Related papers: A Kernel Mean Embedding Approach to Reducing Conse…

We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…

Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows…

Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of…

Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale…

We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference…

This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic…

We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric…

The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…

Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and…

A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…

We present an empirical, gradient-based method for solving data-driven stochastic optimal control problems using the theory of kernel embeddings of distributions. By embedding the integral operator of a stochastic kernel in a reproducing…

We propose a practical Bayesian optimization method over sets, to minimize a black-box function that takes a set as a single input. Because set inputs are permutation-invariant, traditional Gaussian process-based Bayesian optimization…

In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…

Kernel conditional mean embeddings (CMEs) offer a powerful framework for representing conditional distribution, but they often face scalability and expressiveness challenges. In this work, we propose a new method that effectively combines…

We study the comparison problem of distribution equality between two random samples under a right censoring scheme. To address this problem, we design a series of tests based on energy distance and kernel mean embeddings. We calibrate our…