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This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
Leverage score sampling provides an appealing way to perform approximate computations for large matrices. Indeed, it allows to derive faithful approximations with a complexity adapted to the problem at hand. Yet, performing leverage scores…
Random feature mapping (RFM) is a popular method for speeding up kernel methods at the cost of losing a little accuracy. We study kernel ridge regression with random feature mapping (RFM-KRR) and establish novel out-of-sample error upper…
We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
A standard objective in computer experiments is to approximate the behaviour of an unknown function on a compact domain from a few evaluations inside the domain. When little is known about the function, space-filling design is advisable:…
We analyze a new algorithm for probability forecasting of binary observations on the basis of the available data, without making any assumptions about the way the observations are generated. The algorithm is shown to be well calibrated and…
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…
We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…
We study the proximal sampler of Lee, Shen, and Tian (2021) and obtain new convergence guarantees under weaker assumptions than strong log-concavity: namely, our results hold for (1) weakly log-concave targets, and (2) targets satisfying…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…
We investigate statistical properties for a broad class of modern kernel-based regression (KBR) methods. These kernel methods were developed during the last decade and are inspired by convex risk minimization in infinite-dimensional Hilbert…
Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as…
This paper provides a new theoretical lens for understanding the finite-sample performance of kernel-based specification tests, such as the Kernel Conditional Moment (KCM) test. Rather than introducing a fundamentally new test, we isolate…
Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…