While Markov Random Fields (MRFs) are widely used in computer vision, they present a quite challenging inference problem. MRF inference can be accelerated by pre-processing techniques like Dead End Elimination (DEE) or QPBO-based approaches which compute the optimal labeling of a subset of variables. These techniques are guaranteed to never wrongly label a variable but they often leave a large number of variables unlabeled. We address this shortcoming by interpreting pre-processing as a classification problem, which allows us to trade off false positives (i.e., giving a variable an incorrect label) versus false negatives (i.e., failing to label a variable). We describe an efficient discriminative rule that finds optimal solutions for a subset of variables. Our technique provides both per-instance and worst-case guarantees concerning the quality of the solution. Empirical studies were conducted over several benchmark datasets. We obtain a speedup factor of 2 to 12 over expansion moves without preprocessing, and on difficult non-submodular energy functions produce slightly lower energy.
There are also techniques directly finding optimal partial labeling for the multi-label case, but the computational costs for these methods are significant. Kovtun @cite_30 @cite_25 described an approach constructing a series of binary one-verse-the-rest auxiliary problems and solve each of them via graph cuts. MQPBO @cite_24 and generalized roof duality @cite_4 proposed generalizations of QPBO to multi-label MRFs.
@cite_30 @cite_4 @cite_25 @cite_24
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In this paper, we address the problem of multi-instance multi-label learning (MIML) where each example is associated with not only multiple instances but also multiple class labels. In our novel approach, given an MIML example, each instance in the example is only associated with a single label and the label set of the example is the aggregation of all instance labels. Many real-world tasks such as scene classification, text categorization and gene sequence encoding can be properly formalized under our proposed approach. We formulate our MIML problem as a combination of two optimizations: (1) a quadratic programming (QP) that minimizes the empirical risk with L2-norm regularization, and (2) an integer programing (IP) assigning each instance to a single label. We also present an efficient method combining the stochastic gradient decent and alternating optimization approaches to solve our QP and IP optimizations. In our experiments with both an artificially generated data set and real-world applications, i.e. scene classification and text categorization, our proposed method achieves superior performance over existing state-of-the-art MIML methods such as MIMLBOOST, MIMLSVM, M @math MIML and MIMLRBF. We consider the problem of optimizing multilabel MRFs, which is in general NP-hard and ubiquitous in low-level computer vision. One approach for its solution is to formulate it as an integer linear programming and relax the integrality constraints. The approach we consider in this paper is to first convert the multi-label MRF into an equivalent binary-label MRF and then to relax it. The resulting relaxation can be efficiently solved using a maximum flow algorithm. Its solution provides us with a partially optimal labelling of the binary variables. This partial labelling is then easily transferred to the multi-label problem. We study the theoretical properties of the new relaxation and compare it with the standard one. Specifically, we compare tightness, and characterize a subclass of problems where the two relaxations coincide. We propose several combined algorithms based on the technique and demonstrate their performance on challenging computer vision problems. We consider Multiclass and Multilabel classification with extremely large number of classes, of which only few are labeled to each instance. In such setting, standard methods that have training, prediction cost linear to the number of classes become intractable. State-of-the-art methods thus aim to reduce the complexity by exploiting correlation between labels under assumption that the similarity between labels can be captured by structures such as low-rank matrix or balanced tree. However, as the diversity of labels increases in the feature space, structural assumption can be easily violated, which leads to degrade in the testing performance. In this work, we show that a margin-maximizing loss with l1 penalty, in case of Extreme Classification, yields extremely sparse solution both in primal and in dual without sacrificing the expressive power of predictor. We thus propose a Fully-Corrective Block-Coordinate Frank-Wolfe (FC-BCFW) algorithm that exploits both primal and dual sparsity to achieve a complexity sublinear to the number of primal and dual variables. A bi-stochastic search method is proposed to further improve the efficiency. In our experiments on both Multiclass and Multilabel problems, the proposed method achieves significant higher accuracy than existing approaches of Extreme Classification with very competitive training and prediction time. Multi-label problems arise in various domains such as multi-topic document categorization, protein function prediction, and automatic image annotation. One natural way to deal with such problems is to construct a binary classifier for each label, resulting in a set of independent binary classification problems. Since multiple labels share the same input space, and the semantics conveyed by different labels are usually correlated, it is essential to exploit the correlation information contained in different labels. In this paper, we consider a general framework for extracting shared structures in multi-label classification. In this framework, a common subspace is assumed to be shared among multiple labels. We show that the optimal solution to the proposed formulation can be obtained by solving a generalized eigenvalue problem, though the problem is nonconvex. For high-dimensional problems, direct computation of the solution is expensive, and we develop an efficient algorithm for this case. One appealing feature of the proposed framework is that it includes several well-known algorithms as special cases, thus elucidating their intrinsic relationships. We further show that the proposed framework can be extended to the kernel-induced feature space. We have conducted extensive experiments on multi-topic web page categorization and automatic gene expression pattern image annotation tasks, and results demonstrate the effectiveness of the proposed formulation in comparison with several representative algorithms.