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ABSTRACT: This work proposes an algorithm that makes use of partial information to improve the convergence properties of the value iteration algorithm in terms of the overall computational complexity. The algorithm iterates on a series of increasingly refined approximate models that converges to the true model according to an optimal linear rate, which coincides with the convergence rate of the original value iteration algorithm. The paper investigates the properties of the proposed algorithm and features a series of switchover queue examples which illustrates the efficacy of the method.
European Journal of Operational Research 08/2013; 229(1):190-198. · 1.82 Impact Factor
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ABSTRACT: Many iterative algorithms employ operators which are difficult to evaluate exactly, but for which a graduated range of approximations exist. In such cases, coarse-to-fine algorithms are often used, in which a crude initial operator approximation is gradually refined with new iterations. In such algorithms, because the computational complexity increases over iterations, the algorithms convergence rate is properly calculated with respect to cumulative computation time. This suggests the problem of determining an optimal rate of refinement for the operator approximation. This paper shows that, for linearly convergent algorithm, the optimal rate of refinement approaches the rate of convergence of the exact algorithm itself, regardless of the tolerance-complexity relationship. We illustrate this result with an analysis of coarse-to-fine grid algorithms for Markov decision processes with continuous state spaces. Using the methods proposed here we deduce an algorithm that presents optimal complexity results and consists solely of a non-adaptive schedule for the gradual decrease of grid size.
IEEE Transactions on Automatic Control 12/2012; 57(12):3132-3146. · 2.11 Impact Factor
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Journal of pediatric and adolescent gynecology 08/2012; 25(4):280-1. · 0.90 Impact Factor
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ABSTRACT: Donor livers are precious resources and it is, therefore, ethically imperative that we employ optimally sensitive and specific transplant selection criteria. Current selection criteria, the Milan criteria, for liver transplant candidates with hepatocellular carcinoma (HCC) are primarily based on radiographic characteristics of the tumor. Although the Milan criteria result in reasonably high survival and low-recurrence rates, they do not assess an individual patient's tumor biology and recurrence risk. Consequently, it is difficult to predict on an individual basis the risk for recurrent disease. To address this, we employed microarray profiling of microRNA (miRNA) expression from formalin fixed paraffin embedded tissues to define a biomarker that distinguishes between patients with and without HCC recurrence after liver transplant. In our cohort of 64 patients, this biomarker outperforms the Milan criteria in that it identifies patients outside of Milan who did not have recurrent disease and patients within Milan who had recurrence. We also describe a method to account for multifocal tumors in biomarker signature discovery.
American Journal of Transplantation 02/2012; 12(2):428-37. · 6.39 Impact Factor
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A. Almudevar
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ABSTRACT: The problem of location tracking of a mobile station in a wireless network has received considerable attention in recent literature. In many installations, a mobile station transmits a radio frequency signal which is received at a number of base stations, from which location estimation follows. Such an application requires some form of signal-distance calibration, either an empirical signal map, or a model-based method which relies on functional relationships between signal and distance derivable from physical principles. In this paper, we propose an alternative approach in which a time series of received signal strength (RSS) measurements is mapped onto a plane in a manner which preserves the general topological and directional properties of any trajectory of a mobile station. This is accomplished without requiring a signal-distance calibration, or even exact knowledge of the base station locations. A detailed proof of the stability properties of the mapping is given. An implementation protocol is developed, and illustrated with numerical examples.
IEEE Transactions on Signal Processing 08/2008; · 2.63 Impact Factor
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ABSTRACT: Many iterative algorithms rely on operators which may be difficult or impossible to evaluate exactly, but for which approximations are available. Furthermore, a graduated range of approximations may be available, inducing a functional relationship between computational complexity and approximation tolerance. In such a case, a reasonable strategy would be to vary tolerance over iterations, starting with a cruder approximation, then gradually decreasing tolerance as the solution is approached. In this article, it is shown that under general conditions, for linearly convergent algorithms the optimal choice of approximation tolerance convergence rate is the same linear convergence rate as the exact algorithm itself, regardless of the tolerance/complexity relationship. We illustrate this result by presenting a partial information value iteration (PIVI) algorithm for discrete time dynamic programming problems. The proposed algorithm makes use of increasingly accurate partial model information in order to decrease the computational burden of the standard value iteration algorithm. The algorithm is applied to a stochastic network example and compared to value iteration for the purpose of benchmarking.
Decision and Control, 2007 46th IEEE Conference on; 12/2007
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A. Almudevar
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ABSTRACT: The efficient coding of directed graphs can be of importance in data compression algorithms, as well as in graphical modelling applications in artificial intelligence and biological network reconstruction. One type of code commonly used involves the separate coding of node parent sets, and can be shown to have an asymptotic code length proportional to the number of edges. We show the existence of an alternative code, based on graph blocks, which can be shown to be of uniformly shorter length under asymptotically invariant conditions.
