Search

The calibration of urban traffic microsimulation models is addressed in this paper, focusing on the multivariate distribution of traffic features. This allows to take into account day-to-day variability and possibly complex statistical dependencies, enabling robust validation and the computation of more accurate statistics. Variability in traffic models can be obtained, in principle, by suitably tuning origin-destination demand flows, but this becomes problematic for microsimulation models when complex multivariate distributions are considered, due to excessive dimensionality and nonlinearity. Thus, here we investigate how complex multivariate behavior can be achieved by suitably varying only a subset of the parameters ruling the microsimulation dynamics, without imposing any distribution on the demand flows. To this purpose, rather than looking for fixed values of the parameters, we exploit distribution models having the structure of mixtures of uniforms, through which the simulator parameter values can be randomly sampled, thus replacing the simulator inner randomization mechanism. We formalize the optimization of the mixture parameters through a maximum mean discrepancy principle involving the simulator dynamics, which leads to a large-dimensional non-differentiable problem that we solve through a method based on cross-entropy. Preliminary experiments concerning the application of the proposed methodology to the SUMO simulator show how it is possible to capture quite complex multivariate distributions of target flows varying only four parameters. [ABSTRACT FROM AUTHOR]

In this paper, a general method for the numerical solution of maximum-likelihood estimation (MLE) problems is presented; it adopts the deterministic learning (DL) approach to find close approximations to ML estimator functions for the unknown parameters of any given density. The method relies on the choice of a proper neural network and on the deterministic generation of samples of observations of the likelihood function, thus avoiding the problem of generating samples with the unknown density. Under mild assumptions, consistency and convergence with favorable rates to the true ML estimator function can be proved. Simulation results are provided to show the good behavior of the algorithm compared to the corresponding exact solutions. Index Terms--Deterministic learning (DL), discrepancy, maximum-likelihood estimation (MLE), variation.

A methodology to design state estimators for a class of nonlinear continuous-time dynamic systems that is based on neural networks and nonlinear programming is proposed. The estimator has the structure of a Luenberger observer with a linear gain and a parameterized (in general, nonlinear) function, whose argument is an innovation term representing the difference between the current measurement and its prediction. The problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error. Toward this end, if a neural network is used to take on this function, the parameters (i.e., the neural weights) are chosen, together with the gain, by constraining the derivative of a quadratic Lyapunov function for the estimation error to be negative definite on a given compact set. It is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points. The gain is determined by solving a Lyapunov equation. The neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid-point constraints that are not satisfied. Techniques based on low-discrepancy sequences are applied to deal with a small number of sampling points, and, hence, to reduce the computational burden required to optimize the parameters. Numerical results are reported and comparisons with those obtained by the extended Kalman filter are made. Index Terms--Feedforward neural networks, Lyapunov function, offline optimization, penalty function, quasi-random sequences, state observer.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2005.01.022 Byline: Cristiano Cervellera (a), Victoria C.P. Chen (b), Aihong Wen (b) Keywords: Dynamic programming; Large-scale optimization; Applied probability; Neural networks; Natural resources Abstract: A numerical solution to a 30-dimensional water reservoir network optimization problem, based on stochastic dynamic programming, is presented. In such problems the amount of water to be released from each reservoir is chosen to minimize a nonlinear cost (or maximize benefit) function while satisfying proper constraints. Experimental results show how dimensionality issues, given by the large number of basins and realistic modeling of the stochastic inflows, can be mitigated by employing neural approximators for the value functions, and efficient discretizations of the state space, such as orthogonal arrays, Latin hypercube designs and low-discrepancy sequences. Author Affiliation: (a) Institute of Intelligent Systems for Automation, ISSIA-CNR National Research Council of Italy, Genova Branch, Via De Marini 6, Genova 16149, Italy (b) Department of Industrial and Manufacturing Systems Engineering, The University of Texas at Arlington, Campus Box 19017, Arlington, TX 76019-0017, United States

A novel measurement approach for power-flow analysis in medium-voltage (MV) networks, based on load power measurements at low-voltage level in each secondary substation (SS) and only one voltage measurement at the MV level at primary substation busbars, was proposed by the authors in previous works. In this paper, the method is improved to cover the case of temporary unavailability of load power measurements in some SSs. In particular, a new load power estimation method based on artificial neural networks (ANNs) is proposed. The method uses historical data to train the ANNs and the real-time available measurements to obtain the load estimations. The load-flow algorithm is applied with the estimated load powers, and the MV network state variables are obtained. The proposed method is validated for the real MV distribution network of the island of Ustica. The loads of selected SSs are estimated for two full days of different seasons. In comparison with previous works, satisfactory results are obtained in terms of uncertainty in the calculated power flows, thus suggesting the applicability of the proposed method for real-time monitoring of MV distribution networks. [ABSTRACT FROM AUTHOR]

