Marco Zaffalon

Simulation and planning of an intermodal container terminal

A decision support system for management of an intermodal container terminal is presented. Among problems to be solved are the spatial allo cation of containers in the terminal yard, the allo cation of resources, and the scheduling of opera tions to maximise a performance function based on economic indicators. These problems are solved using techniques from optimisation, such as job-shop scheduling, genetic algorithms or mixed-integer linear programming. At the termi nal, the same problems are usually solved by the terminal manager, using only his experience. The manager can trust computer-generated solutions only by validating them by means of a simulation model of the terminal. Thus, the simulation tool also becomes a means to introduce new ap proaches into traditional settings. We focus on the resource allocation problem and describe our modules for optimisation of the allocation process and the simulation of the terminal. The former is based on integer linear programming; the latter is a discrete-event simulation tool based on the pro cess-oriented paradigm. The simulator provides a testbed for checking the validity and robustness of the policy computed by the optimisation module.

The naive credal classifier

Convex sets of probability distributions are also called credal sets. They generalize probability theory by relaxing the requirement that probability values be precise. Classification, i.e. assigning class labels to instances described by a set of attributes, is an important domain of application of Bayesian methods, where the naive Bayes classifier has a surprisingly good performance. This paper proposes a new method of classification which involves extending the naive Bayes classifier to credal sets. Exact and effective solution procedures for naive credal classification are derived, and the related dominance criteria are discussed. Credal classification appears as a new method, based on more realistic assumptions and in the direction of more reliable inferences.

2U: an exact interval propagation algorithm for polytrees with binary variables

Abstract This paper addresses the problem of computing posterior probabilities in a discrete Bayesian network where the conditional distributions of the model belong to convex sets. The computation on a general Bayesian network with convex sets of conditional distributions is formalized as a global optimization problem. It is shown that such a problem can be reduced to a combinatorial problem, suitable to exact algorithmic solutions. An exact propagation algorithm for the updating of a polytree with binary variables is derived. The overall complexity is linear to the size of the network, when the maximum number of parents is fixed.

An optimization methodology for intermodal terminal management

A solution to the problems of resource allocation and scheduling of loading and unloading operations in a container terminal is presented. The two problems are formulated and solved hierarchically. First, the solution of the resource allocation problem returns, over a number of work shifts, a set of quay cranes used to load and unload containers from the moored ships and the set of yard cranes to store those containers on the yard. Then, a scheduling problem is formulated to compute the loading and unloading lists of containers for each allocated crane. The feasibility of the solution is verified against a detailed, discrete-event based, simulation model of the terminal. The simulation results show that the optimized resource allocation, which reduces the costs by [frac13], can be effectively adopted in combination with the optimized loading and unloading list. Moreover, the simulation shows that the optimized lists reduce the number of crane conflicts on the yard and the average length of the truck queues in the terminal.

Reliable diagnoses of dementia by the naive credal classifier inferred from incomplete cognitive data

Dementia is a serious personal, medical and social problem. Recent research indicates early and accurate diagnoses as the key to effectively cope with it. No definitive cure is available but in some cases when the impairment is still mild the disease can be contained. This paper describes a diagnostic tool that jointly uses the naive credal classifier and the most widely used computerized system of cognitive tests in dementia research, the Cognitive Drug Research system. The naive credal classifier extends the discrete naive Bayes classifier to imprecise probabilities. The naive credal classifier models both prior ignorance and ignorance about the likelihood by sets of probability distributions. This is a new way to deal with small and incomplete datasets that departs significantly from most established classification methods. In the empirical study presented here, the naive credal classifier provides reliability and unmatched predictive performance. It delivers up to 95% correct predictions while being very robust with respect to the partial ignorance due to the largely incomplete data. The diagnostic tool also proves to be very effective in discriminating between Alzheimers disease and dementia with Lewy bodies.

Exact credal treatment of missing data

This paper proposes an exact, no-assumptions approach to dealing with incomplete sets of multivariate categorical data. An incomplete data set is regarded as a finite collection of complete data sets, and a joint distribution is obtained from each of them, at a descriptive level. The tools to simultaneously treat all the possible joint distributions compatible with an incomplete set of data are given. In particular, a linear description of the set of distributions is formulated, and it is shown that the computation of bounds on the expectation of real-valued functions under such distributions is both possible and efficient, by means of linear programming. Specific algorithms are also developed whose complexity grows linearly in the number of observations. An analysis is then carried out to estimate population probabilities from incomplete multinomial samples. The descriptive tool extends in a straightforward way to the inferential problem by exploiting Walleys imprecise Dirichlet model.

Epistemic irrelevance in credal nets: The case of imprecise Markov trees

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithms operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.

Distribution of mutual information from complete and incomplete data

Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider sample-to-population inferential approaches. This paper deals with the posterior distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean, and analytical approximations for the variance, skewness and kurtosis are derived. These approximations have a guaranteed accuracy level of the order O(n i3 ), where n is the sample size. Leading order approximations for the mean and the variance are derived in the case of incomplete samples. The derived analytical expressions allow the distribution of mutual information to be approximated reliably and quickly. In fact, the derived expressions can be computed with the same order of complexity needed for descriptive mutual information. This makes the distribution of mutual information become a concrete alternative to descriptive mutual information in many applications which would beneflt from moving to the inductive side. Some of these prospective applications are discussed, and one of them, namely feature selection, is shown to perform signiflcantly better when inductive mutual information is used.

Constraint Logic Programming and Integer Programming approaches and their collaboration in solving an assignment scheduling problem

Generalised Assignment Problems (GAP), traditionally solved by Integer Programming techniques, are addressed in the light of current Constraint Programming methods. A scheduling application from manufacturing, based on a modified GAP, is used to examine the performance of each technique under a variety of problem characteristics. Experimental evidence showed that, for a set of assignment problems, Constraint Logic Programming (CLP) performed consistently better than Integer Programming (IP). Analysis of the CLP and IP processes identified ways in which the search was effective. The insight gained from the analysis led to an Integer Programming approach with significantly improved performance. Finally, the issue of collaboration between the two contrasting approaches is examined with respect to ways in which the solvers can be combined in an effective manner.

Independent natural extension

There is no unique extension of the standard notion of probabilistic independence to the case where probabilities are indeterminate or imprecisely specified. Epistemic independence is an extension that formalises the intuitive idea of mutual irrelevance between different sources of information. This gives epistemic independence very wide scope as well as appeal: this interpretation of independence is often taken as natural also in precise-probabilistic contexts. Nevertheless, epistemic independence has received little attention so far. This paper develops the foundations of this notion for variables assuming values in finite spaces. We define (epistemically) independent products of marginals (or possibly conditionals) and show that there always is a unique least-committal such independent product, which we call the independent natural extension. We supply an explicit formula for it, and study some of its properties, such as associativity, marginalisation and external additivity, which are basic tools to work with the independent natural extension. Additionally, we consider a number of ways in which the standard factorisation formula for independence can be generalised to an imprecise-probabilistic context. We show, under some mild conditions, that when the focus is on least-committal models, using the independent natural extension is equivalent to imposing a so-called strong factorisation property. This is an important outcome for applications as it gives a simple tool to make sure that inferences are consistent with epistemic independence judgements. We discuss the potential of our results for applications in Artificial Intelligence by recalling recent work by some of us, where the independent natural extension was applied to graphical models. It has allowed, for the first time, the development of an exact linear-time algorithm for the imprecise probability updating of credal trees.