Related papers: Online Kernel Sliced Inverse Regression
In this paper, the problem of online distributed zeroth-order optimization subject to a set constraint is studied via a multi-agent network, where each agent can communicate with its immediate neighbors via a time-varying directed graph.…
In applications involving ordinal predictors, common approaches to reduce dimensionality are either extensions of unsupervised techniques such as principal component analysis, or variable selection procedures that rely on modeling the…
We consider the following class of online optimization problems with functional constraints. Assume, that a finite set of convex Lipschitz-continuous non-smooth functionals are given on a closed set of $n$-dimensional vector space. The…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
We study online learning when individual instances are corrupted by adversarially chosen random noise. We assume the noise distribution is unknown, and may change over time with no restriction other than having zero mean and bounded…
Online forecasting under a changing environment has been a problem of increasing importance in many real-world applications. In this paper, we consider the meta-algorithm presented in \citet{zhang2017dynamic} combined with different…
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…
Traditional static functional data analysis is facing new challenges due to streaming data, where data constantly flow in. A major challenge is that storing such an ever-increasing amount of data in memory is nearly impossible. In addition,…
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
We aim at finding the value of an explanatory variable, through its expression in a large data-vector, without knowing the link function between the explanatory variable and the data-space. Sliced Inverse Regression (SIR) method allows for…
We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…
We study online regression with the square loss in a reproducing kernel Hilbert space under a dynamic regret criterion. The learner is compared with a time-varying comparator sequence, and the bounds depend on its path length in the RKHS…
Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the…
Large Language Models (LLMs) have a natural role in answering complex queries about data streams, but the high computational cost of LLM inference makes them infeasible in many such tasks. We propose online cascade learning, the first…
Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fr\'ech\'et dimension reduction methods require that the response metric space be…
This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a…
Batch training of machine learning models based on neural networks is now well established, whereas to date streaming methods are largely based on linear models. To go beyond linear in the online setting, nonparametric methods are of…
The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as…