Reductions of Hidden Information Sources

In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the internal states and mechanisms. Unfortunately, there are often many possible models that are observationally equivalent. Here we show that the situation is not as arbitrary as one would think. We show that generators of hidden stochastic processes can be reduced to a minimal form and compare this reduced representation to that provided by computational mechanics--the epsilon-machine. On the way to developing deeper, measure-theoretic foundations for the latter, we introduce a new two-step reduction process. The first step (internal-event reduction) produces the smallest observationally equivalent sigma-algebra and the second (internal-state reduction) removes sigma-algebra components that are redundant for optimal prediction. For several classes of stochastic dynamical systems these reductions produce representations that are equivalent to epsilon-machines.Comment: 12 pages, 4 figures; 30 citations; Updates at http://www.santafe.edu/~cm

Mean-risk models using two risk measures: A multi-objective approach

This paper proposes a model for portfolio optimisation, in which distributions are characterised and compared on the basis of three statistics: the expected value, the variance and the CVaR at a specified confidence level. The problem is multi-objective and transformed into a single objective problem in which variance is minimised while constraints are imposed on the expected value and CVaR. In the case of discrete random variables, the problem is a quadratic program. The mean-variance (mean-CVaR) efficient solutions that are not dominated with respect to CVaR (variance) are particular efficient solutions of the proposed model. In addition, the model has efficient solutions that are discarded by both mean-variance and mean-CVaR models, although they may improve the return distribution. The model is tested on real data drawn from the FTSE 100 index. An analysis of the return distribution of the chosen portfolios is presented

Avoiding dative overgeneralisation errors: semantics, statistics or both?

Item does not contain fulltextHow do children eventually come to avoid the production of overgeneralisation errors, in particular, those involving the dative (e.g., *I said her "no")? The present study addressed this question by obtaining from adults and children (5-6, 9-10 years) judgements of well-formed and over-general datives with 301 different verbs (44 for children). A significant effect of pre-emption - whereby the use of a verb in the prepositional-object (PO)-dative construction constitutes evidence that double-object (DO)-dative uses are not permitted - was observed for every age group. A significant effect of entrenchment - whereby the use of a verb in any construction constitutes evidence that unattested dative uses are not permitted - was also observed for every age group, with both predictors also accounting for developmental change between ages 5-6 and 9-10 years. Adults demonstrated knowledge of a morphophonological constraint that prohibits Latinate verbs from appearing in the DO-dative construction (e.g., *I suggested her the trip). Verbs' semantic properties (supplied by independent adult raters) explained additional variance for all groups and developmentally, with the relative influence of narrow- vs broad-range semantic properties increasing with age. We conclude by outlining an account of the formation and restriction of argument-structure generalisations designed to accommodate these findings.26 p

Individual biases, cultural evolution, and the statistical nature of language universals: the case of colour naming systems

Language universals have long been attributed to an innate Universal Grammar. An alternative explanation states that linguistic universals emerged independently in every language in response to shared cognitive or perceptual biases. A computational model has recently shown how this could be the case, focusing on the paradigmatic example of the universal properties of colour naming patterns, and producing results in quantitative agreement with the experimental data. Here we investigate the role of an individual perceptual bias in the framework of the model. We study how, and to what extent, the structure of the bias influences the corresponding linguistic universal patterns. We show that the cultural history of a group of speakers introduces population-specific constraints that act against the pressure for uniformity arising from the individual bias, and we clarify the interplay between these two forces