A channel coding perspective of recommendation systems

Authors:
S. T. Aditya;Onkar Dabeer;Bikash Kumar Dey
Affiliations:
Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India;School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India;Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Year:
2009

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Abstract

Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size m × n) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix after unknown row and column permutations, erasures, and errors. We derive upper and lower bounds on the achievable probability of error. For fixed erasure and error probability, we show that there exists a constant C1 such that if the cluster sizes are less than C1 ln(mn), then for any algorithm the probability of error approaches one as m, n → ∞. On the other hand, we show that a simple polynomial time algorithm gives probability of error diminishing to zero provided the cluster sizes are greater than C2 ln(mn) for a suitable constant C2.