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Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an…

Convolutional Neural Networks (ConvNets) have successfully contributed to improve the accuracy of regression-based methods for computer vision tasks such as human pose estimation, landmark localization, and object detection. The network…

Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…

Test-time compute scaling, the practice of spending extra computation during inference via repeated sampling, search, or extended reasoning, has become a powerful lever for improving large language model performance. Yet deploying these…

Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical…

Support vector machine is an important and fundamental technique in machine learning. Soft-margin SVM models have stronger generalization performance compared with the hard-margin SVM. Most existing works use the hinge-loss function which…

A smoothing algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an…

Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust…

We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…

In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…

A new algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an important…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

The rapid advancement of large language models (LLMs) has led to significant improvements in natural language processing but also poses challenges due to their high computational and energy demands. This paper introduces a series of…

Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…

One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum…

Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The…

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…

This paper studies matrix constrained polynomial optimization. We investigate how to get explicit expressions for Lagrange multiplier matrices from the first order optimality conditions. The existence of these expressions can be shown under…

We establish risk bounds for Regularized Empirical Risk Minimizers (RERM) when the loss is Lipschitz and convex and the regularization function is a norm. In a first part, we obtain these results in the i.i.d. setup under subgaussian…