Related papers: Analysis of Nystrom method with sequential ridge l…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…
We study a relaxed version of the column-sampling problem for the Nystr\"om approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as…
We propose new reproducing kernel-based tests for model checking in conditional moment restriction models. By regressing estimated residuals on kernel functions via kernel ridge regression (KRR), we obtain a coefficient function in a…
We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has…
Kernel methods have achieved very good performance on large scale regression and classification problems, by using the Nystr\"om method and preconditioning techniques. The Nystr\"om approximation -- based on a subset of landmarks -- gives a…
Multi-criteria decision-making often requires finding a small representative set from the database. A recently proposed method is the regret minimization set (RMS) query. RMS returns a size $r$ subset $S$ of dataset $D$ that minimizes the…
Consider the classical supervised learning problem: we are given data $(y_i,{\boldsymbol x}_i)$, $i\le n$, with $y_i$ a response and ${\boldsymbol x}_i\in {\mathcal X}$ a covariates vector, and try to learn a model $f:{\mathcal…
In this work, we propose a simple kernel ridge regression (KRR) framework with a dynamic-aware validation strategy for long-term prediction of complex dynamical systems. By employing a data-driven kernel derived from diffusion maps, the…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
Kernel methods underpin many of the most successful approaches in data science and statistics, and they allow representing probability measures as elements of a reproducing kernel Hilbert space without loss of information. Recently, the…
Ridge leverage scores provide a balance between low-rank approximation and regularization, and are ubiquitous in randomized linear algebra and machine learning. Deterministic algorithms are also of interest in the moderately big data…
A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…
We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function…
Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and commonly used in nonparametric…
Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of…
Kernel logistic regression (KLR) is a powerful classification method widely applied across diverse domains. In many real-world scenarios, indefinite kernels capture more domain-specific structural information than positive definite kernels.…