Related papers: Copula-Stein Discrepancy: A Generator-Based Stein …
Uncertain information on input parameters of reliability models is usually modeled by considering these parameters as random, and described by marginal distributions and a dependence structure of these variables. In numerous real-world…
Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by…
In this paper, we report on a correctly scaling novel coupled cluster singles and doubles (CCSD) implementation for arbitrary high-spin open-shell states. The chosen cluster operator is completely spin-free, i.e. employs spatial…
Nonparametric estimation of copula density functions using kernel estimators presents significant challenges. One issue is the potential unboundedness of certain copula density functions at the corners of the unit square. Another is the…
An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods…
We enlarge the number of available functional depths by introducing the kernelized functional spatial depth (KFSD). KFSD is a local-oriented and kernel-based version of the recently proposed functional spatial depth (FSD) that may be useful…
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…
Gradient estimation -- approximating the gradient of an expectation with respect to the parameters of a distribution -- is central to the solution of many machine learning problems. However, when the distribution is discrete, most common…
Every copula $ C $ for a random vector $ {\bf X}=(X_1,\dots,X_d) $ with identically distributed coordinates determines a unique copula $ C_{:d} $ for its order statistic $ {\bf X}_{:d}=(X_{1:d},\dots,X_{d:d}) $. In the present paper we…
Distributed Stein Variational Gradient Descent (DSVGD) is a non-parametric distributed learning framework for federated Bayesian learning, where multiple clients jointly train a machine learning model by communicating a number of non-random…
Stein variational gradient descent (SVGD) is a deterministic particle inference algorithm that provides an efficient alternative to Markov chain Monte Carlo. However, SVGD has been found to suffer from variance underestimation when the…
We study the Stochastic Gradient Descent (SGD) algorithm in nonparametric statistics: kernel regression in particular. The directional bias property of SGD, which is known in the linear regression setting, is generalized to the kernel…
We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model's log-density. We estimate the Stein discrepancy between the data density $p(x)$…
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…
Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a…
The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence,…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
Dataset distillation (DD) aims to compress large-scale datasets into compact synthetic counterparts for efficient model training. However, existing DD methods exhibit substantial performance degradation on long-tailed datasets. We identify…
This paper introduces a nonparametric copula-based index for detecting the strength and monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals. Our index, termed Copula…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…