Related papers: Error Estimates for the Kernel Gain Function Appro…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…

We consider the problem of approximating a truncated Gaussian kernel using Fourier (trigonometric) functions. The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range…

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…

This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with…

3D action recognition was shown to benefit from a covariance representation of the input data (joint 3D positions). A kernel machine feed with such feature is an effective paradigm for 3D action recognition, yielding state-of-the-art…

This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation error are established for posterior…

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…

In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…

A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…

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…

In this paper we consider the problem of estimating the parameters of a Poisson arrival process where the rate function is assumed to lie in the span of a known basis. Our goal is to estimate the basis expansions coefficients given a…

For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect 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…

Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…

This paper proposes a novel parameter selection strategy for kernel-based gradient descent (KGD) algorithms, integrating bias-variance analysis with the splitting method. We introduce the concept of empirical effective dimension to quantify…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…