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Multilevel compositional data are data that are repeatedly measured or clustered within groups and are non-negative and sum to a constant value. These data arise in various settings, such as intensive, longitudinal studies using ecological…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
How to visually localize multiple sound sources in unconstrained videos is a formidable problem, especially when lack of the pairwise sound-object annotations. To solve this problem, we develop a two-stage audiovisual learning framework…
Scientific observations may consist of a large number of variables (features). Identifying a subset of meaningful features is often ignored in unsupervised learning, despite its potential for unraveling clear patterns hidden in the ambient…
Source separation problems are ubiquitous in the physical sciences; any situation where signals are superimposed calls for source separation to estimate the original signals. In this tutorial I will discuss the Bayesian approach to the…
A deep learning approach based on big data is proposed to locate broadband acoustic sources using a single hydrophone in ocean waveguides with uncertain bottom parameters. Several 50-layer residual neural networks, trained on a huge number…
Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly concentrating target distributions. We focus on Gaussian…
Multi-source localization based on received signal strength (RSS) has drawn great interest in wireless sensor networks. However, the shadow fading term caused by obstacles cannot be separated from the received signal, which leads to severe…
Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we…
We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime based on one-step generative transport. Building on the Mean Flows, we learn a fully conditional amortized sampler with a neural-operator…
We consider the problem of local radioelectric property estimation from global electromagnetic scattering measurements. This challenging ill-posed high dimensional inverse problem can be explored by intensive computations of a parallel…
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…
This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are…
The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…
We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…
This paper presents a Bayesian estimation method for the passive localization of an acoustic source in shallow water. Our probabilistic focalization approach estimates the time-varying source location by associating direction of arrival…
We introduce an unsupervised formulation to estimate heteroscedastic uncertainty in retrieval systems. We propose an extension to triplet loss that models data uncertainty for each input. Besides improving performance, our formulation…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…