Related papers: L1-Regularized Functional Support Vector Machine
We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from…
We consider unsupervised classification by means of a latent multinomial variable which categorizes a scalar response into one of L components of a mixture model. This process can be thought as a hierarchical model with first level…
Many of the best statistical classification algorithms are binary classifiers that can only distinguish between one of two classes. The number of possible ways of generalizing binary classification to multi-class increases exponentially…
Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function…
The feature selection in a traditional binary classification algorithm is always used in the stage of dataset preprocessing, which makes the obtained features not necessarily the best ones for the classification algorithm, thus affecting…
We present a lower error bound for approximating linear multivariate operators defined over Hilbert spaces in terms of the error bounds for appropriately constructed linear functionals as long as algorithms use function values. Furthermore,…
Binary Classification plays an important role in machine learning. For linear classification, SVM is the optimal binary classification method. For nonlinear classification, the SVM algorithm needs to complete the classification task by…
We make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation.…
In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size. We first propose a…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
Penalized regression has become a standard tool for model building across a wide range of application domains. Common practice is to tune the amount of penalization to tradeoff bias and variance or to optimize some other measure of…
Multi-class classification methods based on both labeled and unlabeled functional data sets are discussed. We present a semi-supervised logistic model for classification in the context of functional data analysis. Unknown parameters in our…
Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional…
A conventional linear model for functional data involves expressing a response variable $Y$ in terms of the explanatory function $X(t)$, via the model: $Y=a+\int_I b(t)X(t)dt+\hbox{error}$, where $a$ is a scalar, $b$ is an unknown function…
Support vector machine (SVM) is one of the most popular classification algorithms in the machine learning literature. We demonstrate that SVM can be used to balance covariates and estimate average causal effects under the unconfoundedness…
The Support Vector Machine (SVM) is a popular classification paradigm in machine learning and has achieved great success in real applications. However, the standard SVM can not select variables automatically and therefore its solution…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…
We tackle the problem of computing counterfactual explanations -- minimal changes to the features that flip an undesirable model prediction. We propose a solution to this question for linear Support Vector Machine (SVMs) models. Moreover,…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
This paper analyzes a new regularized learning scheme for high dimensional partially linear support vector machine. The proposed approach consists of an empirical risk and the Lasso-type penalty for linear part, as well as the standard…