Related papers: A gradient-based variable selection for binary cla…

Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of…

The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…

We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting…

Multiscale Models are known to be successful in uncovering and analyzing the structures in data at different resolutions. In the current work we propose a feature driven Reproducing Kernel Hilbert space (RKHS), for which the associated…

In this paper, we propose a random gradient-free method for optimization in infinite dimensional Hilbert spaces, applicable to functional optimization in diverse settings. Though such problems are often solved through finite-dimensional…

We consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in…

We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic…

In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…

This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…

We propose a method for variable selection in discriminant analysis with mixed categorical and continuous variables. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating…

We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This…

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…

Random Forests and Gradient Boosting are among the most effective algorithms for supervised learning on tabular data. Both belong to the class of tree-based ensemble methods, where predictions are obtained by aggregating many randomized…

Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…

Reinforcement learning consists of finding policies that maximize an expected cumulative long-term reward in a Markov decision process with unknown transition probabilities and instantaneous rewards. In this paper, we consider the problem…

In this paper we propose a novel variable selection method for two-view settings, or for vector-valued supervised learning problems. Our framework is able to handle extremely large scale selection tasks, where number of data samples could…

We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its…

Feature or variable selection is a problem inherent to large data sets. While many methods have been proposed to deal with this problem, some can scale poorly with the number of predictors in a data set. Screening methods scale linearly…

Estimating Kullback Leibler (KL) divergence from samples of two distributions is essential in many machine learning problems. Variational methods using neural network discriminator have been proposed to achieve this task in a scalable…

We introduce a functional gradient descent trajectory optimization algorithm for robot motion planning in Reproducing Kernel Hilbert Spaces (RKHSs). Functional gradient algorithms are a popular choice for motion planning in complex…