One Hundred Probability and Statistics Inequalities
Herein we present one hundred inequalities culled from various corners of the probability, statistics, and combinatorics literature. We welcome new suggestions.
math.ST↗
arXiv subjects
CNP Slagle
Publications and source records attributed to CNP Slagle.
Matrix Multiplication and Binary Space Partitioning Trees : An Exploration
Herein we explore a dual tree algorithm for matrix multiplication of $A\in \mathbb{R}^{M\times D}$ and $B\in\mathbb{R}^{D\times N}$, very narrowly effective if the normalized rows of $A$ and columns of $B$, treated as vectors in $\mathbb{R}^{D}$, fall into clusters of order proportionate to $\Omega(D^{\tau})$ with radii less than $\arcsin(\epsilon/\sqrt{2})$ on the surface of the unit $D$-ball. The algorithm leverages a pruning rule necessary to guarantee $\epsilon$ precision proportionate to vector magnitude products in the resultant matrix. \textit{ Unfortunately, if the rows and columns are uniformly distributed on the surface of the unit $D$-ball, then the expected points per required cluster approaches zero exponentially fast in $D$; thus, the approach requires a great deal of work to pass muster.}
cs.DS↗