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This paper considers the problem of matrix-variate logistic regression. This paper derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by deriving a lower bound on the minimax risk. The bound depends explicitly on the dimension and distribution of the covariates, the rank and energy of the coefficient matrix, and the number of samples. The resulting bound is proportional to the intrinsic degrees of freedom in the problem, which suggests the sample complexity of the low-rank matrix logistic regression problem can be lower than that for vectorized logistic regression. The proof techniques utilized in this work also set the stage for development of minimax lower bounds for tensor-variate logistic regression problems.more » « less
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Ghassemi, Mohsen ; Shakeri, Zahra ; Sarwate, Anand D. ; Bajwa, Waheed U. ( , IEEE Transactions on Signal Processing)
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Ghassemi, Mohsen ; Sarwate, Anand D. ( , 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton))
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Ghassemi, Mohsen ; Sarwate, Anand D. ; Wright, Rebecca N. ( , Proceedings of the 2016 ACM Workshop on Artificial Intelligence and Security)