Optimal rates for density and mode estimation with expand-and-sparsify representations

ArXi:2602.06175v2 Announce Type: replace-cross Expand-and-sparsify representations are a class of theoretical models that capture sparse representation phenomena observed in the sensory systems of many animals. At a high level, these representations map an input $x \in \mathbb{R}^d$ to a much higher dimension $m \gg d$ via random linear projections before zeroing out all but the $k \ll m$ largest entries. The result is a $k$-sparse vector in $\{0,1\}^m$. We study the suitability of this representation for two fundamental statistical problems: density estimation and mode estimation.