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Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…

This article tackles the old problem of prediction via a nonparametric transformation model (NTM) in a new Bayesian way. Estimation of NTMs is known challenging due to model unidentifiability though appealing because of its robust…

Markov Chain Monte Carlo (MCMC) techniques are now widely used for cosmological parameter estimation. Chains are generated to sample the posterior probability distribution obtained following the Bayesian approach. An important issue is how…

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…

This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…

This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…

To improve the predictability of complex computational models in the experimentally-unknown domains, we propose a Bayesian statistical machine learning framework utilizing the Dirichlet distribution that combines results of several…

In a smooth semi-parametric model, the marginal posterior distribution for a finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of any efficient point-estimator. The assertion…

Machine learning (ML) has shown significant promise in studying complex geophysical dynamical systems, including turbulence and climate processes. Such systems often display sensitive dependence on initial conditions, reflected in positive…

This work introduces a family of univariate constrained mixtures of generalized normal distributions (CMGND) where the location, scale, and shape parameters can be constrained to be equal across any subset of mixture components. An…

We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…

Modern challenges of robustness, fairness, and decision-making in machine learning have led to the formulation of multi-distribution learning (MDL) frameworks in which a predictor is optimized across multiple distributions. We study the…

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…

The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual…

We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…

This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…

In many remote sensing applications one wants to estimate variables or parameters of interest from observations. When the target variable is available at a resolution that matches the remote sensing observations, standard algorithms such as…

Using "soft" targets to improve model performance has been shown to be effective in classification settings, but the usage of soft targets for regression is a much less studied topic in machine learning. The existing literature on the usage…

Which neural networks are similar is a fundamental question for both machine learning and neuroscience. Here, it is proposed to base comparisons on the predictive distributions of linear readouts from intermediate representations. In…

A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…