It is attractive to formulate problems in computer vision and related fields in term of probabilis- tic estimation where the probability models are defined over graphs, such as grammars. The graphical struc- tures, an...It is attractive to formulate problems in computer vision and related fields in term of probabilis- tic estimation where the probability models are defined over graphs, such as grammars. The graphical struc- tures, and the state variables defined over them, give a rich knowledge representation which can describe the complex structures of objects and images. The proba- bility distributions defined over the graphs capture the statistical variability of these structures. These proba- bility models can be learnt from training data with lim- ited amounts of supervision. But learning these models suffers from the difficulty of evaluating the normaliza- tion constant, or partition function, of the probability distributions which can be extremely computationally demanding. This paper shows that by placing bounds on the normalization constant we can obtain compu- rationally tractable approximations. Surprisingly, for certain choices of loss functions, we obtain many of the standard max-margin criteria used in support vector machines （SVMs） and hence we reduce the learning to standard machine learning methods. We show that many machine learning methods can be obtained in this way as approximations to probabilistic methods including multi-class max-margin, ordinal regression, max-margin Markov networks and parsers, multiple- instance learning, and latent SVM. We illustrate this work by computer vision applications including image labeling, object detection and localization, and motion estimation. We speculate that rained by using better bounds better results can be ob- and approximations.展开更多
文摘It is attractive to formulate problems in computer vision and related fields in term of probabilis- tic estimation where the probability models are defined over graphs, such as grammars. The graphical struc- tures, and the state variables defined over them, give a rich knowledge representation which can describe the complex structures of objects and images. The proba- bility distributions defined over the graphs capture the statistical variability of these structures. These proba- bility models can be learnt from training data with lim- ited amounts of supervision. But learning these models suffers from the difficulty of evaluating the normaliza- tion constant, or partition function, of the probability distributions which can be extremely computationally demanding. This paper shows that by placing bounds on the normalization constant we can obtain compu- rationally tractable approximations. Surprisingly, for certain choices of loss functions, we obtain many of the standard max-margin criteria used in support vector machines （SVMs） and hence we reduce the learning to standard machine learning methods. We show that many machine learning methods can be obtained in this way as approximations to probabilistic methods including multi-class max-margin, ordinal regression, max-margin Markov networks and parsers, multiple- instance learning, and latent SVM. We illustrate this work by computer vision applications including image labeling, object detection and localization, and motion estimation. We speculate that rained by using better bounds better results can be ob- and approximations.
