Related papers: Asymptotic mutual information in quadratic estimat…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
Aleatoric uncertainty captures the inherent randomness of the data, such as measurement noise. In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance…
In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…
Estimating mutual information is an important statistics and machine learning problem. To estimate the mutual information from data, a common practice is preparing a set of paired samples $\{(\mathbf{x}_i,\mathbf{y}_i)\}_{i=1}^n…
We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…
The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless,…
This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across…
Following the idea of Bayesian learning via Gaussian mixture model, we organically combine the backward-looking information contained in the historical data and the forward-looking information implied by the market portfolio, which is…
A two-time scale asymptotic method has been introduced to analyze the multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to uncouple the probability density in…
This paper addresses the topic of robust Bayesian compressed sensing over finite fields. For stationary and ergodic sources, it provides asymptotic (with the size of the vector to estimate) necessary and sufficient conditions on the number…
The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to…
We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both…
The first terms of the low-signal-energy asymptotics for the mutual information in the discrete-time Poisson channel are derived and compared to an asymptotic expression of the capacity. In the presence of non-zero additive noise (either…
We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…
This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve…
Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes…
Consider random linear estimation with Gaussian measurement matrices and noise. One can compute infinitesimal variations of the mutual information under infinitesimal variations of the signal-to-noise ratio or of the measurement rate. We…
Efficient information processing is crucial for both living organisms and engineered systems. The mutual information rate, a core concept of information theory, quantifies the amount of information shared between the trajectories of input…
A model to estimate the asymptotic isotropic mutual information of a multiantenna channel is considered. Using a block-based dynamics and the angle diversity of the system, we derived what may be thought of as the operator-valued version of…