Markov chains constitute a common way of modelling the progression of a chronic disease through various severity states. For these models, a transition matrix with the probabilities of moving from one state to another for a specific time interval is usually estimated from cohort data. Quite often, however, the cohort is observed at specific times with intervals that may be greater than the interval of interest. The transition matrix computed then needs to be decomposed in order to estimate the desired interval transition matrix suited to the model. Although simple to implement, this method of matrix decomposition can yet result in an invalid short-interval transition matrix with negative or complex entries. In this paper, we present a method for computing short-interval transition matrices that is based on regularization techniques. Our method operates separately on each row of the invalid short-interval transition matrix aiming to minimize an appropriate distance measure. We test our method on various matrix structures and sizes, and evaluate its performance on a real-life transition model for HIV-infected individuals.

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Abstract. We describe the family of multi-dimensional Bayesian network classifiers which include one or more class variables and multiple feature variables. The family does not require that every feature variable is modelled as being dependent on every class variable, which results in better modelling capabilities than families of models with a single class variable. For the family of multidimensional classifiers, we address the complexity of the classification problem and show that it can be solved in polynomial time for classifiers with a graphical structure of bounded treewidth over their feature variables and a restricted number of class variables. We further describe the learning problem for the subfamily of fully polytree-augmented multi-dimensional classifiers and show that its computational complexity is polynomial in the number of feature variables.

Abstract-The problem of finding an optimal admission policy to an M / M / c queue with one controlled and one uncontrolled arrival stream is addressed in this paper. There are two streams of customers (customers of class 1 and 2) that are generated according to independent Poisson processes with constant arrival rates. The service time probability distribution is exponential and does not depend oil the class of the customers. Upon arrival a class 1 customer may be admitted or rejected, while incoming class 2 customers are always admitted. A statedependent reward is earned each time a new class 1 customer enters the system. When the discount factor is small, we show that there exists a stationary admission policy of a threshold type that maximizes the expected total discounted reward over an infinite horizon. A similar result is also obtained when considering the long-run average reward criterion. The proof relies on a new device that consists of a partial construction of the solution of the dynamic programming equation. Applications arising from teletraffic analysis are proposed.