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Found 27 papers, 2 papers with code
Robust Topological Inference in the Presence of Outliers
The distance function to a compact set plays a crucial role in the paradigm of topological data analysis.
Characteristic and Universal Tensor Product Kernels
Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively.
Minimax Estimation of Quadratic Fourier Functionals
We study estimation of (semi-)inner products between two nonparametric probability distributions, given IID samples from each distribution.
Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings
This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces.
Adaptive Clustering Using Kernel Density Estimators
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters.
Convergence guarantees for kernel-based quadrature rules in misspecified settings
Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super-$\sqrt{n}$ convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high dimensional.
Optimal Rates for Random Fourier Features
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations.
On the Generalization Ability of Online Learning Algorithms for Pairwise Loss Functions
We are also able to analyze a class of memory efficient online learning algorithms for pairwise learning problems that use only a bounded subset of past training samples to update the hypothesis at each step.
Hilbert space embeddings and metrics on probability measures
First, we consider the question of determining the conditions on the kernel $k$ for which $\gamma_k$ is a metric: such $k$ are denoted {\em characteristic kernels}.
Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other.
On integral probability metrics, φ-divergences and binary classification
First, to understand the relation between IPMs and $\phi$-divergences, the necessary and sufficient conditions under which these classes intersect are derived: the total variation distance is shown to be the only non-trivial $\phi$-divergence that is also an IPM.
Information Theory Information Theory
On Kernel Derivative Approximation with Random Fourier Features
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms.
Minimax Estimation of Maximum Mean Discrepancy with Radial Kernels
Maximum Mean Discrepancy (MMD) is a distance on the space of probability measures which has found numerous applications in machine learning and nonparametric testing.
Optimal kernel choice for large-scale two-sample tests
A means of parameter selection for the two-sample test based on the MMD is proposed.
Learning in Hilbert vs. Banach Spaces: A Measure Embedding Viewpoint
The goal of this paper is to investigate the advantages and disadvantages of learning in Banach spaces over Hilbert spaces.
A Fast, Consistent Kernel Two-Sample Test
A kernel embedding of probability distributions into reproducing kernel Hilbert spaces (RKHS) has recently been proposed, which allows the comparison of two probability measures P and Q based on the distance between their respective embeddings: for a sufficiently rich RKHS, this distance is zero if and only if P and Q coincide.
On the Convergence of the Concave-Convex Procedure
In this paper, we follow a different reasoning and show how Zangwills global convergence theory of iterative algorithms provides a natural framework to prove the convergence of CCCP, allowing a more elegant and simple proof.
Characteristic Kernels on Groups and Semigroups
Embeddings of random variables in reproducing kernel Hilbert spaces (RKHSs) may be used to conduct statistical inference based on higher order moments.
Local minimax rates for closeness testing of discrete distributions
We consider the closeness testing problem for discrete distributions.
Gaussian Sketching yields a J-L Lemma in RKHS
The main contribution of the paper is to show that Gaussian sketching of a kernel-Gram matrix $\boldsymbol K$ yields an operator whose counterpart in an RKHS $\mathcal H$, is a \emph{random projection} operator---in the spirit of Johnson-Lindenstrauss (J-L) lemma.
On Distance and Kernel Measures of Conditional Independence
For certain distance and kernel pairs, we show the distance-based conditional independence measures to be equivalent to that of kernel-based measures.
Cycle Consistent Probability Divergences Across Different Spaces
Discrepancy measures between probability distributions are at the core of statistical inference and machine learning.
Shrinkage Estimation of Higher Order Bochner Integrals
We propose estimators that shrink the $U$-statistic estimator of the Bochner integral towards a pre-specified target element in the Hilbert space.
Regularized Stein Variational Gradient Flow
In this work, we propose the Regularized Stein Variational Gradient Flow which interpolates between the Stein Variational Gradient Flow and the Wasserstein Gradient Flow.
Spectral Regularized Kernel Two-Sample Tests
First, we show that the popular MMD (maximum mean discrepancy) two-sample test is not optimal in terms of the separation boundary measured in Hellinger distance.
Kernel $ε$-Greedy for Contextual Bandits
We also show that for any choice of kernel and the corresponding RKHS, we achieve a sub-linear regret rate depending on the intrinsic dimensionality of the RKHS.
Spectral Regularized Kernel Goodness-of-Fit Tests
Maximum mean discrepancy (MMD) has enjoyed a lot of success in many machine learning and statistical applications, including non-parametric hypothesis testing, because of its ability to handle non-Euclidean data.
