Related papers: $L_1$-norm Regularized Indefinite Kernel Logistic …
Regularized empirical risk minimization including support vector machines plays an important role in machine learning theory. In this paper regularized pairwise learning (RPL) methods based on kernels will be investigated. One example is…
Stochastic configuration networks (SCNs), as a class of randomized learner models, are featured by its way of random parameters assignment in the light of a supervisory mechanism, resulting in the universal approximation property at…
We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a…
We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…
Nowadays, several data analysis problems require for complexity reduction, mainly meaning that they target at removing the non-influential covariates from the model and at delivering a sparse model. When categorical covariates are present,…
For high dimensional sparse linear regression problems, we propose a sequential convex relaxation algorithm (iSCRA-TL1) by solving inexactly a sequence of truncated $\ell_1$-norm regularized minimization problems, in which the working index…
We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…
Kernel methods have been extensively utilized in machine learning for classification and prediction tasks due to their ability to capture complex non-linear data patterns. However, single kernel approaches are inherently limited, as they…
The problem of finding the maximum likelihood estimates for the regression coefficients in generalised linear models with an L1 sparsity penalty is shown to be equivalent to minimising the unpenalised maximum log-likelihood function over a…
Regularization techniques such as the lasso (Tibshirani 1996) and elastic net (Zou and Hastie 2005) can be used to improve regression model coefficient estimation and prediction accuracy, as well as to perform variable selection. Ordinal…
Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of…
We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…
Multivariate classification methods using explanatory and predictive models are necessary for characterizing subgroups of patients according to their risk profiles. Popular methods include logistic regression and classification trees with…
We theoretically analyze the typical learning performance of $\ell_{1}$-regularized linear regression ($\ell_1$-LinR) for Ising model selection using the replica method from statistical mechanics. For typical random regular graphs in the…
Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…
We implement extensions of the partial least squares generalized linear regression (PLSGLR) due to Bastien et al. (2005) through its combination with logistic regression and linear discriminant analysis, to get a partial least squares…
Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits…
A regularized minimization model with $l_1$-norm penalty (RP) is introduced for training the autoencoders that belong to a class of two-layer neural networks. We show that the RP can act as an exact penalty model which shares the same…
Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While…
Regularized linear regression is a promising approach for binary classification problems in which the training set has noisy labels since the regularization term can help to avoid interpolating the mislabeled data points. In this paper we…