no code implementations • 4 Feb 2024 • Justin S. Kang, Yigit E. Erginbas, Landon Butler, Ramtin Pedarsani, Kannan Ramchandran
In the case where all interactions are between at most $t = \Theta(n^{\alpha})$ inputs, for $\alpha < 0. 409$, we are able to leverage results from group testing to provide the first algorithm that computes the Mobius transform in $O(Kt\log n)$ sample complexity and $O(K\mathrm{poly}(n))$ time with vanishing error as $K \rightarrow \infty$.