Related papers: Distributed Estimation of Gaussian Correlations
In the context of statistical learning, the Information Bottleneck method seeks a right balance between accuracy and generalization capability through a suitable tradeoff between compression complexity, measured by minimum description…
We present decidability results for a sub-class of "non-interactive" simulation problems, a well-studied class of problems in information theory. A non-interactive simulation problem is specified by two distributions $P(x,y)$ and $Q(u,v)$:…
We consider the problem of transmitting a bivariate Gaussian source over a two-user additive Gaussian multiple-access channel with feedback. Each of the transmitters observes one of the source components and tries to describe it to the…
The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix…
In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…
We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
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…
Given an implicit $n\times n$ matrix $A$ with oracle access $x^TA x$ for any $x\in \mathbb{R}^n$, we study the query complexity of randomized algorithms for estimating the trace of the matrix. This problem has many applications in quantum…
We study the problem of cooperative inference where a group of agents interact over a network and seek to estimate a joint parameter that best explains a set of observations. Agents do not know the network topology or the observations of…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
In this paper, we consider the problem of secret key generation with one-way communication through both a rate-limited public channel and a rate-limited secure channels where the public channel is from Alice to Bob and Eve and the secure…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
This paper studies a distributed state estimation problem for both continuous- and discrete-time linear systems. A simply structured distributed estimator (comprising interconnected local estimators) is first described for estimating the…
We present two analytical formulae for estimating the sensitivity -- namely, the gradient or Jacobian -- at given realizations of an arbitrary-dimensional random vector with respect to its distributional parameters. The first formula…
We present prompt distribution learning for effectively adapting a pre-trained vision-language model to address downstream recognition tasks. Our method not only learns low-bias prompts from a few samples but also captures the distribution…
We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that…