Translation as Weighted Deduction

We present a unified view of many translation algorithms that synthesizes work on deductive parsing, semiring parsing, and efficient approximate search algorithms. This gives rise to clean analyses and compact descriptions that can serve as the basis for modular implementations. We illustrate this with several examples, showing how to build search spaces for several disparate phrase-based search strategies, integrate non-local features, and devise novel models. Although the framework is drawn from parsing and applied to translation, it is applicable to many dynamic programming problems arising in natural language processing and other areas.

Exact sampling and optimisation in statistical machine translation

In Statistical Machine Translation (SMT), inference needs to be performed over a high-complexity discrete distribution de ned by the intersection between a translation hypergraph and a target language model. This distribution is too complex to be represented exactly and one typically resorts to approximation techniques either to perform optimisation { the task of searching for the optimum translation { or sampling { the task of nding a subset of translations that is statistically representative of the goal distribution. Beam-search is an example of an approximate optimisation technique, where maximisation is performed over a heuristically pruned representation of the goal distribution. For inference tasks other than optimisation, rather than nding a single optimum, one is really interested in obtaining a set of probabilistic samples from the distribution. This is the case in training where one wishes to obtain unbiased estimates of expectations in order to t the parameters of a model. Samples are also necessary in consensus decoding where one chooses from a sample of likely translations the one that minimises a loss function. Due to the additional computational challenges posed by sampling, n-best lists, a by-product of optimisation, are typically used as a biased approximation to true probabilistic samples. A more direct procedure is to attempt to directly draw samples from the underlying distribution rather than rely on n-best list approximations. Markov Chain Monte Carlo (MCMC) methods, such as Gibbs sampling, o er a way to overcome the tractability issues in sampling, however their convergence properties are hard to assess. That is, it is di cult to know when, if ever, an MCMC sampler is producing samples that are compatible iii with the goal distribution. Rejection sampling, a Monte Carlo (MC) method, is more fundamental and natural, it o ers strong guarantees, such as unbiased samples, but is typically hard to design for distributions of the kind addressed in SMT, rendering an intractable method. A recent technique that stresses a uni ed view between the two types of inference tasks discussed here | optimisation and sampling | is the OS approach. OS can be seen as a cross between Adaptive Rejection Sampling (an MC method) and A optimisation. In this view the intractable goal distribution is upperbounded by a simpler (thus tractable) proxy distribution, which is then incrementally re ned to be closer to the goal until the maximum is found, or until the sampling performance exceeds a certain level. This thesis introduces an approach to exact optimisation and exact sampling in SMT by addressing the tractability issues associated with the intersection between the translation hypergraph and the language model. The two forms of inference are handled in a uni ed framework based on the OS approach. In short, an intractable goal distribution, over which one wishes to perform inference, is upperbounded by tractable proposal distributions. A proposal represents a relaxed version of the complete space of weighted translation derivations, where relaxation happens with respect to the incorporation of the language model. These proposals give an optimistic view on the true model and allow for easier and faster search using standard dynamic programming techniques. In the OS approach, such proposals are used to perform a form of adaptive rejection sampling. In rejection sampling, samples are drawn from a proposal distribution and accepted or rejected as a function of the mismatch between the proposal and the goal. The technique is adaptive in that rejected samples are used to motivate a re nement of the upperbound proposal that brings it closer to the goal, improving the rate of acceptance. Optimisation can be connected to an extreme form of sampling, thus the framework introduced here suits both exact optimisation and exact iv sampling. Exact optimisation means that the global maximum is found with a certi cate of optimality. Exact sampling means that unbiased samples are independently drawn from the goal distribution. We show that by using this approach exact inference is feasible using only a fraction of the time and space that would be required by a full intersection, without recourse to pruning techniques that only provide approximate solutions. We also show that the vast majority of the entries (n-grams) in a language model can be summarised by shorter and optimistic entries. This means that the computational complexity of our approach is less sensitive to the order of the language model distribution than a full intersection would be. Particularly in the case of sampling, we show that it is possible to draw exact samples compatible with distributions which incorporate a high-order language model component from proxy distributions that are much simpler. In this thesis, exact inference is performed in the context of both hierarchical and phrase-based models of translation, the latter characterising a problem that is NP-complete in nature.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Tropical time series, iterated-sum signatures and quasisymmetric functions

Driven by the need for principled extraction of features from time series, we introduce the iterated-sums signature over any commutative semiring. The case of the tropical semiring is a central, and our motivating, example, as it leads to features of (real-valued) time series that are not easily available using existing signature-type objects

A Formal Model of Ambiguity and its Applications in Machine Translation

Systems that process natural language must cope with and resolve ambiguity. In this dissertation, a model of language processing is advocated in which multiple inputs and multiple analyses of inputs are considered concurrently and a single analysis is only a last resort. Compared to conventional models, this approach can be understood as replacing single-element inputs and outputs with weighted sets of inputs and outputs. Although processing components must deal with sets (rather than individual elements), constraints are imposed on the elements of these sets, and the representations from existing models may be reused. However, to deal efficiently with large (or infinite) sets, compact representations of sets that share structure between elements, such as weighted finite-state transducers and synchronous context-free grammars, are necessary. These representations and algorithms for manipulating them are discussed in depth in depth. To establish the effectiveness and tractability of the proposed processing model, it is applied to several problems in machine translation. Starting with spoken language translation, it is shown that translating a set of transcription hypotheses yields better translations compared to a baseline in which a single (1-best) transcription hypothesis is selected and then translated, independent of the translation model formalism used. More subtle forms of ambiguity that arise even in text-only translation (such as decisions conventionally made during system development about how to preprocess text) are then discussed, and it is shown that the ambiguity-preserving paradigm can be employed in these cases as well, again leading to improved translation quality. A model for supervised learning that learns from training data where sets (rather than single elements) of correct labels are provided for each training instance and use it to learn a model of compound word segmentation is also introduced, which is used as a preprocessing step in machine translation

