Related papers: Kernelized Complete Conditional Stein Discrepancy
Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as an inhomogeneous random graph model (IRG). For general fast goodness-of-fit tests in high dimensions, kernelised…
Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…
Sliced Stein discrepancy (SSD) and its kernelized variants have demonstrated promising successes in goodness-of-fit tests and model learning in high dimensions. Despite their theoretical elegance, their empirical performance depends…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
We investigate properties of goodness-of-fit tests based on the Kernel Stein Discrepancy (KSD). We introduce a strategy to construct a test, called KSDAgg, which aggregates multiple tests with different kernels. KSDAgg avoids splitting the…
This paper formally derives the asymptotic distribution of a goodness-of-fit test based on the Kernel Stein Discrepancy introduced in (Oscar Key et al., "Composite Goodness-of-fit Tests with Kernels", Journal of Machine Learning Research…
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…
Score-based kernelised Stein discrepancy (KSD) tests have emerged as a powerful tool for the goodness of fit tests, especially in high dimensions; however, the test performance may depend on the choice of kernels in an underlying…
Survival Analysis and Reliability Theory are concerned with the analysis of time-to-event data, in which observations correspond to waiting times until an event of interest such as death from a particular disease or failure of a component…
Kernel Stein discrepancy (KSD) is among the most popular goodness-of-fit (GoF) measures on general domains with a large number of successful deployments. One of the main applications of KSD is in constructing powerful GoF tests. However,…
Stein importance sampling is a widely applicable technique based on kernelized Stein discrepancy, which corrects the output of approximate sampling algorithms by reweighting the empirical distribution of the samples. A general analysis of…
Measure transport underpins several recent algorithms for posterior approximation in the Bayesian context, wherein a transport map is sought to minimise the Kullback--Leibler divergence (KLD) from the posterior to the approximation. The KLD…
We completely characterize the class of univariate distributions allowing for a Stein kernel and illustrate our result by means of some concrete distributions. Moreover, we apply our findings to prove a quantitative version of the central…
We introduce higher-order Stein kernels relative to the standard Gaussian measure, which generalize the usual Stein kernels by involving higher-order derivatives of test functions. We relate the associated discrepancies to various metrics…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Uncertainty evaluation is critical in scientific and engineering inverse problems. However, existing benchmarks on Diffusion Inverse Solvers (DIS) primarily focus on reconstruction accuracy but overlook uncertainty and distributional…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to…