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Found 13 papers, 3 papers with code
Minimax Optimal Goodness-of-Fit Testing with Kernel Stein Discrepancy
We explore the minimax optimality of goodness-of-fit tests on general domains using the kernelized Stein discrepancy (KSD).
Statistical Optimality and Computational Efficiency of Nyström Kernel PCA
Various approximation schemes have been proposed in the literature to alleviate these computational issues, and the approximate kernel machines are shown to retain the empirical performance.
Robust Persistence Diagrams using Reproducing Kernels
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram.
Gain with no Pain: Efficient Kernel-PCA by Nyström Sampling
In this paper, we propose and study a Nystr\"om based approach to efficient large scale kernel principal component analysis (PCA).
Approximate Kernel PCA Using Random Features: Computational vs. Statistical Trade-off
We show that the approximate KPCA is both computationally and statistically efficient compared to KPCA in terms of the error associated with reconstructing a kernel function based on its projection onto the corresponding eigenspaces.
Kernel Mean Embedding of Distributions: A Review and Beyond
Next, we discuss the Hilbert space embedding for conditional distributions, give theoretical insights, and review some applications.
Learning Theory for Distribution Regression
In this paper, we study a simple, analytically computable, ridge regression-based alternative to distribution regression, where we embed the distributions to a reproducing kernel Hilbert space, and learn the regressor from the embeddings to the outputs.
Kernel Mean Estimation via Spectral Filtering
The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e. g., when centering a kernel PCA matrix), and it also forms the core inference step of modern kernel methods (e. g., kernel-based non-parametric tests) that rely on embedding probability distributions in RKHSs.
Kernel Mean Shrinkage Estimators
A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is central to kernel methods in that it is used by many classical algorithms such as kernel principal component analysis, and it also forms the core inference step of modern kernel methods that rely on embedding probability distributions in RKHSs.
Two-stage Sampled Learning Theory on Distributions
To the best of our knowledge, the only existing method with consistency guarantees for distribution regression requires kernel density estimation as an intermediate step (which suffers from slow convergence issues in high dimensions), and the domain of the distributions to be compact Euclidean.
Density Estimation in Infinite Dimensional Exponential Families
When $p_0\in\mathcal{P}$, we show that the proposed estimator is consistent, and provide a convergence rate of $n^{-\min\left\{\frac{2}{3},\frac{2\beta+1}{2\beta+2}\right\}}$ in Fisher divergence under the smoothness assumption that $\log p_0\in\mathcal{R}(C^\beta)$ for some $\beta\ge 0$, where $C$ is a certain Hilbert-Schmidt operator on $H$ and $\mathcal{R}(C^\beta)$ denotes the image of $C^\beta$.
Kernel Mean Estimation and Stein's Effect
A mean function in reproducing kernel Hilbert space, or a kernel mean, is an important part of many applications ranging from kernel principal component analysis to Hilbert-space embedding of distributions.
Equivalence of distance-based and RKHS-based statistics in hypothesis testing
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as established in machine learning.
