StructBoost: Boosting Methods for Predicting Structured Output Variables

Abstract

Abstract-Boosting is a method for learning a single accurate predictor by linearly combining a set of less accurate weak learners. Recently, structured learning has found many applications in computer vision. Inspired by structured support vector machines (SSVM), here we propose a new boosting algorithm for structured output prediction, which we refer to as StructBoost. StructBoost supports nonlinear structured learning by combining a set of weak structured learners. As SSVM generalizes SVM, our StructBoost generalizes standard boosting approaches such as AdaBoost, or LPBoost to structured learning. The resulting optimization problem of StructBoost is more challenging than SSVM in the sense that it may involve exponentially many variables and constraints. In contrast, for SSVM one usually has an exponential number of constraints and a cutting-plane method is used. In order to efficiently solve StructBoost, we formulate an equivalent 1-slack formulation and solve it using a combination of cutting planes and column generation. We show the versatility and usefulness of StructBoost on a range of problems such as optimizing the tree loss for hierarchical multi-class classification, optimizing the Pascal overlap criterion for robust visual tracking and learning conditional random field parameters for image segmentation.

Structured Learning of Tree Potentials in CRF for Image Segmentation

“…Moreover, compared to the above mentioned works of [5] and [24], we achieve nonlinear learning on both the unary and the pairwise terms while theirs are limited to nonlinear unary potential learning. The recent work of Shen et al [31] generalizes standard boosting methods to structured learning, which shares similarities to our work here. However, our method bears critical differences from theirs: 1) We design a column generation method for non-linear tree potentials learning in CRFs directly from the SSVMs formulation.…”

“…3) We learn class-wise decision trees (potentials) for each object that appears in the image. This is different from [31]. The work of decision tree fields [28] is close to ours in that they also use decision trees to model the pairwise potentials.…”

“…However, our method bears critical differences from theirs: 1) We design a column generation method for non-linear tree potentials learning in CRFs directly from the SSVMs formulation. Different from the case in [31], which can directly derive column generation method analogous to LPBoost [8], our derivation here is more challenging. This is because we can not obtain the most violated constraint from the constraints of the dual problem, on which the column generation technique relies.…”

“…This is an important difference compared to existing column generation techniques. 2) We develop a CRFs learning method for multi-class semantic segmentation, while [31] only shows CRFs learning for binary foreground/background segmentation. Our experiments on the MSRC-21 dataset shows that our method achieves state-of-theart results.…”

Structured Learning of Binary Codes with Column Generation for Optimizing Ranking Measures

“…Here we exploit the stage-wise learning strategy to speedup the training. In column generation based totallycorrective boosting methods [29,30,31], all the hash function weights w are updated during each column generation iteration. In contrast, in stage-wise boosting, e.g., AdaBoost, only the weight of the newly added weak learner is updated in the current boosting iteration and weights of all previous weak learners are fixed.…”