Related papers: Inference under Information Constraints I: Lower B…
A central server needs to perform statistical inference based on samples that are distributed over multiple users who can each send a message of limited length to the center. We study problems of distribution learning and identity testing…
Independent samples from an unknown probability distribution $\bf p$ on a domain of size $k$ are distributed across $n$ players, with each player holding one sample. Each player can communicate $\ell$ bits to a central referee in a…
We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy of their data while enabling a central server to perform…
We study the role of interactivity in distributed statistical inference under information constraints, e.g., communication constraints and local differential privacy. We focus on the tasks of goodness-of-fit testing and estimation of…
We revisit the problem of Gaussian mean testing in a distributed, communication constrained setting, where each of $n$ users independently observes samples from an unknown $d$-dimensional spherical Gaussian distribution…
Large-scale datasets are increasingly being used to inform decision making. While this effort aims to ground policy in real-world evidence, challenges have arisen as selection bias and other forms of distribution shifts often plague…
A quantum generalized divergence by definition satisfies the data-processing inequality; as such, the relative decrease in such a divergence under the action of a quantum channel is at most one. This relative decrease is formally known as…
Motivated by applications in cyber security, we develop a simple game model for describing how a learning agent's private information influences an observing agent's inference process. The model describes a situation in which one of the…
We derive lower bounds on the Bayes risk in decentralized estimation, where the estimator does not have direct access to the random samples generated conditionally on the random parameter of interest, but only to the data received from…
We prove a general connection between the communication complexity of two-player games and the sample complexity of their multi-player locally private analogues. We use this connection to prove sample complexity lower bounds for locally…
Two familiar notions of correlation are rediscovered as the extreme operating points for distributed synthesis of a discrete memoryless channel, in which a stochastic channel output is generated based on a compressed description of the…
We study common randomness where two parties have access to i.i.d. samples from a known random source, and wish to generate a shared random key using limited (or no) communication with the largest possible probability of agreement. This…
This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized…
We consider the problem of estimating sparse discrete distributions under local differential privacy (LDP) and communication constraints. We characterize the sample complexity for sparse estimation under LDP constraints up to a constant…
The secrecy problem in the state-dependent cognitive interference channel is considered in this paper. In our model, there are a primary and a secondary (cognitive) transmitter-receiver pairs, in which the cognitive transmitter has the…
Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…
We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.…
We consider the problem of learning high-dimensional, nonparametric and structured (e.g. Gaussian) distributions in distributed networks, where each node in the network observes an independent sample from the underlying distribution and can…