Related papers: Nystr\"om Kernel Stein Discrepancy Tests
The problem of comparing the entire second order structure of two functional processes is considered and a $L^2$-type statistic for testing equality of the corresponding spectral density operators is investigated. The test statistic…
Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…
Density ratio estimation (DRE) is a useful tool for quantifying discrepancies between probability distributions, but existing approaches often involve a trade-off between estimation quality and computational efficiency. Classical direct DRE…
Stochastic Gradient Descent (SGD) is very useful in optimization problems with high-dimensional non-convex target functions, and hence constitutes an important component of several Machine Learning and Data Analytics methods. Recently there…
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…
In recent years, quantum computers have emerged as promising candidates for implementing kernels. Quantum Embedding Kernels embed data points into quantum states and calculate their inner product in a high-dimensional Hilbert Space by…
We propose a hybrid method for accurately estimating the score function, i.e., the gradient of the log steady-state density, using a Gaussian Mixture Model (GMM) in conjunction with a bisecting K-means clustering step. Our approach, which…
We provide necessary and sufficient conditions for the uniqueness of the k-means set of a probability distribution. This uniqueness problem is related to the choice of k: depending on the underlying distribution, some values of this…
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…
Deep discriminative approaches, such as decision forests and deep neural networks, have recently found applications in many important real-world scenarios. However, deploying these learning algorithms in safety-critical applications raises…
In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly con- sistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an…
Despite their popularity, the practical performance of asynchronous stochastic gradient descent methods (ASGD) for solving large scale machine learning problems are not as good as theoretical results indicate. We adopt and analyze a…
Cross-validation is a widely used technique for evaluating the performance of prediction models, ranging from simple binary classification to complex precision medicine strategies. It helps correct for optimism bias in error estimates,…
Many particle-based Bayesian inference methods use a single global step size for all parts of the update. In Stein variational gradient descent (SVGD), however, each update combines two qualitatively different effects: attraction toward…
K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as…
Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…
Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…
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…
Kernel methods are powerful tools in various data analysis tasks. Yet, in many cases, their time and space complexity render them impractical for large datasets. Various kernel approximation methods were proposed to overcome this issue,…
The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected…