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We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable…
Predicting multiphysics dynamics is computationally expensive and challenging due to the severe coupling of multi-scale, heterogeneous physical processes. While neural surrogates promise a paradigm shift, the field currently suffers from an…
Linear response theory is a well-established method in physics and chemistry for exploring excitations of many-body systems. In particular, the quasiparticle random-phase approximation (QRPA) provides a powerful microscopic framework by…
In real case applications within the virtual prototyping process, it is not always possible to reduce the complexity of the physical models and to obtain numerical models which can be solved quickly. Usually, every single numerical…
An optimum solution free from degeneration is found to the system of linear algebraic equations with empirical coefficients and right-hand sides. The quadratic risk of estimators of the unknown solution vector is minimized over a class of…
State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
Simulations of optical quantum systems are essential for the development of quantum technologies. However, these simulations are often computationally intensive, especially when repeated evaluations are required for data fitting, parameter…
The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…
This paper presents a discrete-time nonlinear system identification method while satisfying the stability and safety properties of the system with high probability. An Extreme Learning Machine (ELM) is used with a Gaussian assumption on the…
This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…
For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…
Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational…
We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems…
Machine learning techniques are powerful tools for construction of emulators for complex systems. We explore different machine learning methods and conceptual methodologies, ranging from functional approximations to dynamical…
The EM algorithm is a method for finding the maximum likelihood estimate of a model in the presence of missing data. Unfortunately, EM does not produce a parameter covariance matrix for standard errors. Supplemented EM (SEM; Meng & Rubin,…
Supervised learning models have been used in various domains such as lending, college admission, face recognition, natural language processing, etc. However, they may inherit pre-existing biases from training data and exhibit discrimination…
Many robotic sensor estimation problems can characterized in terms of nonlinear measurement systems. These systems are contaminated with noise and may be underdetermined from a single observation. In order to get reliable estimation…
The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…