07-02 Or Zuk , Shiri Margel , Eytan Domany

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

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 propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux-Lie theorem, the phase flow of a Poisson system can be written as the composition of (1) a…

Machine Learning · Computer Science 2020-12-08 Pengzhan Jin , Zhen Zhang , Ioannis G. Kevrekidis , George Em Karniadakis

In this work, we investigated the feasibility of applying deep learning techniques to solve Poisson's equation. A deep convolutional neural network is set up to predict the distribution of electric potential in 2D or 3D cases. With proper…

Computational Physics · Physics 2017-12-18 Tao Shan , Wei Tang , Xunwang Dang , Maokun Li , Fan Yang , Shenheng Xu , Ji Wu

We introduce a new model of membership query (MQ) learning, where the learning algorithm is restricted to query points that are \emph{close} to random examples drawn from the underlying distribution. The learning model is intermediate…

Machine Learning · Computer Science 2013-04-19 Pranjal Awasthi , Vitaly Feldman , Varun Kanade

We give the first polynomial-time approximation scheme (PTAS) for the stochastic load balancing problem when the job sizes follow Poisson distributions. This improves upon the 2-approximation algorithm due to Goel and Indyk (FOCS'99).…

Data Structures and Algorithms · Computer Science 2020-06-24 Anindya De , Sanjeev Khanna , Huan Li , Hesam Nikpey

We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…

Machine Learning · Computer Science 2020-06-05 Adam Klivans , Pravesh K. Kothari , Raghu Meka

We consider the problem of learning high dimensional polynomial transformations of Gaussians. Given samples of the form $p(x)$, where $x\sim N(0, \mathrm{Id}_r)$ is hidden and $p: \mathbb{R}^r \to \mathbb{R}^d$ is a function where every…

Machine Learning · Computer Science 2022-04-11 Sitan Chen , Jerry Li , Yuanzhi Li , Anru R. Zhang

We give a polynomial-time algorithm for learning high-dimensional halfspaces with margins in $d$-dimensional space to within desired TV distance when the ambient distribution is an unknown affine transformation of the $d$-fold product of an…

Machine Learning · Computer Science 2023-11-03 Xinyuan Cao , Santosh S. Vempala

We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube $\{0,1\}^n$. Our main result is the following structural theorem: any submodular function is…

Machine Learning · Computer Science 2013-04-03 Vitaly Feldman , Pravesh Kothari , Jan Vondrak

The problem of learning structural equation models (SEMs) from data is a fundamental problem in causal inference. We develop a new algorithm --- which is computationally and statistically efficient and works in the high-dimensional regime…

Machine Learning · Computer Science 2019-01-30 Asish Ghoshal , Jean Honorio

We give a {\em deterministic} algorithm for approximately computing the fraction of Boolean assignments that satisfy a degree-$2$ polynomial threshold function. Given a degree-2 input polynomial $p(x_1,\dots,x_n)$ and a parameter $\eps >…

Computational Complexity · Computer Science 2013-11-28 Anindya De , Ilias Diakonikolas , Rocco A. Servedio