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...5) m in the classification and regression settings (an additional classification method is discussed in the accompanying technical report [7]). Support Vector Classification: Utilizing the setting of =-=[17]-=-we can have the following minimization problem (the original SVMs can be formulated in the same way): 1 minimize θ,ξ 2 ‖θ‖2 m∑ + C βiξi (6a) i=1 subject to 〈φ(xi, yi) − φ(xi, y), θ〉 ≥ 1 − ξi/∆(yi, y) ...

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... not clear how to incorporate non-linear multivariate loss functions such as MAP loss directly into global optimization problems such as SVM training. We now present a method based on structural SVMs =-=[19]-=- to address this problem. We use the structural SVM formulation, presented in Optimization Problem 1, to learn a w ∈ R N . Optimization Problem 1. (Structural SVM) 1 min w,ξ≥0 2 �w�2 + C n s.t. ∀i, ∀y...

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... are data dependent scalars that can be used for normalization when the examples are of different lengths. q ∈ {1, 2} distinguishes between L1 and L2 slack penalties commonly found in the literature (=-=Tsochantaridis et al., 2005-=-). If we consider the case for which both fi(·) and Li(·) are linear in the state-action frequencies µ as described above (i.e. they factor over state-action pairs), the maximum margin problem becomes...

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...ing points in the image, specifying the box orientation. Then, we sample pairs of rays from two of the vanishing points, which specifies the translation of the walls. We propose a structured learning =-=[25]-=- approach to select the joint set of parameters that is most likely to maximize the similarity to the ground truth box based on global perspective cues. The box layout and surface labels are difficult...

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...entation through the use of kernels [4, 8, 19]. Because of this flexibility of SVMs and their natural generalization to structured output spaces, we make use of the structured output SVM framework of =-=[18]-=-. In particular, we extend the online structured output SVM learning method proposed in [5, 6] and adapt it to the tracking problem. We find experimentally that the use of our framework results in lar...

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...gy (⋆) and the α-expansion-based inference algorithm can be used in supervised settings as well. The label cost terms are included in energy (⋆) linearly and can thus be learned by max-margin methods =-=[54,57]-=-. This approach was recently used for CRF learning, e.g. [53]. Acknowledgements We would like to thank Fredrik Kahl for referring us to the works of Li and Vidal, and for suggesting motion segmentatio...

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...e that is capable of learning dozens of parameters from millions of pixels in minutes. Our algorithm is based on the structured support vector machine (SVMstruct)2 framework of Tsochantaridis et al. =-=[8]-=- and the maximum-margin network learning of Taskar et al. [9,10]. These works were not focused on computer vision problems. They did not explore graph cuts for learning, and instead chose approximate ...

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...er let ξ ≥ 0 such that f(x, y) − f(x, y ′ ) ≥ ∆(y, y ′ ) − ξ for all y ′ ∈ Y. In this case ξ ≥ ∆(y, argmax y ′ ∈Y f(x, y ′ )). The construction of the estimator was suggested in [Taskar et al., 2003, =-=Tsochantaridis et al., 2005-=-], and a special instance of the above lemma is given by Joachims [2005]. While the bound appears quite innocuous, it allows us to describe a much richer class of estimation problems as a convex progr...

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...Pr(y ′ |w,xℓ)fk(xℓ,y ′ ) k =1···K 6. gk = ∑ ℓ gk,ℓ k =1···K 7. wt k = wt−1 k + γt(gk − 2w t−1 k /C) k =1···K (γt = learning rate) 8. Exit if ||g|| ≈ zero 3.4.2 Max-margin Training Max-margin trainers =-=[201, 208]-=- are an extension of support vector machines for training structured models. They are more generally applicable because they require only the computation of the output with the highest score. In contr...

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... all y ∈ Yi, and adding slack variables, we can express this mathematically as following convex program: λ min w,ζi 2 �w�2 + 1 n � i ζi s.t. ∀i w T fi(yi) + ζi ≥ max y∈Yi � w T fi(y) + Li(y) � (3) 2 (=-=Tsochantaridis et al., 2005-=-) describes an alternative formulation for MMSC based around scaling the slack variables by the loss rather than scaling the margin. Subgradient methods are applicable to this formulation as well, tho...