Related papers: Functional Bayesian Filter
The paper provides simple formulas of Bayesian filtering for the exact recursive computation of state conditional probability density functions given quantized innovations signal measurements of a linear stochastic system. This is a topic…
The Boolean Kalman Filter and associated Boolean Dynamical System Theory have been proposed to study the spread of infection on computer networks. Such models feature a network where attacks propagate through, an intrusion detection system…
For recursive circular filtering based on circular statistics, we introduce a general framework for estimation of a circular state based on different circular distributions, specifically the wrapped normal distribution and the von Mises…
We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of…
This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter which provides an exact solution for the linear Gaussian…
Bayesian optimization (BO) is an efficient framework for optimizing expensive black-box functions. However, it is typically formulated as learning an end-to-end mapping from inputs to scalar objectives, thereby discarding the potentially…
We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that…
This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental…
Under the reproducing kernel Hilbert spaces (RKHS), we consider the penalized least-squares of the partially functional linear models (PFLM), whose predictor contains both functional and traditional multivariate parts, and the multivariate…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under…
Due to the limitations of the robotic sensors, during a robotic manipulation task, the acquisition of the object's state can be unreliable and noisy. Combining an accurate model of multi-body dynamic system with Bayesian filtering methods…
Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…
The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…
The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…
We introduce Deep Variational Bayes Filters (DVBF), a new method for unsupervised learning and identification of latent Markovian state space models. Leveraging recent advances in Stochastic Gradient Variational Bayes, DVBF can overcome…
The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm…
We introduce a novel nonlinear Kalman filter that utilizes reparametrization gradients. The widely used parametric approximation is based on a jointly Gaussian assumption of the state-space model, which is in turn equivalent to minimizing…
Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series.…
Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…