Information Theory Workshop, 2007. ITW '07. IEEE; 10/2007
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ABSTRACT: Gene perturbation experiments are commonly used in the reconstruction of gene regulatory networks. Because such experiments are often difficult to perform, it is important to predict on a rational basis those experiments likely to result in the greatest resolution of model uncertainty. When a method for constructing Bayesian posterior densities on the space of network models is available, this provides a means with which to estimate the expected reduction in entropy that would result from a given perturbation experiment. We define an algorithm for selecting perturbation experiments based on this idea, and demonstrate it using a simulation study using a Bayesian network model.
Computational Intelligence in Bioinformatics and Computational Biology, 2005. CIBCB '05. Proceedings of the 2005 IEEE Symposium on; 12/2005
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ABSTRACT: Single measurements of peak oxygen uptake (VO2) have been shown to predict mortality in patients with cystic fibrosis (CF) although no longitudinal study of serial measurements has been reported in children. A study was undertaken to determine whether the initial, final, or the rate of fall of forced expiratory volume in 1 second (FEV1) or peak VO2 was a better predictor of mortality.
Twenty eight children aged 8-17 years with CF performed annual pulmonary function and maximal exercise tests over a 5 year period to determine FEV1 and peak VO2, magnitude of their change over time, and survival over the subsequent 7-8 years. Analysis was done using Kaplan-Meier curves and Cox proportional hazard model.
Peak VO2 fell during the observation period in 70% of the patients, with a mean annual decline of 2.1 ml/min/kg. Initial peak VO2 was not predictive of mortality but rate of decline and final peak VO2 of the series were significant predictors. Patients with peak VO2 less than 32 ml/min/kg exhibited a dramatic increase in mortality, in contrast to those whose peak VO2 exceeded 45 ml/min/kg, none of whom died. The first, last, and rate of decline in FEV1 over time were all significant predictors of mortality.
Higher peak VO2 is a marker for longer survival in CF patients.
Thorax 02/2005; 60(1):50-4. · 6.84 Impact Factor
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ABSTRACT: In this work, we present a discrete model to the production and storage problem with multiple production stages and a single final product, subject to random demand. We present some conditions under which the optimal policy generates positive recurrent states. In addition, we derive a dynamic programming procedure to seek the optimal solution to the problem and provide some numerical examples.
Decision and Control, 2004. CDC. 43rd IEEE Conference on; 01/2005
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A Almudevar
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ABSTRACT: The problem of inferring kinship structure among a sample of individuals using genetic markers is considered with the objective of developing hypothesis tests for genetic relatedness with nearly optimal properties. The class of tests considered are those that are constrained to be permutation invariant, which in this context defines tests whose properties do not depend on the labeling of the individuals. This is appropriate when all individuals are to be treated identically from a statistical point of view. The approach taken is to derive tests that are probably most powerful for a permutation invariant alternative hypothesis that is, in some sense, close to a null hypothesis of mutual independence. This is analagous to the locally most powerful test commonly used in parametric inference. Although the resulting test statistic is a U-statistic, normal approximation theory is found to be inapplicable because of high skewness. As an alternative it is found that a conditional procedure based on the most powerful test statistic can calculate accurate significance levels without much loss in power. Examples are given in which this type of test proves to be more powerful than a number of alternatives considered in the literature, including Queller and Goodknight's (1989) estimate of genetic relatedness, the average number of shared alleles (Blouin, 1996), and the number of feasible sibling triples (Almudevar and Field, 1999).
Biometrics 01/2002; 57(4):1080-8. · 1.83 Impact Factor
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A Almudevar
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ABSTRACT: The problem of assessing the variability in pedigree reconstruction using DNA markers is considered for the special case of single generation samples with no parents present. Error in pedigree reconstruction is measured through a metric imposed on the space of partitions of the individuals into family groups. A confidence set can therefore be taken to be a neighborhood of a point estimate, analogous to the estimation of a parameter in Euclidean space. The coverage probability is estimated using bootstrap techniques. Although the distributional properties of the sample depend on the population genotype frequencies, these are in practice usually unknown. Confidence sets conditioned on a statistic approximately sufficient for these frequencies are compared with confidence sets obtained by substituting frequency estimates directly into the sampling distribution. In two simulation studies, the difference is found to be of some consequence.
Biometrics 10/2001; 57(3):757-63. · 1.83 Impact Factor
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ABSTRACT: In this work, we present an approximate value iteration algorithm for a production and storage model with multiple production stages and a single final product, subject to random demand. We use linear function approximation schemes in subsets of the state space and represent a few key states in a look-up table form. We obtain some promising results and perform sensitivity analysis with respect to the parameters of the algorithm for the benchmark problem studied.
Mechatronics and Automation, 2005 IEEE International Conference;
