In statistical learning for real-world large-scale data problems, one must often resort to “streaming” algorithms which operate sequentially on small batches of data. In this work, we present an analysis of the information-theoretic limits of …

We analyze the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications, such as dictionary learning, blind matrix calibration, sparse …

We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of phase …

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