Related papers: Support Vector Regression: Risk Quadrangle Framewo…

This paper revisits and extends the 2013 development by Rockafellar and Uryasev of the Risk Quadrangle (RQ) as a unified scheme for integrating risk management, optimization, and statistical estimation. The RQ features four…

The paper explores the concept of the \emph{expectile risk measure} within the framework of the Fundamental Risk Quadrangle (FRQ) theory. According to the FRQ theory, a quadrangle comprises four stochastic functions associated with a random…

Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent…

This paper studies the addition of linear constraints to the Support Vector Regression (SVR) when the kernel is linear. Adding those constraints into the problem allows to add prior knowledge on the estimator obtained, such as finding…

Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…

A key problem in deep learning and computational neuroscience is relating the geometrical properties of neural representations to task performance. Here, we consider this problem for continuous decoding tasks where neural variability may…

The Fundamental Risk Quadrangle (FRQ) is a unified framework linking risk management, statistical estimation, and optimization. Distributionally robust optimization (DRO) based on $\varphi$-divergence minimizes the maximal expected loss,…

We propose a twin support vector quantile regression (TSVQR) to capture the heterogeneous and asymmetric information in modern data. Using a quantile parameter, TSVQR effectively depicts the heterogeneous distribution information with…

Quantum coherence and entanglement are fundamental resources in quantum technologies, yet their efficient estimation for unknown states by employing minimal resources in experimental settings remains challenging, particularly in…

We propose a novel algorithm, TR-SVR, for solving unconstrained stochastic optimization problems. This method builds on the trust-region framework, which effectively balances local and global exploration in optimization tasks. TR-SVR…

A new realized conditional autoregressive Value-at-Risk (VaR) framework is proposed, through incorporating a measurement equation into the original quantile regression model. The framework is further extended by employing various Expected…

This paper proposes a novel '$\nu$-support vector quantile regression' ($\nu$-SVQR) model for the quantile estimation. It can facilitate the automatic control over accuracy by creating a suitable asymmetric $\epsilon$-insensitive zone…

The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions…

Hierarchical support vector regression (HSVR) models a function from data as a linear combination of SVR models at a range of scales, starting at a coarse scale and moving to finer scales as the hierarchy continues. In the original…

Support vector machines (SVMs) appeared in the early nineties as optimal margin classifiers in the context of Vapnik's statistical learning theory. Since then SVMs have been successfully applied to real-world data analysis problems, often…

Symbolic Regression (SR) is a well-established framework for generating interpretable or white-box predictive models. Although SR has been successfully applied to create interpretable estimates of the average of the outcome, it is currently…

The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for…

A popular machine-learning model for regression tasks, including stock-market prediction, weather forecasting and real-estate pricing, is the classical support vector regression (SVR). However, a practically realisable quantum SVR remains…

Anomaly detection (AD) involves identifying observations or events that deviate in some way from the rest of the data. Machine learning techniques have shown success in automating this process by detecting hidden patterns and deviations in…

We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic…