Learning structured outputs with general structures is computationally challenging, except for tree-structured models. Thus we propose an efficient boosting-based algorithm AdaBoost.MRF for this task. The idea is based on the realization that a graph is a superimposition of trees. Different from most existing work, our algorithm can handle partial labelling, and thus is particularly attractive in practice where reliable labels are often sparsely observed. In addition, our method works exclusively on trees and thus is guaranteed to converge. We apply the AdaBoost.MRF algorithm to an indoor video surveillance scenario, where activities are modelled at multiple levels.
Conditional random fields are an example of structured output models @cite_13 @cite_1 @cite_10 . Learning in structured output models can be based on principles other than maximum likelihood, for example, large-margin @cite_13 @cite_1 , or search @cite_10 . With the latter, the computation of feature expectation is replaced by finding the most probable labelling. Learning with partial labels have been addressed in the past decade @cite_31 @cite_36 @cite_6 . Related problems include weak supervision @cite_18 and indirect supervision @cite_24 . Partial labels arise when only some components of @math are observed, i.e., @math where @math and @math are observed and missing components respectively. In the CRF setting, parameter learning requires to maximise the conditional incomplete log-likelihood instead, which can be shown to be: where @math . The gradient @math can now be derived as: where @math denotes the missing components associated with clique @math . Equations ) and ) reveal that learning depends on the inference ability to compute @math , @math and local clique distributions @math .
@cite_13 @cite_18 @cite_36 @cite_1 @cite_6 @cite_24 @cite_31 @cite_10
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Conditional Random Fields (CRFs) are widely known to scale poorly, particularly for tasks with large numbers of states or with richly connected graphical structures. This is a consequence of inference having a time complexity which is at best quadratic in the number of states. This paper describes a novel parameterisation of the CRF which ties the majority of clique potentials, while allowing individual potentials for a subset of the labellings. This has two beneficial effects: the parameter space of the model (and thus the propensity to over-fit) is reduced, and the time complexity of training and decoding becomes sub-quadratic. On a standard natural language task, we reduce CRF training time four-fold, with no loss in accuracy. We also show how inference can be performed efficiently in richly connected graphs, in which current methods are intractable. Conditional random fields (CRF) are widely used for predicting output variables that have some internal structure. Most of the CRF research has been done on structured classification where the outputs are discrete. In this study we propose a CRF probabilistic model for structured regression that uses multiple non-structured predictors as its features. We construct features as squared prediction errors and show that this results in a Gaussian predictor. Learning becomes a convex optimization problem leading to a global solution for a set of parameters. Inference can be conveniently conducted through matrix computation. Experimental results on the remote sensing problem of estimating Aerosol Optical Depth (AOD) provide strong evidence that the proposed CRF model successfully exploits the inherent spatio-temporal properties of AOD data. The experiments revealed that CRF are more accurate than the baseline neural network and domain-based predictors. This paper studies active learning in structured probabilistic models such as Conditional Random Fields (CRFs). This is a challenging problem because unlike unstructured prediction problems such as binary or multi-class classification, structured prediction problems involve a distribution with an exponentially-large support, for instance, over the space of all possible segmentations of an image. Thus, the entropy of such models is typically intractable to compute. We propose a crude yet surprisingly effective histogram approximation to the Gibbs distribution, which replaces the exponentially-large support with a coarsened distribution that may be viewed as a histogram over M bins. We show that our approach outperforms a number of baselines and results in a 90 -reduction in the number of annotations needed to achieve nearly the same accuracy as learning from the entire dataset. Hierarchical conditional random fields have been successfully applied to object segmentation. One reason is their ability to incorporate contextual information at different scales. However, these models do not allow multiple labels to be assigned to a single node. At higher scales in the image, this yields an oversimplified model, since multiple classes can be reasonable expected to appear within one region. This simplified model especially limits the impact that observations at larger scales may have on the CRF model. Neglecting the information at larger scales is undesirable since class-label estimates based on these scales are more reliable than at smaller, noisier scales. To address this problem, we propose a new potential, called harmony potential, which can encode any possible combination of class labels. We propose an effective sampling strategy that renders tractable the underlying optimization problem. Results show that our approach obtains state-of-the-art results on two challenging datasets: Pascal VOC 2009 and MSRC-21.