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We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
We introduce MESSY estimation, a Maximum-Entropy based Stochastic and Symbolic densitY estimation method. The proposed approach recovers probability density functions symbolically from samples using moments of a Gradient flow in which the…
Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
There has been a wide interest to extend univariate and multivariate nonparametric procedures to clustered and hierarchical data. Traditionally, parametric mixed models have been used to account for the correlation structures among the…
State estimation in water distribution networks (WDN), the problem of estimating all unknown network heads and flows given select measurements, is challenging due to the nonconvexity of hydraulic models and significant uncertainty from…
We propose Amortized Posterior Sampling (APS), a novel variational inference approach for efficient posterior sampling in inverse problems. Our method trains a conditional flow model to minimize the divergence between the variational…
Gaussian processes provide a flexible framework for spatial prediction, but their computational cost limits applicability to large-scale data with large sample size $n$. Predictive processes (PPs), a popular low-rank approximation, mitigate…
The path-specific effect (PSE) is of primary interest in mediation analysis when multiple intermediate variables between treatment and outcome are observed, as it can isolate the specific effect through each mediator, thus mitigating…
Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
Dimension reduction, widely used in science, maps high-dimensional data into low-dimensional space. We investigate a basic mathematical model underlying the techniques of stochastic neighborhood embedding (SNE) and its popular variant…
This paper considers the problem of distributed estimation in a sensor network, where multiple sensors are deployed to infer the state of a linear time-invariant (LTI) Gaussian system. By proposing a lossless decomposition of Kalman filter,…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
The comparison of subnational areas is ubiquitous but survey samples of these areas are often biased or prohibitively small. Researchers turn to methods such as multilevel regression and poststratification (MRP) to improve the efficiency of…
Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…
A general framework of spatio-spectral segmentation for multi-spectral images is introduced in this paper. The method is based on classification-driven stochastic watershed (WS) by Monte Carlo simulations, and it gives more regular and…
Motivated by modeling and analysis of mass-spectrometry data, a semi- and nonparametric model is proposed that consists of a linear parametric component for individual location and scale and a nonparametric regression function for the…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…