Related papers: Support Vector Regression: Risk Quadrangle Framewo…

The main goal of statistical learning theory is to provide a fundamental framework for the problem of decision making and model construction based on sets of data. Here, we present a brief introduction to the fundamentals of statistical…

Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…

Techniques for reducing the variance of gradient estimates used in stochastic programming algorithms for convex finite-sum problems have received a great deal of attention in recent years. By leveraging dissipativity theory from control, we…

Multivariate density estimation is of great interest in various scientific and engineering disciplines. In this work, we introduce a new framework called Variance-Reduced Sketching (VRS), specifically designed to estimate multivariate…

In this paper we study variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions. We introduce stochastic approximation schemes that employ an empirical estimate of the CVaR at each iteration to…

This paper focuses on a class of variational inequalities (VIs), where the map defining the VI is given by the component-wise conditional value-at-risk (CVaR) of a random function. We focus on solving the VI using sample average…

Expected Shortfall (ES), also known as superquantile or Conditional Value-at-Risk, has been recognized as an important measure in risk analysis and stochastic optimization, and is also finding applications beyond these areas. In finance, it…

This paper presents a unified framework to tackle estimation problems in Digital Signal Processing (DSP) using Support Vector Machines (SVMs). The use of SVMs in estimation problems has been traditionally limited to its mere use as a…

We address the problem of model selection for Support Vector Machine (SVM) classification. For fixed functional form of the kernel, model selection amounts to tuning kernel parameters and the slack penalty coefficient $C$. We begin by…

We derive the asymptotic risk function of regularized empirical risk minimization (ERM) estimators tuned by $n$-fold cross-validation (CV). The out-of-sample prediction loss of such estimators converges in distribution to the squared-error…

Virtually all state-of-the-art methods for training supervised machine learning models are variants of SGD enhanced with a number of additional tricks, such as minibatching, momentum, and adaptive stepsizes. One of the tricks that works so…

We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted…

In this paper we propose a class of structural vector autoregressions (SVARs) characterized by structural breaks (SVAR-WB). Together with standard restrictions on the parameters and on functions of them, we also consider constraints across…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

Stochastic Variance-Reduced Cubic regularization (SVRC) algorithms have received increasing attention due to its improved gradient/Hessian complexities (i.e., number of queries to stochastic gradient/Hessian oracles) to find local minima…

Support Vector Machine (SVM) is an efficient classification approach, which finds a hyperplane to separate data from different classes. This hyperplane is determined by support vectors. In existing SVM formulations, the objective function…

The deep neural network suffers from many fundamental issues in machine learning. For example, it often gets trapped into a local minimum in training, and its prediction uncertainty is hard to be assessed. To address these issues, we…

This paper proposes a unified control framework based on Response-Aware Risk-Constrained Control Barrier Function for dynamic safety boundary control of vehicles. Addressing the problem of physical model parameter mismatch, the framework…

Turbulence modeling within the RANS equations' framework is essential in engineering due to its high efficiency. Field inversion and machine learning (FIML) techniques have improved RANS models' predictive capabilities for separated flows.…

A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale.…