1 code implementation • 9 Mar 2024 • Prarabdh Shukla, Gagan Raj Gupta, Kunal Dutta
We rigorously prove that DiffRed achieves a general upper bound of $O\left(\sqrt{\frac{1-p}{k_2}}\right)$ on Stress and $O\left(\frac{(1-p)}{\sqrt{k_2*\rho(A^{*})}}\right)$ on M1 where $p$ is the fraction of variance explained by the first $k_1$ principal components and $\rho(A^{*})$ is the stable rank of $A^{*}$.
no code implementations • 19 Nov 2021 • Kunal Dutta, Arijit Ghosh, Shay Moran
We study the connections between three seemingly different combinatorial structures - "uniform" brackets in statistics and probability theory, "containers" in online and distributed learning theory, and "combinatorial Macbeath regions", or Mnets in discrete and computational geometry.
no code implementations • 12 Dec 2014 • Kunal Dutta, Arijit Ghosh
We prove a size-sensitive version of Haussler's Packing lemma~\cite{Haussler92spherepacking} for set-systems with bounded primal shatter dimension, which have an additional {\em size-sensitive property}.