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In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…
The analysis of human microbiome data is often based on dimension-reduced graphical displays and clustering derived from vectors of microbial abundances in each sample. Common to these ordination methods is the use of biologically motivated…
Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform…
We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…
Modeling multiple sampling densities within a hierarchical framework enables borrowing of information across samples. These density random effects can act as kernels in latent variable models to represent exchangeable subgroups or clusters.…
Structural graph parameters play an important role in parameterized complexity, including in kernelization. Notably, vertex cover, neighborhood diversity, twin-cover, and modular-width have been studied extensively in the last few years.…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
Motivated by second order asymptotic results, we characterize the convergence in law of double integrals, with respect to Poisson random measures, toward a standard Gaussian distribution. Our conditions are expressed in terms of…
We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random…
Markov kernels play a decisive role in probability and mathematical statistics theories, and are an extension of the concepts of sigma-field and statistic. Concepts such as independence, sufficiency, completeness, ancillarity or conditional…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
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…
We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection $\{(S_i,l_i)\}_{i=1}^n$, where each $S_i$ is a sample drawn from the probability distribution of $X_i…
Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less…
We show that the incorporation of any new piece of information allows for improved decision making in the sense that the expected costs of an optimal decision decrease (or, in boundary cases where no or not enough new information is…
Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…
The log-determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
Many leading classification algorithms output a classifier that is a weighted average of kernel evaluations. Optimizing these weights is a nontrivial problem that still attracts much research effort. Furthermore, explaining these methods to…