Using Interior Point Methods for Large-scale Support Vector Machine training

Support Vector Machines (SVMs) are powerful machine learning techniques for classification and regression, but the training stage involves a convex quadratic optimization program that is most often computationally expensive. Traditionally, active-set methods have been used rather than interior point methods, due to the Hessian in the standard dual formulation being completely dense. But as active-set methods are essentially sequential, they may not be adequate for machine learning challenges of the future. Additionally, training time may be limited, or data may grow so large that cluster-computing approaches need to be considered. Interior point methods have the potential to answer these concerns directly. They scale efficiently, they can provide good early approximations, and they are suitable for parallel and multi-core environments. To apply them to SVM training, it is necessary to address directly the most computationally expensive aspect of the algorithm. We therefore present an exact reformulation of the standard linear SVM training optimization problem that exploits separability of terms in the objective. By so doing, per-iteration computational complexity is reduced from O(n3) to O(n). We show how this reformulation can be applied to many machine learning problems in the SVM family. Implementation issues relating to specializing the algorithm are explored through extensive numerical experiments. They show that the performance of our algorithm for large dense or noisy data sets is consistent and highly competitive, and in some cases can out perform all other approaches by a large margin. Unlike active set methods, performance is largely unaffected by noisy data. We also show how, by exploiting the block structure of the augmented system matrix, a hybrid MPI/Open MP implementation of the algorithm enables data and linear algebra computations to be efficiently partitioned amongst parallel processing nodes in a clustered computing environment. The applicability of our technique is extended to nonlinear SVMs by low-rank approximation of the kernel matrix. We develop a heuristic designed to represent clusters using a small number of features. Additionally, an early approximation scheme reduces the number of samples that need to be considered. Both elements improve the computational efficiency of the training phase. Taken as a whole, this thesis shows that with suitable problem formulation and efficient implementation techniques, interior point methods are a viable optimization technology to apply to large-scale SVM training, and are able to provide state-of-the-art performance

Automatic Generation of Story Highlights

In this paper we present a joint content selection and compression model for single-document summarization. The model operates over a phrase-based representation of the source document which we obtain by merging information from PCFG parse trees and dependency graphs. Using an integer linear programming formulation, the model learns to select and combine phrases subject to length, coverage and grammar constraints. We evaluate the approach on the task of generating “story highlights”—a small number of brief, self-contained sentences that allow readers to quickly gather information on news stories. Experimental results show that the model’s output is comparable to human-written highlights in terms of both grammaticality and content.

Multiple aspect summarization using integer linear programming

Multi-document summarization involves many aspects of content selection and sur-face realization. The summaries must be informative, succinct, grammatical, and obey stylistic writing conventions. We present a method where such individual aspects are learned separately from data (without any hand-engineering) but optimized jointly using an integer linear programme. The ILP framework allows us to combine the decisions of the expert learners and to select and rewrite source content through a mixture of objective setting, soft and hard constraints. Experimental results on the TAC-08 data set show that our model achieves state-of-the-art performance using ROUGE and signifi-cantly improves the informativeness of the summaries.

Title Generation with Quasi-Synchronous Grammar

The task of selecting information and rendering it appropriately appears in multiple contexts in summarization. In this paper we present a model that simultaneously optimizes selection and rendering preferences. The model operates over a phrase-based representation of the source document which we obtain by merging PCFG parse trees and dependency graphs. Selection preferences for individual phrases are learned discriminatively, while a quasi-synchronous grammar (Smith and Eisner, 2006) captures rendering preferences such as paraphrases and compressions. Based on an integer linear programming formulation, the model learns to generate summaries that satisfy both types of preferences, while ensuring that length, topic coverage and grammar constraints are met. Experiments on headline and image caption generation show that our method obtains state-of-the-art performance using essentially the same model for both tasks without any major modifications.

Exploiting separability in large-scale linear support vector machine training

Linear support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using interior point methods, which requires only O(n) operations per iteration. Through exploiting the separability of the Hessian, we provide a unified approach, from an optimization perspective, to 1-norm classification, 2-norm classification, universum classification, ordinal regression and ɛ-insensitive regression. Our approach has the added advantage of obtaining the hyperplane weights and bias directly from the solver. Numerical experiments indicate that, in contrast to existing methods, the algorithm is largely unaffected by noisy data, and they show training times for our implementation are consistent and highly competitive. We discuss the effect of using multiple correctors, and monitoring the angle of the normal to the hyperplane to determine termination

Using interior point methods for large-scale support vector machine training

Support Vector Machines (SVMs) are powerful machine learning techniques for classification and regression, but the training stage involves a convex quadratic optimization program that is most often computationally expensive. Traditionally, active-set methods have been used rather than interior point methods, due to the Hessian in the standard dual formulation being completely dense. But as active-set methods are essentially sequential, they may not be adequate for machine learning challenges of the future. Additionally, training time may be limited, or data may grow so large that cluster-computing approaches need to be considered. Interior point methods have the potential to answer these concerns directly. They scale efficiently, they can provide good early approximations, and they are suitable for parallel and multi-core environments. To apply them to SVM training, it is necessary to address directly the most computationally expensive aspect of the algorithm. We therefore present an exact reformulation of the standard linear SVM training optimization problem that exploits separability of terms in the objective. By so doing, per-iteration computational complexity is reduced from O(n3) to O(n). We show how this reformulation can be applied to many machine learning problems in the SVM family. Implementation issues relating to specializing the algorithm are explored through extensive numerical experiments. They show that the performance of our algorithm for large dense or noisy data sets is consistent and highly competitive, and in some cases can out perform all other approaches by a large margin. Unlike active set methods, performance is largely unaffected by noisy data. We also show how, by exploiting the block structure of the augmented system matrix, a hybrid MPI/Open MP implementation of the algorithm enables data and linear algebra computations to be efficiently partitioned amongst parallel processing nodes in a clustered computing environment. The applicability of our technique is extended to nonlinear SVMs by low-rank approximation of the kernel matrix. We develop a heuristic designed to represent clusters using a small number of features. Additionally, an early approximation scheme reduces the number of samples that need to be considered. Both elements improve the computational efficiency of the training phase. Taken as a whole, this thesis shows that with suitable problem formulation and efficient implementation techniques, interior point methods are a viable optimization technology to apply to large-scale SVM training, and are able to provide state-of-the-art performance.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

WikiSimple: Automatic Simplification of Wikipedia Articles

Text simplification aims to rewrite text into simpler versions and thus make information accessible to a broader audience (e.g., non-native speakers, children, and individuals with language impairments). In this paper, we propose a model that simplifies documents automatically while selecting their most important content and rewriting them in a simpler style. We learn content selection rules from same-topic Wikipedia articles written in the main encyclopedia and its Simple English variant. We also use the revision histories of Simple Wikipedia articles to learn a quasi-synchronous grammar of simplification rewrite rules. Based on an integer linear programming formulation, we develop a joint model where preferences based on content and style are optimized simultaneously. Experiments on simplifying main Wikipedia articles show that our method significantly reduces the reading difficulty, while still capturing the important content