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Dynamic Tree Block Coordinate Ascent
"... This paper proposes a novel Linear Programming (LP) based algorithm, called Dynamic TreeBlock Coordinate Ascent (DTBCA), for performing maximum a posteriori (MAP) inference in probabilistic graphical models. Unlike traditional message passing algorithms, which operate uniformly on the whole factor ..."
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Cited by 15 (5 self)
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This paper proposes a novel Linear Programming (LP) based algorithm, called Dynamic TreeBlock Coordinate Ascent (DTBCA), for performing maximum a posteriori (MAP) inference in probabilistic graphical models. Unlike traditional message passing algorithms, which operate uniformly on the whole factor graph, our method dynamically chooses regions of the factor graph on which to focus messagepassing efforts. We propose two criteria for selecting regions, including an efficiently computable upperbound on the increase in the objective possible by passing messages in any particular region. This bound is derived from the theory of primaldual methods from combinatorial optimization, and the forest that maximizes the bounds can be chosen efficiently using a maximumspanningtreelike algorithm. Experimental results show that our dynamic schedules significantly speed up stateoftheart LPbased messagepassing algorithms on a wide variety of realworld problems. 1.
Graph Cuts is a MaxProduct Algorithm
"... The maximum a posteriori (MAP) configuration of binary variable models with submodular graphstructured energy functions can be found efficiently and exactly by graph cuts. Maxproduct belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexa ..."
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Cited by 6 (1 self)
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The maximum a posteriori (MAP) configuration of binary variable models with submodular graphstructured energy functions can be found efficiently and exactly by graph cuts. Maxproduct belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP converges to a suboptimal fixed point (Kulesza & Pereira, 2008). In this work, we show that under a particular scheduling and damping scheme, MP is equivalent to graph cuts, and thus optimal. We explain the apparent contradiction by showing that with proper scheduling and damping, MP always converges to an optimal fixed point. Thus, the canonical counterexample only shows the suboptimality of MP with a particular suboptimal choice of schedule and damping. With proper choices, MP is optimal. 1