This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a technique to constrain the search space based on the topology of the model. When pursued to the full search depth, the algorithm is guaranteed to converge to a global optimum, passing through a series of monotonously improving local optima that are guaranteed to be optimal within a given and increasing Hamming distance. For a search depth of 1, it specializes to Iterated Conditional Modes. Between these extremes, a useful tradeoff between approximation quality and runtime is established. Experiments on models derived from both illustrative and real problems show that approximations found with limited search depth match or improve those obtained by state-of-the-art methods based on message passing and linear programming.
The Lazy Flipper is related in at least four ways to existing work. First of all, it generalizes Iterated Conditional Modes (ICM) for binary variables @cite_5 . While ICM leaves all variables except one fixed in each step, the Lazy Flipper can optimize over larger (for small models: all) connected subgraphs of a graphical model. Furthermore, it extends Block-ICM @cite_14 that optimizes over specific subsets of variables in grid graphs to irregular and higher-order graphical models.
@cite_5 @cite_14
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We present an iterative approximate solution to the multidimensional assignment problem under general cost functions. The method maintains a feasible solution at every step, and is guaranteed to converge. It is similar to the iterated conditional modes (ICM) algorithm, but applied at each step to a block of variables representing correspondences between two adjacent frames, with the optimal conditional mode being calculated exactly as the solution to a two-frame linear assignment problem. Experiments with ground-truthed trajectory data show that the method outperforms both network-flow data association and greedy recursive filtering using a constant velocity motion model. Transductive Confidence Machine (TCM) and its computationally efficient modification, inductive confidence machine (ICM), are ways of complementing machine-learning algorithms with practically useful measures of confidence. We show that when TCM and ICM are used in the on-line mode, their confidence measures are well-calibrated, in the sense that predictive regions at confidence level 1- spl delta will be wrong with relative frequency at most spl delta (approaching spl delta in the case of randomised TCM and ICM) in the long run. This is not just an asymptotic phenomenon: actually the error probability of randomised TCM and ICM is d at every trial and errors happen independently at different trials.