Viterbi Training for PCFGs: Hardness Results and Competitiveness of Uniform Initialization

We consider the search for a maximum likelihood assignment of hidden derivations and grammar weights for a probabilistic context-free grammar, the problem approximately solved by “Viterbi training.” We show that solving and even approximating Viterbi training for PCFGs is NP-hard. We motivate the use of uniformat-random initialization for Viterbi EM as an optimal initializer in absence of further information about the correct model parameters, providing an approximate bound on the log-likelihood.

Empirical Risk Minimization for Probabilistic Grammars: Sample Complexity and Hardness of Learning

Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. They are used ubiquitously in computational linguistics. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of probabilistic grammars using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting. By making assumptions about the underlying distribution that are appropriate for natural language scenarios, we are able to derive distribution-dependent sample complexity bounds for probabilistic grammars. We also give simple algorithms for carrying out empirical risk minimization using this framework in both the supervised and unsupervised settings. In the unsupervised case, we show that the problem of minimizing empirical risk is NP-hard. We therefore suggest an approximate algorithm, similar to expectation-maximization, to minimize the empirical risk. Learning from data is central to contemporary computational linguistics. It is in common in such learning to estimate a model in a parametric family using the maximum likelihood principle. This principle applies in the supervised case (i.e., using annotate

Discrete Logarithms in Generalized Jacobians

D\'ech\`ene has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect product of an elliptic curve and a multiplicative group of a finite field. We explain why her proposal has no advantages over simply taking the direct product of groups. We then argue that generalized Jacobians offer poorer security and efficiency than standard Jacobians

Empirical Risk Minimization with Approximations of Probabilistic Grammars

Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of the parameters of a fixed probabilistic grammar using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting.

Joint Morphological and Syntactic Disambiguation

In morphologically rich languages, should morphological and syntactic disambiguation be treated sequentially or as a single problem? We describe several efficient, probabilistically interpretable ways to apply joint inference to morphological and syntactic disambiguation using lattice parsing. Joint inference is shown to compare favorably to pipeline parsing methods across a variety of component models. State-of-the-art performance on Hebrew Treebank parsing is demonstrated using the new method. The benefits of joint inference are modest with the current component models, but appear to increase as components themselves improve

Drawing Boundaries

In “On Drawing Lines on a Map” (1995), I suggested that the different ways we have of drawing lines on maps open up a new perspective on ontology, resting on a distinction between two sorts of boundaries: fiat and bona fide. “Fiat” means, roughly: human-demarcation-induced. “Bona fide” means, again roughly: a boundary constituted by some real physical discontinuity. I presented a general typology of boundaries based on this opposition and showed how it generates a corresponding typology of the different sorts of objects which boundaries determine or demarcate. In this paper, I describe how the theory of fiat boundaries has evolved since 1995, how it has been applied in areas such as property law and political geography, and how it is being used in contemporary work in formal and applied ontology, especially within the framework of Basic Formal Ontology

Modularity in support of design for re-use

We explore the structuring principle of modularity with the objective of analysing its current ability to meet the requirements of a 're-use' centred approach to design. We aim to highlight the correlation's between modular design and 're-use', and argue that it has the potential to aid the little-supported process of 'design-for-re-use'. In fulfilment of this objective we not only identify the requirements of 'design-for-re-use', but also propose how modular design principles can be extended to support 'design-for-re-use'

Re-using knowledge : why, what and where

Previously the 're-use' focus has centred on specific and/or standard parts, more recently however, [standard components] are being developed...to enable both the re-use of the part and the experience associated with that part'. This notion is further extended by Finger who states that 'designers may re-use a prior design in it's entirety,...may re-use an existing shape for a different function, or may re-use a feature from another design'. Reinforcing this notion we currently consider re-use to reflect the utilisation of any knowledge gained from a design activity and not just past designs of artefacts. Our research concerns the improvement of formal 're-use' support and as such we have identified a need to gain a better understanding of how design knowledge can be utilised to support 're-use'. Thus, we discuss the requirements of successful 're-use' and attempt to ascertain within this skeleton: what knowledge can be re-used; how to maximise its' applicability; and where and when it can be utilised in new design

Body dissatisfaction, appearance investment and wellbeing: how older obese men orient to 'aesthetic health' [forthcoming]

Most research on male body image to date has focused on young men using quantitative methods. The study reported here is based on qualitative interviews with a sample of older men (n = 30) on a weight management programme, and we asked them about body-related feelings. The interviews were all transcribed and analysed using thematic analysis. Our results indicate that although body weight was typically minimised, body image was a key concern, with many examples of body consciousness and body dissatisfaction evident. On the other hand, post-programme weight loss was associated with a transformative shift in body image, with the men emphasising enhanced body confidence, self-esteem and psychological wellbeing. We conclude by highlighting the need to recognise and address appearance issues and/as health concerns for middle-aged and older men

Properties of perturbative multi-particle amplitudes in ϕk\phi^k and O(N)O(N) theories

Threshold amplitudes are considered for multi-particle production in $\phi^k$ and $O(N) ~\phi^4$ theories. It is found that the disappearance of tree-level threshold amplitudes of $2$ on-shell particles producing a large number of particles occurs in $\phi^k$ theory only for $k=3$ and $k=4$. The one-loop correction to the threshold amplitude for a highly virtual scalar particle decaying into $n$ particles in an $O(N)$ model is derived.Comment: 7 pages, LaTex, TPI-MINN-92/60-