Related papers: A Kernel-based Consensual Aggregation for Regressi…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed variance estimator is based…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
In this paper, we develop a consensus algorithm for distributed computation of the Riemannian center of mass (RCM) on Lie Groups. The algorithm is built upon a distributed optimization reformulation that allows developing an intrinsic,…
We construct a family of estimators for a regression function based on a sample following a qdistribution. Our approach is nonparametric, using kernel methods built from operations that leverage the properties of q-calculus. Furthermore,…
An ensemble method is introduced that utilizes randomization and loss function gradients to compute a prediction. Multiple weakly-correlated estimators approximate the gradient at randomly sampled points on the error surface and are…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is…
Deep learning's successes are often attributed to its ability to automatically discover new representations of the data, rather than relying on handcrafted features like other learning methods. We show, however, that deep networks learned…
Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…
Distributed machine learning has recently become a critical paradigm for training large models on vast datasets. We examine the stochastic optimization problem for deep learning within synchronous parallel computing environments under…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…