Related papers: Linear Support Vector Regression with Linear Const…
In structured output learning, obtaining labelled data for real-world applications is usually costly, while unlabelled examples are available in abundance. Semi-supervised structured classification has been developed to handle large amounts…
Business optimization is becoming increasingly important because all business activities aim to maximize the profit and performance of products and services, under limited resources and appropriate constraints. Recent developments in…
An accurate load forecasting has always been one of the main indispensable parts in the operation and planning of power systems. Among different time horizons of forecasting, while short-term load forecasting (STLF) and long-term load…
We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of…
We consider linear random coefficient regression models, where the regressors are allowed to have a finite support. First, we investigate identifiability, and show that the means and the variances and covariances of the random coefficients…
Localized support vector machines solve SVMs on many spatially defined small chunks and one of their main characteristics besides the computational benefit compared to global SVMs is the freedom of choosing arbitrary kernel and…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…
The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming…
The parameters of support vector machines (SVMs) such as the penalty parameter and the kernel parameters have a great impact on the classification accuracy and the complexity of the SVM model. Therefore, the model selection in SVM involves…
Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the…
Classification algorithms face difficulties when one or more classes have limited training data. We are particularly interested in classification trees, due to their interpretability and flexibility. When data are limited in one or more of…
Support vector machine (SVM) training is an active research area since the dawn of the method. In recent years there has been increasing interest in specialized solvers for the important case of linear models. The algorithm presented by…
We propose a new convex loss for Support Vector Machines, both for the binary classification and for the regression models. Therefore, we show the mathematical derivation of the dual problems and we experiment with them on several small…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…