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We propose an automated nonlinear model reduction and mesh adaptation framework for rapid and reliable solution of parameterized advection-dominated problems, with emphasis on compressible flows. The key features of our approach are…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems. Our key idea for making the proposed PMM to be efficient is to…
This paper proposes an Adaptive Stochastic Model Predictive Control (MPC) strategy for stable linear time-invariant systems in the presence of bounded disturbances. We consider multi-input, multi-output systems that can be expressed by a…
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…
A simulation is useful when the phenomenon of interest is either expensive to regenerate or irreproducible with the same context. Recently, Bayesian inference on the distribution of the simulation input parameter has been implemented…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
Modern multivariate machine learning and statistical methodologies estimate parameters of interest while leveraging prior knowledge of the association between outcome variables. The methods that do allow for estimation of relationships do…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We study computational aspects of a key problem in robust statistics -- the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large…
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…
High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension…
Support vector machines (SVMs) with sparsity-inducing nonconvex penalties have received considerable attentions for the characteristics of automatic classification and variable selection. However, it is quite challenging to solve the…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Material properties such as permeability fields in heterogeneous porous media are often represented as discontinuous, piecewise constant data tied to a given spatial discretization. Such representations are inherently mesh-dependent,…
In this paper, we introduce a proximal-proximal majorization-minimization (PPMM) algorithm for nonconvex tuning-free robust regression problems. The basic idea is to apply the proximal majorization-minimization algorithm to solve the…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of Large Language Models (LLMs), which aim to identify and mitigate intermediate errors in the reasoning processes. However, the…