Related papers: Convex Support Vector Regression
This paper investigates Support Vector Regression (SVR) within the framework of the Risk Quadrangle (RQ) theory. Every RQ includes four stochastic functionals -- error, regret, risk, and \emph{deviation}, bound together by a so-called…
An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner…
Support vector machine (SVM) is a well-known statistical technique for classification problems in machine learning and other fields. An important question for SVM is the selection of covariates (or features) for the model. Many studies have…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
In this paper, we develop a new approach to the very short-term point forecasting of electricity prices in the continuous market. It is based on the Support Vector Regression with a kernel correction built on additional forecast of…
Load forecasting has always been a challenge for grid operators due to the growing complexity of power systems. The increase in extreme weather and the need for energy from customers has led to load forecasting sometimes failing. This…
We investigate the nonlinear regression problem under L2 loss (square loss) functions. Traditional nonlinear regression models often result in non-convex optimization problems with respect to the parameter set. We show that a convex…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…
This paper introduces a new type of regression methodology named as Convex-Area-Wise Linear Regression(CALR), which separates given datasets by disjoint convex areas and fits different linear regression models for different areas. This…
Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…
We propose a new, nonparametric method for multivariate regression subject to convexity or concavity constraints on the response function. Convexity constraints are common in economics, statistics, operations research, financial engineering…
In this paper, we proposed a new technique, {\em variance controlled stochastic gradient} (VCSG), to improve the performance of the stochastic variance reduced gradient (SVRG) algorithm. To avoid over-reducing the variance of gradient by…
We propose a novel support vector regression approach called e-Distance Weighted Support Vector Regression (e-DWSVR).e-DWSVR specifically addresses two challenging issues in support vector regression: first, the process of noisy data;…
We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression. Support functions uniquely characterize a compact set up to closure of convexification, and are sublinear…
Quantifying uncertainty in predictions or, more generally, estimating the posterior conditional distribution, is a core challenge in machine learning and statistics. We introduce Convex Nonparanormal Regression (CNR), a conditional…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
Tackling pattern recognition problems in areas such as computer vision, bioinformatics, speech or text recognition is often done best by taking into account task-specific statistical relations between output variables. In structured…
The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models…
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes…