Convergence of a generalized version of the modified SMO algorithms given by Keerthi et al. for SVM classifier design is proved. The convergence results are also extended to modified SMO algorithms for solving ν-SVM classifier problems.

Abstract-This paper points out an important source of inefficiency in Smola and Schölkopf's sequential minimal optimization (SMO) algorithm for support vector machine (SVM) regression that is caused by the use of a single threshold value. Using clues from the KKT conditions for the dual problem, two threshold parameters are employed to derive modifications of SMO for regression. These modified algorithms perform significantly faster than the original SMO on the datasets tried.Index Terms-Quadratic programming, regression, sequential minimal optimization (SMO) algorithm, support vector machine (SVM).

Abstract-In this paper we give a new fast iterative algorithm for support vector machine (SVM) classifier design. The basic problem treated is one that does not allow classification violations. The problem is converted to a problem of computing the nearest point between two convex polytopes. The suitability of two classical nearest point algorithms, due to Gilbert, and Mitchell et al., is studied. Ideas from both these algorithms are combined and modified to derive our fast algorithm. For problems which require classification violations to be allowed, the violations are quadratically penalized and an idea due to Cortes and Vapnik and Frieß is used to convert it to a problem in which there are no classification violations. Comparative computational evaluation of our algorithm against powerful SVM methods such as Platt's sequential minimal optimization shows that our algorithm is very competitive.Index Terms-Classification, nearest point algorithm, quadratic programming, support vector machine.

Distantly-supervised Relation Extraction (RE) methods train an extractor by automatically aligning relation instances in a Knowledge Base (KB) with unstructured text. In addition to relation instances, KBs often contain other relevant side information, such as aliases of relations (e.g., founded and co-founded are aliases for the relation founderOfCompany). RE models usually ignore such readily available side information. In this paper, we propose RESIDE, a distantly-supervised neural relation extraction method which utilizes additional side information from KBs for improved relation extraction. It uses entity type and relation alias information for imposing soft constraints while predicting relations. RE-SIDE employs Graph Convolution Networks (GCN) to encode syntactic information from text and improves performance even when limited side information is available. Through extensive experiments on benchmark datasets, we demonstrate RESIDE's effectiveness. We have made RESIDE's source code available to encourage reproducible research.

Word embeddings have been widely adopted across several NLP applications. Most existing word embedding methods utilize sequential context of a word to learn its embedding. While there have been some attempts at utilizing syntactic context of a word, such methods result in an explosion of the vocabulary size. In this paper, we overcome this problem by proposing SynGCN, a flexible Graph Convolution based method for learning word embeddings. SynGCN utilizes the dependency context of a word without increasing the vocabulary size. Word embeddings learned by SynGCN outperform existing methods on various intrinsic and extrinsic tasks and provide an advantage when used with ELMo. We also propose SemGCN, an effective framework for incorporating diverse semantic knowledge for further enhancing learned word representations. We make the source code of both models available to encourage reproducible research.