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Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed…

This paper proposes a consensus-based distributed nonlinear filter with kernel mean embedding (KME). This fills with gap of posterior density approximation with KME for distributed nonlinear dynamic systems. To approximate the posterior…

A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…

We propose a system identification method, Non-Markovian Optimization-based Modeling for Approximate Dynamics with Spatially-homogeneous memory (NOMADS), for identifying linear dynamical systems from a set of multi-dimensional time-series…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…

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 consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…

A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…

We introduce a unified framework for learning the spatio-temporal dynamics of vector valued functions by combining operator valued reproducing kernel Hilbert spaces (OV-RKHS) with kernel based Koopman operator methods. The approach enables…

In this work, we develop and study an empirical projection operator scheme for solving nonparametric regression problems. This scheme is based on an approximate projection of the regression function over a suitable reproducing kernel…

This paper designs novel nonparametric Bellman mappings in reproducing kernel Hilbert spaces (RKHSs) for reinforcement learning (RL). The proposed mappings benefit from the rich approximating properties of RKHSs, adopt no assumptions on the…

One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale…

This paper derives a new class of vector-valued reproducing kernel Hilbert spaces (vRKHS) defined in terms of operator-valued kernels for the representation of functional uncertainty arising in nonparametric adaptive control methods. These…

In this paper, an adaptive non-parametric method is proposed to estimate the scalar-valued nonlinear function that appears in uncertain systems governed by ordinary differential equations (ODEs). By employing an infinite-dimensional…

A mathematical model for variable selection in functional regression models with scalar response is proposed. By "variable selection" we mean a procedure to replace the whole trajectories of the functional explanatory variables with their…

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…

We consider policy evaluation in infinite-horizon discounted Markov decision problems (MDPs) with infinite spaces. We reformulate this task a compositional stochastic program with a function-valued decision variable that belongs to a…

Understanding the behaviour of a quantum system coupled to its environment is of fundamental interest in the general field of quantum technologies. It also has important repercussions on foundational problems in physics, such as the process…