Enrico Fagiuoli

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.

New partial orderings and applications

New concepts of partial stochastic orderings are introduced, and the relations among them and the classical partial orderings are shown. Relevance of these partial orderings in aging properties classification is discussed, and new classes of life distributions, based on them, are proposed. An application to stochastic comparison between Poisson shock models is proposed.

Preservation of certain classes of life distributions under Poisson shock models

Recently defined classes of life distributions are considered, and some relationships among them are proposed. The life distribution H of a device subject to shocks occurring randomly according to a Poisson process is also considered, and sufficient conditions for H to belong to these classes are discussed.

A characterization of the dilation order and its applications

LetX andY be two random variables with finite expectationsEX andEY, respectively. ThenX is said to be smaller thanY in the dilation order ifE[ϕ(X-EX)]≤E[ϕ(Y-EY)] for any convex functionϕ for which the expectations exist. In this paper we obtain a new characterization of the dilation order. This characterization enables us to give new interpretations to the dilation order, and using them we identify conditions which imply the dilation order. A sample of applications of the new characterization is given.

Tree-Based Credal Networks for Classification

Bayesian networks are models for uncertain reasoning which are achieving a growing importance also for the data mining task of classification. Credal networks extend Bayesian nets to sets of distributions, or credal sets. This paper extends a state-of-the-art Bayesian net for classification, called tree-augmented naive Bayes classifier, to credal sets originated from probability intervals. This extension is a basis to address the fundamental problem of prior ignorance about the distribution that generates the data, which is a commonplace in data mining applications. This issue is often neglected, but addressing it properly is a key to ultimately draw reliable conclusions from the inferred models. In this paper we formalize the new model, develop an exact linear-time classification algorithm, and evaluate the credal net-based classifier on a number of real data sets. The empirical analysis shows that the new classifier is good and reliable, and raises a problem of excessive caution that is discussed in the paper. Overall, given the favorable trade-off between expressiveness and efficient computation, the newly proposed classifier appears to be a good candidate for the wide-scale application of reliable classifiers based on credal networks, to real and complex tasks.

Mean residual life and increasing convex comparison of shock models

Two devices are subjected to shocks arriving according to a general counting process. Let M1 and M2 be the random number of shocks that cause the failure of the first and the second device, respectively. We find conditions on the counting process such that the mean residual life ordering, the increasing convex ordering and the expectation ordering between M1 and M2 are preserved in the random lifetimes of the two devices.

A Note about Redundancy in Influence Diagrams

Influence Diagrams (IDs) are formal tools for modelling decision processes and for computing optimal strategies under risk. Like Bayesian networks, influence diagrams exploit the sparsity of the dependency relationships among the random variables in order to reduce computational complexity. In this note, we initially observe that an influence diagram can have some arcs that are not necessary for a complete description of the model. We show that while it may not be easy to detect such arcs, it is important, since a redundant graphical structure can exponentially increase the computational time of a solution procedure. Then we define a graphical criterion that is shown to allow the identification and removal of the redundant parts of an ID. This technical result is significant because it precisely defines what is relevant to know at the time of a decision. Furthermore, it allows a redundant influence diagram to be transformed into another ID, that can be used to compute the optimal policy in an equivalent but more efficient way.

Constant rebalanced portfolios and side-information

In recent years much work has been carried out to design and analyse online investment strategies based on constant rebalanced portfolios. A constant rebalanced portfolio is a sequential investment strategy that maintains fixed through time, trading period by trading period, the wealth distribution among a set of assets. In this framework, Cover proposed the universal portfolio, which is competitive with the best constant rebalanced portfolio determined in hindsight, i.e. the constant rebalanced portfolio obtained by assuming perfect knowledge of future stock prices. However, the constant rebalanced portfolio is designed to deal with the portfolio selection problem in the case where no additional information concerning the stock market, is available. To overcome this limitation, Cover and Ordentlich proposed the state constant rebalanced portfolio, which is capable of appropriately exploiting the available side-information concerning the stock market. In this paper we study and analyse the topic introduced by Cover and Ordentlich and focus our attention on the interplay between constant rebalanced portfolios and side-information. We introduce a mathematical framework to deal with the constant rebalanced portfolio in the case where side-information, concerning the stock market, is available. The mathematical framework defines and analyses the mixture best constant rebalanced portfolio, which we propose as the investment benchmark to be considered in the case where side-information, concerning the stock market, is available. The mixture best constant rebalanced portfolio outperforms the best constant rebalanced portfolio by an exponential factor in terms of the achieved wealth and therefore offers an interesting opportunity for side-information specialized online investment algorithms. We describe a new online investment algorithm that exploits the definition of the mixture best constant rebalanced portfolio and the available side-information. The performance of the proposed online investment algorithm is investigated through a set of numerical experiments concerning four major stock market data sets, namely DJIA, S&P500, TSE and NYSE. The results emphasize the relevance of the proposed online investment strategy and underline the central role of the quality of the side-information in outperforming the best constant rebalanced portfolio.

Computation of the makespan in a transfer line with station breakdowns using stochastic Petri nets

Abstract In this paper the authors developed a Petri net model of a transfer line, whose machines are subject to failure, considering both blocking and rerouting of workpieces when a machine fails. The introduction in the net of the marked token is shown to allow the computation of the makespan of the system.

A knowledge-based diagnostic system for the business-process ordering of a plant

Abstract The objective of this paper is the description of a tool developed in order to diagnose a potential failure in a managerial process, giving an early warning well before the actual failure arises. Moreover, this tool can diagnose the factors which generated the failure and assist in formulating corrective actions. The business process analysed in this paper is the ordering process; focus has been put on some important process indicators, monitored using modelling and simulation methods like System Dynamics, Multivariate Statistical Process Control, and Time Series Analysis. All the information obtained by these methods is integrated into an Expert System that contains the knowledge about the process and warns the process owner about potential “out-of-control” situations. This tool acts as an instrument panel which gives to the process owner a global vision of the entire process.