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Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…
Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…
A new approach to $L_2$-consistent estimation of a general density functional using $k$-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities…
Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…
We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a…
Spectral density estimation is a core problem of system identification, which is an important research area of system control and signal processing. There have been numerous results on the design of spectral density estimators. However to…
By subjecting a dynamical system to a series of short pulses and varying several time delays we can obtain multidimensional characteristic measures of the system. Multidimensional Kullback-Leibler response function (KLRF), which are based…
Error estimates are rigorously derived for a semi-discrete version of a conservative spectral method for approximating the space-homogeneous Fokker-Planck-Landau (FPL) equation associated to hard potentials. The analysis included shows that…
While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel…
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. We obtain closed formulas for the expected model approximation errors,…
Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…
We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L^2 function, a given likelihood function has an alternative representation as a product of…
While covariance matrices have been widely studied in many scientific fields, relatively limited progress has been made on estimating conditional covariances that permits a large covariance matrix to vary with high-dimensional subject-level…
In this work, we present formulations for regularized Kullback-Leibler and R\'enyi divergences via the Alpha Log-Determinant (Log-Det) divergences between positive Hilbert-Schmidt operators on Hilbert spaces in two different settings,…
In this paper, we delve deeper into the Kullback-Leibler (KL) Divergence loss and mathematically prove that it is equivalent to the Decoupled Kullback-Leibler (DKL) Divergence loss that consists of 1) a weighted Mean Square Error (wMSE)…
Discrete diffusion models have achieved strong empirical performance in text and other symbolic domains, with masked (absorbing-rate) variants emerging as competitive alternatives to autoregressive models. Among existing samplers, the Euler…
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…