Estimating Maximally Probable Constrained Relations by Mathematical Programming

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a linear order on a set). We contribute a family of probability measures on the set of all relations between two finite, non-empty sets, which offers a joint abstraction of multi-label classification, correlation clustering and ranking by linear ordering. Estimating (learning) a maximally probable measure, given (a training set of) related and unrelated pairs, is a convex optimization problem. Estimating (inferring) a maximally probable relation, given a measure, is a 01-linear program. It is solved in linear time for maps. It is NP-hard for equivalence relations and linear orders. Practical solutions for all three cases are shown in experiments with real data. Finally, estimating a maximally probable measure and relation jointly is posed as a mixed-integer nonlinear program. This formulation suggests a mathematical programming approach to semi-supervised learning.Comment: 16 page

Linguistic Analysis of Non-ITG Word Reordering between Language Pairs with Different Word Order Typologies

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The Linear Ordering Problem Revisited

The Linear Ordering Problem is a popular combinatorial optimisation problem which has been extensively addressed in the literature. However, in spite of its popularity, little is known about the characteristics of this problem. This paper studies a procedure to extract static information from an instance of the problem, and proposes a method to incorporate the obtained knowledge in order to improve the performance of local search-based algorithms. The procedure introduced identifies the positions where the indexes cannot generate local optima for the insert neighbourhood, and thus global optima solutions. This information is then used to propose a restricted insert neighbourhood that discards the insert operations which move indexes to positions where optimal solutions are not generated. In order to measure the efficiency of the proposed restricted insert neighbourhood system, two state-of-the-art algorithms for the LOP that include local search procedures have been modified. Conducted experiments confirm that the restricted versions of the algorithms outperform the classical designs systematically. The statistical test included in the experimentation reports significant differences in all the cases, which validates the efficiency of our proposal

A Survey of Word Reordering in Statistical Machine Translation: Computational Models and Language Phenomena

Word reordering is one of the most difficult aspects of statistical machine translation (SMT), and an important factor of its quality and efficiency. Despite the vast amount of research published to date, the interest of the community in this problem has not decreased, and no single method appears to be strongly dominant across language pairs. Instead, the choice of the optimal approach for a new translation task still seems to be mostly driven by empirical trials. To orientate the reader in this vast and complex research area, we present a comprehensive survey of word reordering viewed as a statistical modeling challenge and as a natural language phenomenon. The survey describes in detail how word reordering is modeled within different string-based and tree-based SMT frameworks and as a stand-alone task, including systematic overviews of the literature in advanced reordering modeling. We then question why some approaches are more successful than others in different language pairs. We argue that, besides measuring the amount of reordering, it is important to understand which kinds of reordering occur in a given language pair. To this end, we conduct a qualitative analysis of word reordering phenomena in a diverse sample of language pairs, based on a large collection of linguistic knowledge. Empirical results in the SMT literature are shown to support the hypothesis that a few linguistic facts can be very useful to anticipate the reordering characteristics of a language pair and to select the SMT framework that best suits them.Comment: 44 pages, to appear in Computational Linguistic

Syntax-based machine translation using dependency grammars and discriminative machine learning

Machine translation underwent huge improvements since the groundbreaking introduction of statistical methods in the early 2000s, going from very domain-specific systems that still performed relatively poorly despite the painstakingly crafting of thousands of ad-hoc rules, to general-purpose systems automatically trained on large collections of bilingual texts which manage to deliver understandable translations that convey the general meaning of the original input. These approaches however still perform quite below the level of human translators, typically failing to convey detailed meaning and register, and producing translations that, while readable, are often ungrammatical and unidiomatic. This quality gap, which is considerably large compared to most other natural language processing tasks, has been the focus of the research in recent years, with the development of increasingly sophisticated models that attempt to exploit the syntactical structure of human languages, leveraging the technology of statistical parsers, as well as advanced machine learning methods such as marging-based structured prediction algorithms and neural networks. The translation software itself became more complex in order to accommodate for the sophistication of these advanced models: the main translation engine (the decoder) is now often combined with a pre-processor which reorders the words of the source sentences to a target language word order, or with a post-processor that ranks and selects a translation according according to fine model from a list of candidate translations generated by a coarse model. In this thesis we investigate the statistical machine translation problem from various angles, focusing on translation from non-analytic languages whose syntax is best described by fluid non-projective dependency grammars rather than the relatively strict phrase-structure grammars or projectivedependency grammars which are most commonly used in the literature. We propose a framework for modeling word reordering phenomena between language pairs as transitions on non-projective source dependency parse graphs. We quantitatively characterize reordering phenomena for the German-to-English language pair as captured by this framework, specifically investigating the incidence and effects of the non-projectivity of source syntax and the non-locality of word movement w.r.t. the graph structure. We evaluated several variants of hand-coded pre-ordering rules in order to assess the impact of these phenomena on translation quality. We propose a class of dependency-based source pre-ordering approaches that reorder sentences based on a flexible models trained by SVMs and and several recurrent neural network architectures. We also propose a class of translation reranking models, both syntax-free and source dependency-based, which make use of a type of neural networks known as graph echo state networks which is highly flexible and requires extremely little training resources, overcoming one of the main limitations of neural network models for natural language processing tasks

Learning Linear Ordering Problems for Better Translation ∗

We apply machine learning to the Linear Ordering Problem in order to learn sentence-specific reordering models for machine translation. We demonstrate that even when these models are used as a mere preprocessing step for German-English translation, they significantly outperform Moses ’ integrated lexicalized reordering model. Our models are trained on automatically aligned bitext. Their form is simple but novel. They assess, based on features of the input sentence, how strongly each pair of input word tokens wi, wj would like to reverse their relative order. Combining all these pairwise preferences to find the best global reordering is NP-hard. However, we present a non-trivial O(n3) algorithm, based on chart parsing, that at least finds the best reordering within a certain exponentially large neighborhood. We show how to iterate this reordering process within a local search algorithm, which we use in training.