Tropical time series, iterated-sums signatures and quasisymmetric functions

Driven by the need for principled extraction of features from time series, we introduce the iterated-sums signature over any commutative semiring. The case of the tropical semiring is a central, and our motivating, example, as it leads to features of (real-valued) time series that are not easily available using existing signature-type objects.Comment: fix notational errors, clarify certain proof

Tensors and tensor decompositions for combining external information with knowledge graph embeddings

The task of knowledge graph (KG) completion, where one is given an incomplete KG as a list of facts, and is asked to give high scores to correct but unseen triples, has been a well-studied problem in the NLP community. A simple but surprisingly robust approach for solving this task emerged as learning low dimensional embeddings for entities and relations by approximating the underlying KG directly through a scoring function. Knowledge graphs have a natural representation as a binary three way array, also known as a 3rd order tensor, and certain classes of scoring functions can be characterized as finding a low-rank decomposition of this tensor. This dissertation extends this characterization, and investigates the suitability of tensors for modelling both knowledge graphs and related data, for learning low-rank representations of entities and relations that incorporate information from heterogeneous sources, and for reasoning with paths and rules using the learned representations. Specifically, we present two joint tensor decomposition models for integrating external information in the process of learning KG embeddings. Our first model is a joint tensor-tensor decomposition model that learns representations based on both KG facts and type information on entities and relations. Our second model is a joint tensor-matrix decomposition for integrating cooccurrence information between entities and words from an entity linked corpus into knowledge graph embeddings, in order to learn better representations for the entities that are rarely seen in the knowledge graph. We also investigate tensors as tools for enabling multi-step reasoning using learned embedding representations. To this end, we extend theoretical results for semiring weighted logic programs to tensors of semirings. Our results are broadly applicable to any area that uses dynamic programming algorithms for calculating tensor values. Such applications include incorporating embeddings of paths and rules for knowledge graph completion, and syntactic parsing with latent variable grammar

Graphical Models with Structured Factors, Neural Factors, and Approximation-aware Training

This thesis broadens the space of rich yet practical models for structured prediction. We introduce a general framework for modeling with four ingredients: (1) latent variables, (2) structural constraints, (3) learned (neural) feature representations of the inputs, and (4) training that takes the approximations made during inference into account. The thesis builds up to this framework through an empirical study of three NLP tasks: semantic role labeling, relation extraction, and dependency parsing -- obtaining state-of-the-art results on the former two. We apply the resulting graphical models with structured and neural factors, and approximation-aware learning to jointly model part-of-speech tags, a syntactic dependency parse, and semantic roles in a low-resource setting where the syntax is unobserved. We present an alternative view of these models as neural networks with a topology inspired by inference on graphical models that encode our intuitions about the data

Iterative parameter mixing for distributed large-margin training of structured predictors for natural language processing

The development of distributed training strategies for statistical prediction functions is important for applications of machine learning, generally, and the development of distributed structured prediction training strategies is important for natural language processing (NLP), in particular. With ever-growing data sets this is, first, because, it is easier to increase computational capacity by adding more processor nodes than it is to increase the power of individual processor nodes, and, second, because data sets are often collected and stored in different locations. Iterative parameter mixing (IPM) is a distributed training strategy in which each node in a network of processors optimizes a regularized average loss objective on its own subset of the total available training data, making stochastic (per-example) updates to its own estimate of the optimal weight vector, and communicating with the other nodes by periodically averaging estimates of the optimal vector across the network. This algorithm has been contrasted with a close relative, called here the single-mixture optimization algorithm, in which each node stochastically optimizes an average loss objective on its own subset of the training data, operating in isolation until convergence, at which point the average of the independently created estimates is returned. Recent empirical results have suggested that this IPM strategy produces better models than the single-mixture algorithm, and the results of this thesis add to this picture. The contributions of this thesis are as follows. The first contribution is to produce and analyze an algorithm for decentralized stochastic optimization of regularized average loss objective functions. This algorithm, which we call the distributed regularized dual averaging algorithm, improves over prior work on distributed dual averaging by providing a simpler algorithm (used in the rest of the thesis), better convergence bounds for the case of regularized average loss functions, and certain technical results that are used in the sequel. The central contribution of this thesis is to give an optimization-theoretic justification for the IPM algorithm. While past work has focused primarily on its empirical test-time performance, we give a novel perspective on this algorithm by showing that, in the context of the distributed dual averaging algorithm, IPM constitutes a convergent optimization algorithm for arbitrary convex functions, while the single-mixture distribution algorithm is not. Experiments indeed confirm that the superior test-time performance of models trained using IPM, compared to single-mixture, correlates with better optimization of the objective value on the training set, a fact not previously reported. Furthermore, our analysis of general non-smooth functions justifies the use of distributed large-margin (support vector machine [SVM]) training of structured predictors, which we show yields better test performance than the IPM perceptron algorithm, the only version of the IPM to have previously been given a theoretical justification. Our results confirm that IPM training can reach the same level of test performance as a sequentially trained model and can reach better accuracies when one has a fixed budget of training time. Finally, we use the reduction in training time that distributed training allows to experiment with adding higher-order dependency features to a state-of-the-art phrase-structure parsing model. We demonstrate that adding these features improves out-of-domain parsing results of even the strongest phrase-structure parsing models, yielding a new state-of-the-art for the popular train-test pairs considered. In addition, we show that a feature-bagging strategy, in which component models are trained separately and later combined, is sometimes necessary to avoid feature under-training and get the best performance out of large feature sets

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers