Related papers: Large-scale Nonlinear Variable Selection via Kerne…
This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features.We present theoretical properties of this method and show that it is uniformly consistent in finding the…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory.…
Kernel methods form a powerful, versatile, and theoretically-grounded unifying framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the kernel trick to perform pairwise evaluations…
Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…
Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…
This article proposes a performance analysis of kernel least squares support vector machines (LS-SVMs) based on a random matrix approach, in the regime where both the dimension of data $p$ and their number $n$ grow large at the same rate.…
The process generates substantial amounts of data with highly complex structures, leading to the development of numerous nonlinear statistical methods. However, most of these methods rely on computations involving large-scale dense kernel…
We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence…
This paper addresses a kernel-based learning problem for a network of agents locally observing a latent multidimensional, nonlinear phenomenon in a noisy environment. We propose a learning algorithm that requires only mild a priori…
We propose the introduction of nonlinear operation into the feature generation process in convolutional neural networks. This nonlinearity can be implemented in various ways. First we discuss the use of nonlinearities in the process of data…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…
We propose a novel approach to model selection for simulator-based statistical models. The proposed approach defines a mixture of candidate models, and then iteratively updates the weight coefficients for those models as well as the…
Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…
We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and…
Variable selection is essential in high-dimensional data analysis. Although various variable selection methods have been developed, most rely on the linear model assumption. This article proposes a nonparametric variable selection method…
Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which…