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Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms…
The crucial step in designing a particle filter for a particular application is the choice of importance density. The optimal scheme is to use the conditional posterior density of the state, but this cannot be sampled or calculated…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for…
Often in applications such as rare events estimation or optimal control it is required that one calculates the principal eigen-function and eigen-value of a non-negative integral kernel. Except in the finite-dimensional case, usually…
The goal of this note is to show that continuous functions may be approximated using scattered translates of the Poisson kernel.
This paper presents a simple and efficient method to convolve an image with a Gaussian kernel. The computation is performed in a constant number of operations per pixel using running sums along the image rows and columns. We investigate the…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
This paper is concerned with the convergence and the error analysis for the feedback particle filter (FPF) algorithm. The FPF is a controlled interacting particle system where the control law is designed to solve the nonlinear filtering…
A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…
Reinforcement learning utilizing kernel ridge regression to predict the expected value function represents a powerful method with great representational capacity. This setting is a highly versatile framework amenable to analytical results.…
Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing a loss function derived from the governing equations and…
We present a probabilistic framework for both (i) determining the initial settings of kernel adaptive filters (KAFs) and (ii) constructing fully-adaptive KAFs whereby in addition to weights and dictionaries, kernel parameters are learnt…
Feedback particle filter (FPF) is a Monte-Carlo (MC) algorithm to approximate the solution of a stochastic filtering problem. In contrast to conventional particle filters, the Bayesian update step in FPF is implemented via a mean-field type…
Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian…
Error entropy is a important nonlinear similarity measure, and it has received increasing attention in many practical applications. The default kernel function of error entropy criterion is Gaussian kernel function, however, which is not…