Related papers: Convergence Analysis of regularised Nystr\"om meth…

We develop two approaches for analyzing the approximation error bound for the Nystr\"{o}m method, one based on the concentration inequality of integral operator, and one based on the compressive sensing theory. We show that the…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

One of the major limits of kernel ridge regression (KRR) is that storing and manipulating the kernel matrix K_n for n samples requires O(n^2) space, which rapidly becomes unfeasible for large n. Nystrom approximations reduce the space…

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…

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…

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

Conventional seismic techniques for detecting the subsurface geologic features are challenged by limited data coverage, computational inefficiency, and subjective human factors. We developed a novel data-driven geological feature detection…

This paper focuses on learning rate analysis of Nystr\"{o}m regularization with sequential sub-sampling for $\tau$-mixing time series. Using a recently developed Banach-valued Bernstein inequality for $\tau$-mixing sequences and an integral…

In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

We develop an improved bound for the approximation error of the Nystr\"{o}m method under the assumption that there is a large eigengap in the spectrum of kernel matrix. This is based on the empirical observation that the eigengap has a…

This paper is concerned with functional learning by utilizing two-stage sampled distribution regression. We study a multi-penalty regularization algorithm for distribution regression under the framework of learning theory. The algorithm…

An increasing number of systems are being designed by gathering significant amounts of data and then optimizing the system parameters directly using the obtained data. Often this is done without analyzing the dataset structure. As task…

We consider the problem of minimizing a sum of $n$ functions over a convex parameter set $\mathcal{C} \subset \mathbb{R}^p$ where $n\gg p\gg 1$. In this regime, algorithms which utilize sub-sampling techniques are known to be effective. In…

This paper proposes a new nonlinear approach for additive functional regression with functional response based on kernel methods along with some slight reformulation and implementation of the linear regression and the spectral additive…

Recently, deep learning has been widely applied in functional data analysis (FDA) with notable empirical success. However, the infinite dimensionality of functional data necessitates an effective dimension reduction approach for functional…