Related papers: A Note on Optimizing Distributions using Kernel Me…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…
Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this…
We propose an (offline) multi-dimensional distributional reinforcement learning framework (KE-DRL) that leverages Hilbert space mappings to estimate the kernel mean embedding of the multi-dimensional value distribution under a proposed…
This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…
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…
In this work we consider the problem of numerical integration, i.e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand. We focus on the setting in which the target…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic…
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…
In the context of kernel density estimation, we give a characterization of the kernels for which the parametric mean integrated squared error rate $n^{-1}$ may be obtained, where $n$ is the sample size. Also, for the cases where this rate…
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…
Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…
The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…
This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…
Estimating the kernel mean in a reproducing kernel Hilbert space is a critical component in many kernel learning algorithms. Given a finite sample, the standard estimate of the target kernel mean is the empirical average. Previous works…