arXiv research

RKHSMetaMod estimates complex models' Hoeffding decomposition for sensitivity analysis.

Framework for transferring discount curve estimates across fixed-income product classes.

Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics. However in many cases, this knowledge is not available. To overcome this issue, we introduce a general framework for nonparametric ODE models using penalized regression in Reproducing Kerne…

Kernel $ε$-Greedy optimizes multi-armed bandits with covariates for sub-linear regret.

Optimal CATE estimation with structured contrast functions using KRR.

HARFE approximates sparse additive functions using random features and ridge regression.

This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the introduced regression models in an approximation theory view. Algorithmically, we c…

OKRidge solves sparse ridge regression problems for nonlinear systems.

Spectrally-truncated KRR outperforms full KRR for large data.

New kernel methods estimate complex causal relationships.

Proposes CCME framework for estimating heterogeneous treatment effects.

Study the cost of overfitting in noisy KRR models.

Paper proposes a method for early stopping in regression using reproducing kernels.

New method approximates complex kernel norms with random features, making learning tractable.

This paper improves computational efficiency in kernel ridge regression under covariate shift.

Regularization is used to find a solution that both fits the data and is sufficiently smooth, and thereby is very effective for designing and refining learning algorithms. But the influence of its exponent remains poorly understood. In particular, it is unclear how the exponent of the reproducing kernel Hilbert space~(…

Optimal scoring framework for kernel classification with feature selection.

Study evaluates RKHS choices for assessing graph models using KSD tests.

We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches and multi-passes over the data. We show that optimal generalization error bounds c…

This paper aims to solve a basic problem in distributed statistical inference: how many machines can we use in parallel computing? In kernel ridge regression, we address this question in two important settings: nonparametric estimation and hypothesis testing. Specifically, we find a range for the number of machines und…

New algorithm improves regression error bounds and accelerates performance for low noise.

Simplifies NL models by approximating them as LPV systems and identifying NL subterms.

Paper proposes tensor sparse PCA for improved face recognition accuracy.

New algorithm learns Koopman operator online, with complexity control and convergence guarantees.

We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of the associated unknown parameters. Due to the presence of outliers, common techni…

Proposes a gradient-based variable selection method for binary classification in RKHS.

We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods for approximating Gaussian …

Optimally tackles covariate shift in RKHS-based nonparametric regression.

The paper develops a method to learn SDE drift functions from sparse, noisy data.

The paper proposes a gradient-based method for multi-penalty Ridge regression.

Joint sparsity regularization in multi-task learning has attracted much attention in recent years. The traditional convex formulation employs the group Lasso relaxation to achieve joint sparsity across tasks. Although this approach leads to a simple convex formulation, it suffers from several issues due to the loosenes…

Efficiently performs robust and sparse kernel regression.

When the design matrix has orthonormal columns, "soft thresholding" the ordinary least squares (OLS) solution produces the Lasso solution [Tibshirani, 1996]. If one uses the Puffer preconditioned Lasso [Jia and Rohe, 2012], then this result generalizes from orthonormal designs to full rank designs (Theorem 1). Theorem …

New algorithm tackles high-dimensional simulation optimization, converging efficiently.

We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings minimise, providing an intuitive understanding of the embeddings and a justificatio…

Proposes a new ridge estimator for smooth covariates with adaptive centering.

Kernel balancing weights are generalized as KRRR, providing better confidence intervals for treatment effects.

We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework. The data set of size n is partitioned into $m=O(n^α)$ disjoint subsets. On each subset, some spectral regularization method (belonging to a large class, including in particular K…

Noiseless KRR achieves optimal rates and exhibits saturation effects.

Bayesian EM method improves ridge regression tuning without LOOCV's limitations.

Study optimizes learning rates for conditional mean embedding estimates.

Develops a new method for learning ODEs from sparse data.

New method for causal inference with complex treatment compositions.

Kernel Dynamic Mode Decomposition reconstructs dynamical systems using Laplacian kernel.

New RL method handles large state-action spaces with complex models.

Paper learns optimal kernels for Gaussian process regression in aerodynamics.

Develops first and second-order pseudo-mirror descent methods for nonnegative function estimation.

Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account manifold geometry is typically done via (1) embedding the manifolds in tangent space…