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We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…

Machine Learning · Computer Science 2013-05-15 Siu-On Chan , Ilias Diakonikolas , Rocco A. Servedio , Xiaorui Sun

In this paper, we study high-dimensional estimation from truncated samples. We focus on two fundamental and classical problems: (i) inference of sparse Gaussian graphical models and (ii) support recovery of sparse linear models. (i) For…

Machine Learning · Statistics 2020-06-18 Arnab Bhattacharyya , Rathin Desai , Sai Ganesh Nagarajan , Ioannis Panageas

We consider the following basic, and very broad, statistical problem: Given a known high-dimensional distribution ${\cal D}$ over $\mathbb{R}^n$ and a collection of data points in $\mathbb{R}^n$, distinguish between the two possibilities…

Computational Complexity · Computer Science 2024-11-25 Anindya De , Huan Li , Shivam Nadimpalli , Rocco A. Servedio

We study the problem of computationally efficient proper agnostic learning of multidimensional concept classes under the Gaussian distribution. In this setting, given i.i.d. labeled samples from an unknown distribution over $\mathbb{R}^d…

Data Structures and Algorithms · Computer Science 2026-05-28 Sergei Tikhonov , Arsen Vasilyan

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

Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…

Machine Learning · Statistics 2020-07-03 Stijn de Waele

We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…

Data Structures and Algorithms · Computer Science 2015-06-03 Jayadev Acharya , Ilias Diakonikolas , Jerry Li , Ludwig Schmidt

We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…

Computation · Statistics 2013-06-06 Ari Pakman , Liam Paninski

We study the problem of list-decodable Gaussian covariance estimation. Given a multiset $T$ of $n$ points in $\mathbb R^d$ such that an unknown $\alpha<1/2$ fraction of points in $T$ are i.i.d. samples from an unknown Gaussian…

Data Structures and Algorithms · Computer Science 2023-05-02 Ilias Diakonikolas , Daniel M. Kane , Jasper C. H. Lee , Ankit Pensia , Thanasis Pittas

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

Machine Learning · Computer Science 2018-11-26 Yu Cheng , Ilias Diakonikolas , Rong Ge

Recent work of Klivans, Stavropoulos, and Vasilyan initiated the study of testable learning with distribution shift (TDS learning), where a learner is given labeled samples from training distribution $\mathcal{D}$, unlabeled samples from…

Data Structures and Algorithms · Computer Science 2024-05-22 Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

We consider the problem of linear regression with self-selection bias in the unknown-index setting, as introduced in recent work by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [STOC 2023]. In this model, one observes $m$ i.i.d.…

Statistics Theory · Mathematics 2024-02-23 Jason Gaitonde , Elchanan Mossel

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 inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…

Methodology · Statistics 2025-12-01 Angus Lewis , Antonio Parrella , John Maclean , Andrew J. Black

We give the first polynomial-time algorithm to estimate the mean of a $d$-variate probability distribution with bounded covariance from $\tilde{O}(d)$ independent samples subject to pure differential privacy. Prior algorithms for this…

Data Structures and Algorithms · Computer Science 2022-06-06 Samuel B. Hopkins , Gautam Kamath , Mahbod Majid

We study the problem of list-decodable Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. We develop a set of techniques that yield new efficient algorithms with significantly improved…

Data Structures and Algorithms · Computer Science 2017-11-21 Ilias Diakonikolas , Daniel M. Kane , Alistair Stewart

This paper is devoted to the estimation of the shift parameter in a semiparametric regression model when the distribution of the observation times is unknown. Hence, we propose to use a stochastic algorithm which takes into account the…

Statistics Theory · Mathematics 2013-12-23 Philippe Fraysse

We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…

Data Structures and Algorithms · Computer Science 2017-11-21 Samuel B. Hopkins , Jerry Li

We give the first polynomial time algorithm for \emph{list-decodable covariance estimation}. For any $\alpha > 0$, our algorithm takes input a sample $Y \subseteq \mathbb{R}^d$ of size $n\geq d^{\mathsf{poly}(1/\alpha)}$ obtained by…

Data Structures and Algorithms · Computer Science 2022-06-23 Misha Ivkov , Pravesh K. Kothari

Learning from data in the presence of outliers is a fundamental problem in statistics. Until recently, no computationally efficient algorithms were known to compute the mean of a high dimensional distribution under natural assumptions in…

Data Structures and Algorithms · Computer Science 2021-01-22 Yeshwanth Cherapanamjeri , Sidhanth Mohanty , Morris Yau