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In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…

Data Structures and Algorithms · Computer Science 2023-06-02 Daniel Alabi , Pravesh K. Kothari , Pranay Tankala , Prayaag Venkat , Fred Zhang

This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the…

Optimization and Control · Mathematics 2025-09-03 Yaqun Yang , Jinlong Lei , Guanghui Wen , Yiguang Hong

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…

Statistics Theory · Mathematics 2016-12-26 Xi Chen , Adityanand Guntuboyina , Yuchen Zhang

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…

Quantum Physics · Physics 2021-03-17 Simon Morelli , Ayaka Usui , Elizabeth Agudelo , Nicolai Friis

We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…

Machine Learning · Statistics 2025-09-29 Mario Gómez , Guanqun Ma , Tom Needham , Bei Wang

Recent work established a generalized-Fano framework for lower bounding prior-predictive (Bayesian) CVaR in interactive statistical decision making. In this paper, we show how to instantiate that framework in concrete interactive problems…

Machine Learning · Computer Science 2026-04-15 Raghav Bongole , Tobias J. Oechtering , Mikael Skoglund

We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…

Computation · Statistics 2022-07-19 Ricardo Baptista , Youssef Marzouk , Olivier Zahm

The emergence of the Internet-of-Things and cyber-physical systems necessitates the coordination of access to limited communication resources in an autonomous and distributed fashion. Herein, the optimal design of a wireless sensing system…

Systems and Control · Electrical Eng. & Systems 2020-05-26 Xu Zhang , Marcos M. Vasconcelos , Wei Cui , Urbashi Mitra

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…

Signal Processing · Electrical Eng. & Systems 2022-02-15 Alice Cicirello , Filippo Giunta

We present a local minimax lower bound on the excess cost of designing a linear-quadratic controller from offline data. The bound is valid for any offline exploration policy that consists of a stabilizing controller and an energy bounded…

Systems and Control · Electrical Eng. & Systems 2023-03-29 Bruce D. Lee , Ingvar Ziemann , Anastasios Tsiamis , Henrik Sandberg , Nikolai Matni

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other…

Information Theory · Computer Science 2022-05-19 Adrien Vandenbroucque , Amedeo Roberto Esposito , Michael Gastpar

We prove a tight lower bound (up to constant factors) on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex. This lower bound also implies a tight lower bound…

Cryptography and Security · Computer Science 2021-05-17 Jonathan Ullman

We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…

Statistics Theory · Mathematics 2024-03-27 Lucas da Rocha Schwengber , Roberto Imbuzeiro Oliveira

Consider the problem of nonparametric estimation of an unknown $\beta$-H\"older smooth density $p_{XY}$ at a given point, where $X$ and $Y$ are both $d$ dimensional. An infinite sequence of i.i.d.\ samples $(X_i,Y_i)$ are generated…

Information Theory · Computer Science 2023-08-29 Jingbo Liu

Motivated by the need for computationally tractable spatial methods in neuroimaging studies, we develop a distributed and integrated framework for estimation and inference of Gaussian process model parameters with ultra-high-dimensional…

Methodology · Statistics 2024-02-09 Emily C. Hector , Brian J. Reich , Ani Eloyan

Estimating high-dimensional covariance matrices is a key task across many fields. This paper explores the theoretical limits of distributed covariance estimation in a feature-split setting, where communication between agents is constrained.…

Machine Learning · Statistics 2025-07-24 Mohammad Reza Rahmani , Mohammad Hossein Yassaee , Mohammad Reza Aref

In this work, we study the problem of distributed mean estimation with $1$-bit communication constraints when the variance is unknown. We focus on the specific case where each user has access to one i.i.d. sample drawn from a distribution…

Information Theory · Computer Science 2025-10-10 Ritesh Kumar , Shashank Vatedka

We introduce a framework for Bayesian experimental design (BED) with implicit models, where the data-generating distribution is intractable but sampling from it is still possible. In order to find optimal experimental designs for such…

Machine Learning · Statistics 2021-05-11 Steven Kleinegesse , Michael U. Gutmann

One of the most complex tasks of decision making and planning is to gather information. This task becomes even more complex when the state is high-dimensional and its belief cannot be expressed with a parametric distribution. Although the…

Artificial Intelligence · Computer Science 2022-09-26 Gilad Rotman , Vadim Indelman

The performance of algorithmic decision rules is largely dependent on the quality of training datasets available to them. Biases in these datasets can raise economic and ethical concerns due to the resulting algorithms' disparate treatment…

Machine Learning · Computer Science 2025-04-14 Yifan Yang , Yang Liu , Parinaz Naghizadeh