arXiv:2608.29265v1 Announce Type: cross
Abstract: Kernel density estimation (KDE) is one of the most fundamental statistical estimators of density functions. Its direct implementation on a dataset of...
By Xie Wang, Nicolas Langren\'e, Wen Chen
arXiv:2609.15179v1 Announce Type: cross
Abstract: The Gaussian kernel is a widely used similarity measure underlying kernel methods such as kernel PCA and spectral clustering, but computing Gaussian...
By Soumik Dutta, Kunal Dutta
arXiv:2409. 08469v4 Announce Type: replace-cross Abstract: We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics.
By Sayan Banerjee, Krishnakumar Balasubramanian, Promit Ghosal
arXiv:2609. 02155v1 Announce Type: new Abstract: The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal.
By Piyush Sao
arXiv:2004. 05813v3 Announce Type: replace-cross Abstract: Suppose that we are given independent, identically distributed random samples $x_1,\cdots,x_n$ from a mixture at most $k$ many $d$-dimensional spherical Gaussian distributions $\mu_1,\cdots,\mu_{k_0}$ of identical and known variance $\sigma^2$ in each coordinate, such that the minimum $\ell^2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $2\Delta\sigma \min\{\sqrt{d},\sqrt k\}$, where $\Delta>C_0$, and $C_0$ is a sufficiently large universal constant.
By Somnath Chakraborty, Hariharan Narayanan
Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem. Standard subspace embeddings guarantee that the cost of the regress...