Related papers: Asymptotic mutual information in quadratic estimat…
Recent progress has shown that the generalization error of the Gibbs algorithm can be exactly characterized using the symmetrized KL information between the learned hypothesis and the entire training dataset. However, evaluating such a…
We introduce the quantum indirect estimation theory, which provides a general framework to address the problem of which ensemble averages can be estimated by means of an available set of measuring apparatuses, e. g. estimate the ensemble…
We consider the problem of estimating mutual information between dependent data, an important problem in many science and engineering applications. We propose a data-driven, non-parametric estimator of mutual information in this paper. The…
In this paper, we address the fusion problem in wireless sensor networks, where the cross-correlation between the estimates is unknown. To solve the problem within the Bayesian framework, we assume that the covariance matrix has a prior…
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and…
This paper is concerned with the problem of reconstructing an unknown rank-one matrix with prior structural information from noisy observations. While computing the Bayes-optimal estimator seems intractable in general due to its nonconvex…
We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of…
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
This brief note considers the problem of estimating temporal synergy and integrated information in dyadic dynamical processes. One of the standard estimators of dynamic synergy is based on the minimal mutual information between sets of…
Interactions among sensors can provide, in addition to entanglement, an important resource for boosting the precision in quantum estimation protocols. Dephasing noise, however, remains a leading source of decoherence in state-of-the-art…
The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…
We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of…
We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero,…
We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm in the context of stochastic convex optimization. Despite increasing interest in…
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and…
We propose a Bayesian framework for the received-signal-strength-based cooperative localization problem with unknown path loss exponent. Our purpose is to infer the marginal posterior of each unknown parameter: the position or the path loss…
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…