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This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…

Statistics Theory · Mathematics 2018-08-29 Stanislav Minsker , Nate Strawn

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

Statistics Theory · Mathematics 2023-03-17 Anna Scampicchio , Elena Arcari , Melanie N. Zeilinger

The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…

Methodology · Statistics 2018-11-13 Susanne Ditlevsen , Adeline Samson

The paper considers distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents' local expectation-valued convex cost functions. Due to the stochasticity in gradient…

Optimization and Control · Mathematics 2022-04-07 Jinlong Lei , Peng Yi , Jie Chen , Yiguang Hong

We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…

Optimization and Control · Mathematics 2024-05-15 Joshua Cutler , Mateo Díaz , Dmitriy Drusvyatskiy

We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…

Cryptography and Security · Computer Science 2017-11-13 Vishesh Karwa , Salil Vadhan

Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…

Machine Learning · Computer Science 2020-03-10 Jun Han

We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…

Machine Learning · Statistics 2021-01-14 Wenjing Liao , Mauro Maggioni , Stefano Vigogna

There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…

Statistics Theory · Mathematics 2023-11-22 Trung Dang , Jasper C. H. Lee , Maoyuan Song , Paul Valiant

Given a convex function $f\colon\mathbb{R}^{d}\to\mathbb{R}$, the problem of sampling from a distribution $\propto e^{-f(x)}$ is called log-concave sampling. This task has wide applications in machine learning, physics, statistics, etc. In…

Quantum Physics · Physics 2023-12-11 Andrew M. Childs , Tongyang Li , Jin-Peng Liu , Chunhao Wang , Ruizhe Zhang

We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…

Computational Complexity · Computer Science 2016-08-16 Vitaly Feldman , Elena Grigorescu , Lev Reyzin , Santosh Vempala , Ying Xiao

Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…

Numerical Analysis · Mathematics 2023-11-14 Aleksei G. Sorokin , Jagadeeswaran Rathinavel

We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…

Optimization and Control · Mathematics 2019-12-05 Wenjie Huang , William B. Haskell

The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…

Computer Vision and Pattern Recognition · Computer Science 2015-04-22 Ognjen Arandjelovic , Duc-Son Pham , Svetha Venkatesh

We study the approximation of expectations $\operatorname{E}(f(X))$ for solutions $X$ of stochastic differential equations and functionals $f$ on the path space by means of Monte Carlo algorithms that only use random bits instead of random…

Numerical Analysis · Mathematics 2023-01-10 Michael B. Giles , Mario Hefter , Lukas Mayer , Klaus Ritter

We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…

Multiagent Systems · Computer Science 2018-05-11 Gianluigi Pillonetto , Luca Schenato , Damiano Varagnolo

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Machine Learning · Statistics 2015-06-15 Zhaoshi Meng , Dennis Wei , Ami Wiesel , Alfred O. Hero

Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex nonsmooth losses (such as modern deep networks), the population…

Machine Learning · Computer Science 2018-10-19 Chi Jin , Lydia T. Liu , Rong Ge , Michael I. Jordan

In stochastic convex optimization the goal is to minimize a convex function $F(x) \doteq {\mathbf E}_{{\mathbf f}\sim D}[{\mathbf f}(x)]$ over a convex set $\cal K \subset {\mathbb R}^d$ where $D$ is some unknown distribution and each…

Machine Learning · Computer Science 2016-12-28 Vitaly Feldman

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian…

Computation · Statistics 2022-10-26 Hamza Ruzayqat , Alexandros Beskos , Dan Crisan , Ajay Jasra , Nikolas Kantas