Many classes of images exhibit sparse structuring of statistical dependency. Each variable has strong statistical dependency with a small number of other variables and negligible dependency with the remaining ones. Such structuring makes it possible to construct a powerful classifier by only representing the stronger dependencies among the variables. In particular, a semi-naive Bayes classifier compactly represents sparseness. A semi-naive Bayes classifier decomposes the input variables into subsets and represents statistical dependency within each subset, while treating the subsets as statistically independent. However, learning the structure of a semi-naive Bayes classifier is known to be NP complete. The high dimensionality of images makes statistical structure learning especially challenging. This paper describes an algorithm that searches for the structure of a semi-naive Bayes classifier in this large space of possible structures. The algorithm seeks to optimize two cost functions: a localized error in the log-likelihood ratio function to restrict the structure and a global classification error to choose the final structure. We use this approach to train detectors for several objects including faces, eyes, ears, telephones, push-carts, and door-handles. These detectors perform robustly with a high detection rate and low false alarm rate in unconstrained settings over a wide range of variation in background scenery and lighting.
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