An analysis of chaining in multi-label classification

The idea of classifier chains has recently been introduced as a promising technique for multi-label classification. However, despite being intuitively appealing and showing strong performance in empirical studies, still very little is known about the main principles underlying this type of method. In this paper, we provide a detailed probabilistic analysis of classifier chains from a risk minimization perspective, thereby helping to gain a better understanding of this approach. As a main result, we clarify that the original chaining method seeks to approximate the joint mode of the conditional distribution of label vectors in a greedy manner. As a result of a theoretical regret analysis, we conclude that this approach can perform quite poorly in terms of subset 0/1 loss. Therefore, we present an enhanced inference procedure for which the worst-case regret can be upper-bounded far more tightly. In addition, we show that a probabilistic variant of chaining, which can be utilized for any loss function, becomes tractable by using Monte Carlo sampling. Finally, we present experimental results confirming the validity of our theoretical findings

Efficient Multi-Template Learning for Structured Prediction

Conditional random field (CRF) and Structural Support Vector Machine (Structural SVM) are two state-of-the-art methods for structured prediction which captures the interdependencies among output variables. The success of these methods is attributed to the fact that their discriminative models are able to account for overlapping features on the whole input observations. These features are usually generated by applying a given set of templates on labeled data, but improper templates may lead to degraded performance. To alleviate this issue, in this paper, we propose a novel multiple template learning paradigm to learn structured prediction and the importance of each template simultaneously, so that hundreds of arbitrary templates could be added into the learning model without caution. This paradigm can be formulated as a special multiple kernel learning problem with exponential number of constraints. Then we introduce an efficient cutting plane algorithm to solve this problem in the primal, and its convergence is presented. We also evaluate the proposed learning paradigm on two widely-studied structured prediction tasks, \emph{i.e.} sequence labeling and dependency parsing. Extensive experimental results show that the proposed method outperforms CRFs and Structural SVMs due to exploiting the importance of each template. Our complexity analysis and empirical results also show that our proposed method is more efficient than OnlineMKL on very sparse and high-dimensional data. We further extend this paradigm for structured prediction using generalized $p$-block norm regularization with $p>1$, and experiments show competitive performances when $p \in [1,2)$

Blending Learning and Inference in Structured Prediction

In this paper we derive an efficient algorithm to learn the parameters of structured predictors in general graphical models. This algorithm blends the learning and inference tasks, which results in a significant speedup over traditional approaches, such as conditional random fields and structured support vector machines. For this purpose we utilize the structures of the predictors to describe a low dimensional structured prediction task which encourages local consistencies within the different structures while learning the parameters of the model. Convexity of the learning task provides the means to enforce the consistencies between the different parts. The inference-learning blending algorithm that we propose is guaranteed to converge to the optimum of the low dimensional primal and dual programs. Unlike many of the existing approaches, the inference-learning blending allows us to learn efficiently high-order graphical models, over regions of any size, and very large number of parameters. We demonstrate the effectiveness of our approach, while presenting state-of-the-art results in stereo estimation, semantic segmentation, shape reconstruction, and indoor scene understanding

Structured learning of sum-of-submodular higher order energy functions

Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow \cite{KZ:PAMI04} has had significant impact in computer vision \cite{BVZ:PAMI01,Kwatra:SIGGRAPH03,Rother:GrabCut04}. In this paper we address the important class of sum-of-submodular (SoS) functions \cite{Arora:ECCV12,Kolmogorov:DAM12}, which can be efficiently minimized via a variant of max flow called submodular flow \cite{Edmonds:ADM77}. SoS functions can naturally express higher order priors involving, e.g., local image patches; however, it is difficult to fully exploit their expressive power because they have so many parameters. Rather than trying to formulate existing higher order priors as an SoS function, we take a discriminative learning approach, effectively searching the space of SoS functions for a higher order prior that performs well on our training set. We adopt a structural SVM approach \cite{Joachims/etal/09a,Tsochantaridis/etal/04} and formulate the training problem in terms of quadratic programming; as a result we can efficiently search the space of SoS priors via an extended cutting-plane algorithm. We also show how the state-of-the-art max flow method for vision problems \cite{Goldberg:ESA11} can be modified to efficiently solve the submodular flow problem. Experimental comparisons are made against the OpenCV implementation of the GrabCut interactive segmentation technique \cite{Rother:GrabCut04}, which uses hand-tuned parameters instead of machine learning. On a standard dataset \cite{Gulshan:CVPR10} our method learns higher order priors with hundreds of parameter values, and produces significantly better segmentations. While our focus is on binary labeling problems, we show that our techniques can be naturally generalized to handle more than two labels

Iterative Instance Segmentation

Existing methods for pixel-wise labelling tasks generally disregard the underlying structure of labellings, often leading to predictions that are visually implausible. While incorporating structure into the model should improve prediction quality, doing so is challenging - manually specifying the form of structural constraints may be impractical and inference often becomes intractable even if structural constraints are given. We sidestep this problem by reducing structured prediction to a sequence of unconstrained prediction problems and demonstrate that this approach is capable of automatically discovering priors on shape, contiguity of region predictions and smoothness of region contours from data without any a priori specification. On the instance segmentation task, this method outperforms the state-of-the-art, achieving a mean $\mathrm{AP}^{r}$ of 63.6% at 50% overlap and 43.3% at 70% overlap.Comment: 13 pages, 10 figures; IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 201