2023/08/27 by William He, He, William, Shivam Nadimpalli +1
Computer Science · #Algorithms and Data Compression #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning and Algorithms #Machine Learning and Data Classification #Probability (math.PR) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2308.13992
openalex publication_date 2023/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the basic statistical problem of detecting truncation of the uniform distribution on the Boolean hypercube by juntas. More concretely, we give upper and lower bounds on the problem of distinguishing between i.i.d. sample access to either (a) the uniform distribution over \0,1\n, or (b) the uniform distribution over \0,1\n conditioned on the satisfying assignments of a k-junta f: \0,1\n→\0,1\. We show that (up to constant factors) min\2k + logn\choose k, 2k/2log1/2n\choose k\ samples suffice for this task and also show that a logn\choose k dependence on sample complexity is unavoidable. Our results suggest that testing junta truncation requires learning the set of relevant variables of the junta.