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This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators'…

Numerical Analysis · Computer Science 2015-04-16 Martin Drohmann , Kevin Carlberg

Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…

Methodology · Statistics 2017-06-13 Kei Hirose , Hironori Fujisawa , Jun Sese

In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a…

Systems and Control · Computer Science 2012-04-03 Uwe D. Hanebeck , Jannik Steinbring

This paper addresses the multi-faceted problem of robot grasping, where multiple criteria may conflict and differ in importance. We introduce a probabilistic framework, Grasp Ranking and Criteria Evaluation (GRaCE), which employs…

Robotics · Computer Science 2024-05-30 Tasbolat Taunyazov , Kelvin Lin , Harold Soh

A genetic algorithm procedure is demonstrated that refines the selection of interpolation points of the discrete empirical interpolation method (DEIM) when used for constructing reduced order models for time dependent and/or parametrized…

Numerical Analysis · Mathematics 2016-07-27 Syuzanna Sargsyan , Steven L. Brunton , J. Nathan Kutz

Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise…

Machine Learning · Statistics 2016-05-16 Christopher J. Moore , Alvin J. K. Chua , Christopher P. L. Berry , Jonathan R. Gair

We show that standard extragradient methods (i.e. mirror prox and dual extrapolation) recover optimal accelerated rates for first-order minimization of smooth convex functions. To obtain this result we provide a fine-grained…

Optimization and Control · Mathematics 2021-07-16 Michael B. Cohen , Aaron Sidford , Kevin Tian

We propose a conjugate and calibrated Gaussian process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison geometry to map simplex-valued class probabilities to an…

Machine Learning · Computer Science 2026-03-18 Bernardo Williams , Harsha Vardhan Tetali , Arto Klami , Marcelo Hartmann

The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…

Computation · Statistics 2012-09-04 Björn Bornkamp

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…

Data Structures and Algorithms · Computer Science 2015-12-15 Laura Rebollo-Neira

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

Optimization and Control · Mathematics 2023-12-05 Yurii Nesterov

Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model,…

Machine Learning · Statistics 2022-04-12 Jiahao Zhang , Shiqi Zhang , Guang Lin

We revisit FedExProx - a recently proposed distributed optimization method designed to enhance convergence properties of parallel proximal algorithms via extrapolation. In the process, we uncover a surprising flaw: its known theoretical…

Optimization and Control · Mathematics 2026-04-21 Wojciech Anyszka , Kaja Gruntkowska , Alexander Tyurin , Peter Richtárik

Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…

Optimization and Control · Mathematics 2024-11-12 Ruichen Jiang , Michał Dereziński , Aryan Mokhtari

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Machine Learning · Computer Science 2021-01-07 Laura Swiler , Mamikon Gulian , Ari Frankel , Cosmin Safta , John Jakeman

We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…

Astrophysics · Physics 2009-11-07 Tomoaki Matsumoto , Tomoyuki Hanawa

The paper presents numerical experiments and some theoretical developments in prediction with expert advice (PEA). One experiment deals with predicting electricity consumption depending on temperature and uses real data. As the pattern of…

Artificial Intelligence · Computer Science 2021-09-30 Vladimir V'yugin , Vladimir Trunov

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…

The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…

Optimization and Control · Mathematics 2024-01-30 Mihai I. Florea

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…

Optimization and Control · Mathematics 2024-09-17 Amon Lahr , Andrea Zanelli , Andrea Carron , Melanie N. Zeilinger