  In this paper, we consider the streaming memory-limited matrix completion
problem when the observed entries are noisy versions of a small random fraction
of the original entries. We are interested in scenarios where the matrix size
is very large so the matrix is very hard to store and manipulate. Here, columns
of the observed matrix are presented sequentially and the goal is to complete
the missing entries after one pass on the data with limited memory space and
limited computational complexity. We propose a streaming algorithm which
produces an estimate of the original matrix with a vanishing mean square error,
uses memory space scaling linearly with the ambient dimension of the matrix,
i.e. the memory required to store the output alone, and spends computations as
much as the number of non-zero entries of the input matrix.
