665 research outputs found
Sufficient conditions for convergence of the Sum-Product Algorithm
We derive novel conditions that guarantee convergence of the Sum-Product
algorithm (also known as Loopy Belief Propagation or simply Belief Propagation)
to a unique fixed point, irrespective of the initial messages. The
computational complexity of the conditions is polynomial in the number of
variables. In contrast with previously existing conditions, our results are
directly applicable to arbitrary factor graphs (with discrete variables) and
are shown to be valid also in the case of factors containing zeros, under some
additional conditions. We compare our bounds with existing ones, numerically
and, if possible, analytically. For binary variables with pairwise
interactions, we derive sufficient conditions that take into account local
evidence (i.e., single variable factors) and the type of pair interactions
(attractive or repulsive). It is shown empirically that this bound outperforms
existing bounds.Comment: 15 pages, 5 figures. Major changes and new results in this revised
version. Submitted to IEEE Transactions on Information Theor
GraphLab: A New Framework for Parallel Machine Learning
Designing and implementing efficient, provably correct parallel machine
learning (ML) algorithms is challenging. Existing high-level parallel
abstractions like MapReduce are insufficiently expressive while low-level tools
like MPI and Pthreads leave ML experts repeatedly solving the same design
challenges. By targeting common patterns in ML, we developed GraphLab, which
improves upon abstractions like MapReduce by compactly expressing asynchronous
iterative algorithms with sparse computational dependencies while ensuring data
consistency and achieving a high degree of parallel performance. We demonstrate
the expressiveness of the GraphLab framework by designing and implementing
parallel versions of belief propagation, Gibbs sampling, Co-EM, Lasso and
Compressed Sensing. We show that using GraphLab we can achieve excellent
parallel performance on large scale real-world problems
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