Related papers: Hilbert Space Embeddings of Predictive State Repre…

Learning from examples is one of the key problems in science and engineering. It deals with function reconstruction from a finite set of direct and noisy samples. Regularization in reproducing kernel Hilbert spaces (RKHSs) is widely used to…

Since its introduction, the Discrete Variable Representation (DVR) basis set has become an invaluable representation of state vectors and Hermitian operators in non-relativistic quantum dynamics and spectroscopy calculations. On the other…

This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…

Predictive equivalence in discrete stochastic processes have been applied with great success to identify randomness and structure in statistical physics and chaotic dynamical systems and to inferring hidden Markov models. We examine the…

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…

The successor representation (SR) provides a powerful framework for decoupling predictive dynamics from rewards, enabling rapid generalisation across reward configurations. However, the classical SR is limited by its inherent policy…

In this paper we consider self-supervised representation learning to improve sample efficiency in reinforcement learning (RL). We propose a forward prediction objective for simultaneously learning embeddings of states and action sequences.…

Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…

This work explores how to learn robust and generalizable state representation from image-based observations with deep reinforcement learning methods. Addressing the computational complexity, stringent assumptions and representation collapse…

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…

While reinforcement learning has achieved considerable successes in recent years, state-of-the-art models are often still limited by the size of state and action spaces. Model-free reinforcement learning approaches use some form of state…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

Reasoning from sequences of raw sensory data is a ubiquitous problem across fields ranging from medical devices to robotics. These problems often involve using long sequences of raw sensor data (e.g. magnetometers, piezoresistors) to…

When robots learn reward functions using high capacity models that take raw state directly as input, they need to both learn a representation for what matters in the task -- the task ``features" -- as well as how to combine these features…

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…

Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference…

Intelligent agents can cope with sensory-rich environments by learning task-agnostic state abstractions. In this paper, we propose an algorithm to approximate causal states, which are the coarsest partition of the joint history of actions…

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…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…