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The selection of the most appropriate algorithm to solve a given problem instance, known as algorithm selection, is driven by the potential to capitalize on the complementary performance of different algorithms across sets of problem…
Classical molecular dynamics (MD) simulations enable modeling of materials and examination of microscopic details that are not accessible experimentally. The predictive capability of MD relies on the force field (FF) used to describe…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
The selection problem of an optimal set of sensors estimating the snapshot of high-dimensional data is considered. The objective functions based on various criteria of optimal design are adopted to the greedy method: D-optimality,…
Numerous estimators have been proposed for factor analysis, and their statistical properties have been extensively studied. In the early 2000s, a novel matrix factorization-based approach, known as Matrix Decomposition Factor Analysis…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly…
Local Differential Privacy (LDP) addresses significant privacy concerns in sensitive data collection. In this work, we focus on numerical data collection under LDP, targeting a significant gap in the literature: existing LDP mechanisms are…
Statistical matching is an effective method for estimating causal effects in which treated units are paired with control units with ``similar'' values of confounding covariates prior to performing estimation. In this way, matching helps…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…
We present a general framework that utilizes different efficient data structures to improve various sparsification problems involving an iterative process. We also provide insights and characterization for different iterative process, and…
Recent work on approximate linear programming (ALP) techniques for first-order Markov Decision Processes (FOMDPs) represents the value function linearly w.r.t. a set of first-order basis functions and uses linear programming techniques to…
Consider $K$ processes, each generating a sequence of identical and independent random variables. The probability measures of these processes have random parameters that must be estimated. Specifically, they share a parameter $\theta$…
In this paper we consider the problem of computing an $\epsilon$-optimal policy of a discounted Markov Decision Process (DMDP) provided we can only access its transition function through a generative sampling model that given any…
Distributed Constraint Optimization Problems (DCOPs) are a widely studied constraint handling framework. The objective of a DCOP algorithm is to optimize a global objective function that can be described as the aggregation of a number of…
Large language models (LLMs) continue to struggle with mathematical reasoning, and common post-training pipelines often reduce each generated solution to a binary outcome: correct or incorrect. This perspective is limiting in practice, as…
Diffusion Probabilistic Models (DPMs) have demonstrated exceptional capability of generating high-quality and diverse images, but their practical application is hindered by the intensive computational cost during inference. The DPM…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…
Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…