Related papers: Indicator Functions: Distilling the Information fr…
Current tools for multivariate density estimation struggle when the density is concentrated near a nonlinear subspace or manifold. Most approaches require choice of a kernel, with the multivariate Gaussian by far the most commonly used.…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
A distributed detection scheme where the sensors transmit with constant modulus signals over a Gaussian multiple access channel is considered. The deflection coefficient of the proposed scheme is shown to depend on the characteristic…
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information…
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…
This paper introduces Bayesian supervised and unsupervised segmentation algorithms aimed at oceanic segmentation of SAR images. The data term, \emph{i.e}., the density of the observed backscattered signal given the region, is modeled by a…
We introduce a novel unbiased, cross-correlation estimator for the one-point statistics of cosmological random fields. One-point statistics are a useful tool for analysis of highly non-Gaussian density fields, while cross-correlations…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
In continuation to a recent work on the statistical--mechanical analysis of minimum mean square error (MMSE) estimation in Gaussian noise via its relation to the mutual information (the I-MMSE relation), here we propose a simple and more…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
Image acquisition and segmentation are likely to introduce noise. Further image processing such as image registration and parameterization can introduce additional noise. It is thus imperative to reduce noise measurements and boost signal.…
The data functions that are studied in the course of functional data analysis are assembled from discrete data, and the level of smoothing that is used is generally that which is appropriate for accurate approximation of the conceptually…
Markov Random Field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
The flow size distribution is a useful metric for traffic modeling and management. Its estimation based on sampled data, however, is problematic. Previous work has shown that flow sampling (FS) offers enormous statistical benefits over…
In many applications, status information of a general spatial process, in contrast to a point information source, is of interest. In this paper, we consider a system where status information is drawn from a random field and transmitted to a…
Famously, the quantum Fisher information -- the maximum Fisher information over all physical measurements -- is additive for independent copies of a system and the optimal measurement acts locally. We are left to wonder: does the same hold…
We derive upper bounds on the Wasserstein distance ($W_1$), with respect to $\sup$-norm, between any continuous $\mathbb{R}^d$ valued random field indexed by the $n$-sphere and the Gaussian, based on Stein's method. We develop a novel…
We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…
A large fraction of the information collected by cosmological surveys is simply discarded to avoid lengthscales which are difficult to model theoretically. We introduce a new technique which enables the extraction of useful information from…