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    Pandora's Box Problem with Order Constraints

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    The Pandora's Box Problem, originally formalized by Weitzman in 1979, models selection from set of random, alternative options, when evaluation is costly. This includes, for example, the problem of hiring a skilled worker, where only one hire can be made, but the evaluation of each candidate is an expensive procedure. Weitzman showed that the Pandora's Box Problem admits an elegant, simple solution, where the options are considered in decreasing order of reservation value,i.e., the value that reduces to zero the expected marginal gain for opening the box. We study for the first time this problem when order - or precedence - constraints are imposed between the boxes. We show that, despite the difficulty of defining reservation values for the boxes which take into account both in-depth and in-breath exploration of the various options, greedy optimal strategies exist and can be efficiently computed for tree-like order constraints. We also prove that finding approximately optimal adaptive search strategies is NP-hard when certain matroid constraints are used to further restrict the set of boxes which may be opened, or when the order constraints are given as reachability constraints on a DAG. We complement the above result by giving approximate adaptive search strategies based on a connection between optimal adaptive strategies and non-adaptive strategies with bounded adaptivity gap for a carefully relaxed version of the problem

    Sequential Optimization for Efficient High-Quality Object Proposal Generation

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    We are motivated by the need for a generic object proposal generation algorithm which achieves good balance between object detection recall, proposal localization quality and computational efficiency. We propose a novel object proposal algorithm, BING++, which inherits the virtue of good computational efficiency of BING but significantly improves its proposal localization quality. At high level we formulate the problem of object proposal generation from a novel probabilistic perspective, based on which our BING++ manages to improve the localization quality by employing edges and segments to estimate object boundaries and update the proposals sequentially. We propose learning the parameters efficiently by searching for approximate solutions in a quantized parameter space for complexity reduction. We demonstrate the generalization of BING++ with the same fixed parameters across different object classes and datasets. Empirically our BING++ can run at half speed of BING on CPU, but significantly improve the localization quality by 18.5% and 16.7% on both VOC2007 and Microhsoft COCO datasets, respectively. Compared with other state-of-the-art approaches, BING++ can achieve comparable performance, but run significantly faster.Comment: Accepted by TPAM

    Sequential optimization for efficient high-quality object proposal generation

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    We are motivated by the need for a generic object proposal generation algorithm which achieves good balance between object detection recall, proposal localization quality and computational efficiency. We propose a novel object proposal algorithm, BING ++, which inherits the virtue of good computational efficiency of BING [1] but significantly improves its proposal localization quality. At high level we formulate the problem of object proposal generation from a novel probabilistic perspective, based on which our BING++ manages to improve the localization quality by employing edges and segments to estimate object boundaries and update the proposals sequentially. We propose learning the parameters efficiently by searching for approximate solutions in a quantized parameter space for complexity reduction. We demonstrate the generalization of BING++ with the same fixed parameters across different object classes and datasets. Empirically our BING++ can run at half speed of BING on CPU, but significantly improve the localization quality by 18.5 and 16.7 percent on both VOC2007 and Microhsoft COCO datasets, respectively. Compared with other state-of-the-art approaches, BING++ can achieve comparable performance, but run significantly faster
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