We introduce regularized Frank-Wolfe, a general and effective algorithm for inference and learning of dense conditional random fields (CRFs). The algorithm optimizes a nonconvex continuous relaxation of the CRF inference problem using vanilla Frank-Wolfe with approximate updates, which are equivalent to minimizing a regularized energy function. Our proposed method is a generalization of existing algorithms such as mean field or concave-convex procedure. This perspective not only offers a unified analysis of these algorithms, but also allows an easy way of exploring different variants that potentially yield better performance. We illustrate this in our empirical results on standard semantic segmentation datasets, where several instantiations of our regularized Frank-Wolfe outperform mean field inference, both as a standalone component and as an end-to-end trainable layer in a neural network. We also show that dense CRFs, coupled with our new algorithms, produce significant improvements over strong CNN baselines.

We introduce regularized Frank-Wolfe, a general and effective algorithm for inference and learning of dense conditional random fields (CRFs). The algorithm optimizes a nonconvex continuous relaxation of the CRF inference problem using vanilla Frank-Wolfe with approximate updates, which are equivalent to minimizing a regularized energy function. Our proposed method is a generalization of existing algorithms such as mean field or concave-convex procedure. This perspective not only offers a unified analysis of these algorithms, but also allows an easy way of exploring different variants that potentially yield better performance. We illustrate this in our empirical results on standard semantic segmentation datasets, where several instantiations of our regularized Frank-Wolfe outperform mean field inference, both as a standalone component and as an end-to-end trainable layer in a neural network. We also show that dense CRFs, coupled with our new algorithms, produce significant improvements over strong CNN baselines.

Semantic segmentation is a fundamental problem in computer vision.

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In particular, we will be interested in log-supermodular (LSM) potential functions as they encourage agreement between the variables upon which theyoperate.

This paper investigates part-of-speech tagging, an important task in Natural Language Processing (NLP) for the Nagamese language. The Nagamese language, a.k.a. Naga Pidgin, is an Assamese-lexified Creole language developed primarily as a means of communication in trade between the Nagas and people from Assam in northeast India. A substantial amount of work in part-of-speech-tagging has been done for resource-rich languages like English, Hindi, etc. However, no work has been done in the Nagamese language. To the best of our knowledge, this is the first attempt at part-of-speech tagging for the Nagamese Language. The aim of this work is to identify the part-of-speech for a given sentence in the Nagamese language. An annotated corpus of 16,112 tokens is created and applied machine learning technique known as Conditional Random Fields (CRF). Using CRF, an overall tagging accuracy of 85.70%; precision, recall of 86%, and f1-score of 85% is achieved. Keywords. Nagamese, NLP, part-of-speech, machine learning, CRF.

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Deep structured output learning shows great promise in tasks like semantic image segmentation. We proffer a new, efficient deep structured model learning scheme, in which we show how deep Convolutional Neural Networks (CNNs) can be used to directly estimate the messages in message passing inference for structured prediction with Conditional Random Fields (CRFs). With such CNN message estimators, we obviate the need to learn or evaluate potential functions for message calculation. This confers significant efficiency for learning, since otherwise when performing structured learning for a CRF with CNN potentials it is necessary to undertake expensive inference for every stochastic gradient iteration. The network output dimension of message estimators is the same as the number of classes, rather than exponentially growing in the order of the potentials. Hence it is more scalable for cases that involve a large number of classes. We apply our method to semantic image segmentation and achieve impressive performance, which demonstrates the effectiveness and usefulness of our CNN message learning method.