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Learning to Understand: Identifying Interactions via the Mobius Transform
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 $K \rightarrow \infty$.
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