We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we prove that a distribution on the unit interval is computable if and only if its moments are uniformly computable.

In this paper, we propose a new algorithm for exploratory projection pursuit. The basis of the algorithm is the insight that previous approaches used fairly narrow definitions of interestingness / non interestingness. We argue that allowing these definitions to depend on the problem / data at hand is a more natural approach in an exploratory technique. This also allows our technique much greater applicability than the approaches extant in the literature. Complementing this insight, we propose a class of projection indices based on the spatial distribution function that can make use of such information. Finally, with the help of real datasets, we demonstrate how a range of multivariate exploratory tasks can be addressed with our algorithm. The examples further demonstrate that the proposed indices are quite capable of focussing on the interesting structure in the data, even when this structure is otherwise hard to detect or arises from very subtle patterns.

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.

In this paper, we present a novel decentralised management technique that allows electricity micro-storage devices, deployed within individual homes as part of a smart electricity grid, to converge to profitable and efficient behaviours. Specifically, we propose the use of software agents, residing on the users' smart meters, to automate and optimise the charging cycle of micro-storage devices in the home to minimise its costs, and we present a study of both the theoretical underpinnings and the implications of a practical solution, of using software agents for such micro-storage management. First, by formalising the strategic choice each agent makes in deciding when to charge its battery, we develop a game-theoretic framework within which we can analyse the competitive equilibria of an electricity grid populated by such agents and hence predict the best consumption profile for that population given their battery properties and individual load profiles. Our framework also allows us to compute theoretical bounds on the amount of storage that will be adopted by the population. Second, to analyse the practical implications of micro-storage deployments in the grid, we present a novel algorithm that each agent can use to optimise its battery storage profile in order to minimise its owner's costs. This algorithm uses a learning strategy that allows it to adapt as the price of electricity changes in real-time, and we show that the adoption of these strategies results in the system converging to the theoretical equilibria. Finally, we empirically evaluate the adoption of our micro-storage management technique within a complex setting, based on the UK electricity market, where agents may have widely varying load profiles, battery types, and learning rates. In this case, our approach yields savings of up to 14% in energy cost for an average consumer using a storage device with a capacity of less than 4.5 kWh and up to a 7% reduction in carbon emissions resulting from electricity generation (with only domestic consumers adopting micro-storage and, commercial and industrial consumers not changing their demand). Moreover, corroborating our theoretical bound, an equilibrium is shown to exist where no more than 48% of households would wish to own storage devices and where social welfare would also be improved (yielding overall annual savings of nearly £1.5B).

Many Artificial Intelligence tasks cannot be evaluated with a single quality criterion and some sort of weighted combination is needed to provide system rankings. A problem of weighted combination measures is that slight changes in the relative weights may produce substantial changes in the system rankings. This paper introduces the Unanimous Improvement Ratio (UIR), a measure that complements standard metric combination criteria (such as van Rijsbergens F-measure) and indicates how robust the measured differences are to changes in the relative weights of the individual metrics. UIR is meant to elucidate whether a perceived difference between two systems is an artifact of how individual metrics are weighted. Besides discussing the theoretical foundations of UIR, this paper presents empirical results that confirm the validity and usefulness of the metric for the Text Clustering problem, where there is a tradeoff between precision and recall based metrics and results are particularly sensitive to the weighting scheme used to combine them. Remarkably, our experiments show that UIR can be used as a predictor of how well differences between systems measured on a given test bed will also hold in a different test bed.

In this paper a method is proposed for performance evaluation of road traffic control systems. The method is designed to be implemented in an on-line simulation environment, which enables optimisation of adaptive traffic control strategies. Performance measures are computed using a fuzzy cellular traffic model, formulated as a hybrid system combining cellular automata and fuzzy calculus. Experimental results show that the introduced method allows the performance to be evaluated using imprecise traffic measurements. Moreover, the fuzzy definitions of performance measures are convenient for uncertainty determination in traffic control decisions.

As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe even more complex probabilistic models and inference algorithms. What are the limits of mechanizing probabilistic inference? We investigate the computability of conditional probability, a fundamental notion in probability theory and a cornerstone of Bayesian statistics, and show that there are computable joint distributions with noncomputable conditional distributions, ruling out the prospect of general inference algorithms, even inefficient ones. Specifically, we construct a pair of computable random variables in the unit interval such that the conditional distribution of the first variable given the second encodes the halting problem. Nevertheless, probabilistic inference is possible in many common modeling settings, and we prove several results giving broadly applicable conditions under which conditional distributions are computable. In particular, conditional distributions become computable when measurements are corrupted by independent computable noise with a sufficiently smooth density.

Suppose that multiple experts (or learning algorithms) provide us with alternative Bayesian network (BN) structures over a domain, and that we are interested in combining them into a single consensus BN structure. Specifically, we are interested in that the consensus BN structure only represents independences all the given BN structures agree upon and that it has as few parameters associated as possible. In this paper, we prove that there may exist several non-equivalent consensus BN structures and that finding one of them is NP-hard. Thus, we decide to resort to heuristics to find an approximated consensus BN structure. In this paper, we consider the heuristic proposed by Matzkevich and Abramson, which builds upon two algorithms, called Methods A and B, for efficiently deriving the minimal directed independence map of a BN structure relative to a given node ordering. Methods A and B are claimed to be correct although no proof is provided (a proof is just sketched). In this paper, we show that Methods A and B are not correct and propose a correction of them.

Adaptation to changing environments is a hallmark of biological systems. Diversity in traits is necessary for adaptation and can influence the survival of a population faced with novelty. In habitats that remain stable over many generations, stabilizing selection reduces trait differences within populations, thereby appearing to remove the diversity needed for heritable adaptive responses in new environments. Paradoxically, field studies have documented numerous populations under long periods of stabilizing selection and evolutionary stasis that have rapidly evolved under changed environmental conditions. In this article, we review how cryptic genetic variation (CGV) resolves this diversity paradox by allowing populations in a stable environment to gradually accumulate hidden genetic diversity that is revealed as trait differences when environments change. Instead of being in conflict, environmental stasis supports CGV accumulation and thus appears to facilitate rapid adaptation in new environments as suggested by recent CGV studies. Similarly, degeneracy has been found to support both genetic and non-genetic adaptation at many levels of biological organization. Degenerate, as opposed to diverse or redundant, ensembles appear functionally redundant in certain environmental contexts but functionally diverse in others. CGV and degeneracy paradigms for adaptation are integrated in this review, revealing a common set of principles that support adaptation at multiple levels of biological organization. Though a discussion of simulation studies, molecular-based experimental systems, principles from population genetics, and field experiments, we demonstrate that CGV and degeneracy reflect complementary top-down and bottom-up, respectively, conceptualizations of the same basic phenomenon and arguably capture a universal feature of biological adaptive processes.

It is now well known that decentralised optimisation can be formulated as a potential game, and game-theoretical learning algorithms can be used to find an optimum. One of the most common learning techniques in game theory is fictitious play. However fictitious play is founded on an implicit assumption that opponents' strategies are stationary. We present a novel variation of fictitious play that allows the use of a more realistic model of opponent strategy. It uses a heuristic approach, from the online streaming data literature, to adaptively update the weights assigned to recently observed actions. We compare the results of the proposed algorithm with those of stochastic and geometric fictitious play in a simple strategic form game, a vehicle target assignment game and a disaster management problem. In all the tests the rate of convergence of the proposed algorithm was similar or better than the variations of fictitious play we compared it with. The new algorithm therefore improves the performance of game-theoretical learning in decentralised optimisation.