This paper studies distributions which
can be ``approximated'' by sampling algorithms in time polynomial in
the length of their outputs. First, it is known that if
polynomial-time samplable distributions are polynomial-time
computable, then NP collapses to P. This paper shows by a simple
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A recommendation system suggests products to users based on data about user preferences. It is typically modeled by a problem of completing an $m\times n$ matrix of small rank $k$. We give the first classical algorithm to produce a recommendation in $O(\text{poly}(k)\text{polylog}(m,n))$ time, which is an exponential improvement on previous ... more >>>