Related papers: Distributed Gaussian Mean Testing under Communicat…
We consider the problem of estimating the arithmetic average of a finite collection of real vectors stored in a distributed fashion across several compute nodes subject to a communication budget constraint. Our analysis does not rely on any…
It is of fundamental importance to find algorithms obtaining optimal performance for learning of statistical models in distributed and communication limited systems. Aiming at characterizing the optimal strategies, we consider learning of…
We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…
We consider a problem of statistical mean estimation in which the samples are not observed directly, but are instead observed by a relay (``teacher'') that transmits information through a memoryless channel to the decoder (``student''), who…
We study the two-user Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and confidential messages. In this channel, the transmitter sends a common message to both users, and a confidential message to each user…
We present simple differentially private estimators for the mean and covariance of multivariate sub-Gaussian data that are accurate at small sample sizes. We demonstrate the effectiveness of our algorithms both theoretically and empirically…
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…
This work concerns the behavior of "good" (capacity achieving) codes in several multi-user settings in the Gaussian regime, in terms of their minimum mean-square error (MMSE) behavior. The settings investigated in this context include the…
We consider the problem of distributed estimation, where local processors observe independent samples conditioned on a common random parameter of interest, map the observations to a finite number of bits, and send these bits to a remote…
We study high-dimensional mean estimation in a collaborative setting where data is contributed by $N$ users in batches of size $n$. In this environment, a learner seeks to recover the mean $\mu$ of a true distribution $P$ from a collection…
We study the power versus distortion trade-off for the distributed transmission of a memoryless bi-variate Gaussian source over a two-to-one average-power limited Gaussian multiple-access channel. In this problem, each of two separate…
We study private broadcasting of two messages to two groups of receivers over independent parallel channels. One group consists of an arbitrary number of receivers interested in a common message, whereas the other group has only one…
We consider symmetric two-user Gaussian interference channel with common messages. We derive an upper bound on the sum capacity, and show that the upper bound is tight in the low interference regime, where the optimal transmission scheme is…
We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $\mu = \frac 1n\sum_{v = 1}^n…
This paper addresses a unified approach towards communication in decentralized wireless networks of separate transmitter-receiver pairs. In general, users are unaware of each other's codebooks and there is no central controller to assign…
We study the problem of estimating a function of many parameters acquired by sensors that are distributed in space, e.g., the spatial gradient of a field. We restrict ourselves to a setting where the distributed sensors are probed with…
In this paper, we generalize the fundamental relation between the mutual information and the minimum mean squared error (MMSE) by Guo, Shamai, and Verdu [1] to K-User Gaussian channels. We prove that the derivative of the multiuser mutual…
In this paper, fading Gaussian multiuser channels are considered. If the channel is perfectly known to the transmitter, capacity has been established for many cases in which the channels may satisfy certain information theoretic orders such…
Consider a Gaussian memoryless multiple source with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components are sampled and compressed with the objective of…
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…