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Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…

We study generalization properties of kernel regularized least squares regression based on a partitioning approach. We show that optimal rates of convergence are preserved if the number of local sets grows sufficiently slowly with the…

Random forests are one of the most popular machine learning methods due to their accuracy and variable importance assessment. However, random forests only provide variable importance in a global sense. There is an increasing need for such…

We consider the problem of estimating a regression function when a covariate is measured with error. Using the local polynomial estimator of Delaigle, Fan, and Carroll (2009) as a benchmark, we propose an alternative way of solving the…

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…

Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation…

This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…

High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…

Estimating software effort has been a largely unsolved problem for decades. One of the main reasons that hinders building accurate estimation models is the often heterogeneous nature of software data with a complex structure. Typically,…

Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…

This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…

Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in…

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…

We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential…

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

We propose generalized random forests, a method for non-parametric statistical estimation based on random forests (Breiman, 2001) that can be used to fit any quantity of interest identified as the solution to a set of local moment…

We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either…

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…

This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…