This paper investigates the use of lattice point sets as an efficient method to sample uniformly the state space of discrete-time dynamic systems for the solution of finite-horizon optimal control problems using approximate dynamic programming. Lattice point sets are a kind of discretization method, commonly employed for efficient numerical integration, providing a regular and balanced sampling of the state space based on the repetition of elementary unit cells. A convergence analysis of the approximate solution of the control problem to the optimal one is provided, pointing out that such sampling schemes allow one to efficiently exploit possible regularities of the cost-to-go functions. Furthermore, it is shown that a higher accuracy may be obtained through suitable transformations of the state vector of the dynamic system. Another advantage of lattice point sets over other sampling schemes is the possibility of evaluating a priori the goodness of a given set over another through the explicit computation of a specific parameter. Simulation results concerning the optimal control of a water reservoirs system are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Approximate dynamic programming (ADP) is the standard tool to solve Markovian decision problems under general hypotheses on the system and the cost equations. It is known that one of the key issues of the procedure is how to generate an efficient sampling of the state space, needed for the approximation of the value function, in order to cope with the well-known phenomenon of the curse of dimensionality. The most common approaches in the literature are either aimed at a uniform covering of the state space or driven by the actual evolution of the system trajectories. Concerning the latter approach, F -discrepancy, a quantity closely related to the Kolmogorov–Smirnov statistic, that measures how strictly a set of random points represents a probability distribution, has been recently proposed for an efficient ADP framework in the finite-horizon case. In this paper, we extend this framework to infinite-horizon discounted problems, providing a constructive algorithm to generate efficient sampling points driven by the system behavior. Then, the algorithm is refined with the aim of acquiring a more balanced covering of the state space, thus addressing possible drawbacks of a pure system-driven sampling approach to obtain, in fact, an efficient hybrid between the latter and the pure uniform design. A theoretical analysis is provided through the introduction of an original notion of the F -discrepancy and the proof of its properties. Simulation tests are provided to showcase the behavior of the proposed sampling method. [ABSTRACT FROM PUBLISHER]

In this paper, we discuss how the extreme learning machine (ELM) framework can be effectively employed in the unsupervised context of multivariate density estimation. In particular, two algorithms are introduced, one for the estimation of the cumulative distribution function underlying the observed data, and one for the estimation of the probability density function. The algorithms rely on the concept of F -discrepancy, which is closely related to the Kolmogorov–Smirnov criterion for goodness of fit. Both methods retain the key feature of the ELM of providing the solution through random assignment of the hidden feature map and a very light computational burden. A theoretical analysis is provided, discussing convergence under proper hypotheses on the chosen activation functions. Simulation tests show how ELMs can be successfully employed in the density estimation framework, as a possible alternative to other standard methods. [ABSTRACT FROM PUBLISHER]

In this paper, we address the problem of generating efficient state sample points for the solution of continuous-state finite-horizon Markovian decision problems through approximate dynamic programming. It is known that the selection of sampling points at which the value function is observed is a key factor when such function is approximated by a model based on a finite number of evaluations. A standard approach consists in generating these points through a random or deterministic procedure, aiming at a balanced covering of the state space. Yet, this solution may not be efficient if the state trajectories are not uniformly distributed. Here, we propose to exploit F -discrepancy, a quantity that measures how closely a set of random points represents a probability distribution, and introduce an example of an algorithm based on such concept to automatically select point sets that are efficient with respect to the underlying Markovian process. An error analysis of the approximate solution is provided, showing how the proposed algorithm enables convergence under suitable regularity hypotheses. Then, simulation results are provided concerning an inventory forecasting test problem. The tests confirm in general the important role of F -discrepancy, and show how the proposed algorithm is able to yield better results than uniform sampling, using sets even 50 times smaller. [ABSTRACT FROM PUBLISHER]

Graphical models are statistical models supported on a graph structure: nodes represent random variables, and missing edges represent probabilistic relationship of conditional independence. This makes them suited to model the behavior of complex systems that are difficult to model through mathematical equations. In this work, this possibility is exploited in a context of diagnostics and fault detection. Specifically, the fault detection problem is reduced to the evaluation of a conditional probability. The relevant conditional distribution is derived from the analysis of a suitable graphical model taking advantage of the so-called Markov properties. As a case study, we consider diagnostics of a hybrid bus, characterized by the combined use of a diesel engine and an electrical engine. The aim of the study is to verify the correct operation of the electrical system, in particular the status of the battery. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Predictive control is investigated as a paradigm for the allocation of handling resources to transfer containers inside intermodal terminals. The decisions on the allocation of such resources are derived from the minimization of performance cost functions that measure the lay times of carriers over a forward horizon basing on a model of the container flows. Such a model allows one to take advantage of the information available in real time on the arrival or departure of carriers with the corresponding amounts of containers scheduled for loading or unloading. The resulting strategy of resource allocation can be regarded as a feedback control law and is obtained by solving nonlinear programming problems online. Since the computation may be too expensive, a technique based on the idea of approximating offline such a law is proposed. The approximation is performed by using neural networks, which allow one to construct an approximate feedback controller and generate the corresponding online control actions with a negligible computational burden. The effectiveness of the approach is shown via simulations in a case study. [ABSTRACT FROM PUBLISHER]

Future road vehicles are expected to support point-to-point and long-range wireless connectivity as a standard feature, allowing data transfers while moving. In this vein, it is possible to forecast and develop new communication paradigms, as well as new infrastructures to take advantage of peculiarities of vehicular networks. This article introduces an optimized framework, on the basis of peer-to-peer principles, to manage content replication and dissemination through a mobile vehicular network. This is obtained through a discrete-time dynamic system over which an optimization problem must be solved in real time. Such a solution enables two different operations: (a) to overcome bandwidth limitations for distributing information among vehicles (e.g., traffic or security bulletins and multimedia contents) in an efficient way; (b) to use the vehicular flow as a virtual backbone to deliver data to different spatial locations without the need of a fixed network infrastructure. Simulations are provided to show the effectiveness of the proposed approach, with respect to classic peer-to-peer distribution schemes directly “ported” over the vehicular network. A direct comparison with an infrastructure-oriented solution is also presented. [ABSTRACT FROM AUTHOR]

In this brief, the use of lattice point sets (LPSs) is investigated in the context of general learning problems (including function estimation and dynamic optimization), in the case where the classic empirical risk minimization (ERM) principle is considered and there is freedom to choose the sampling points of the input space. Here it is proved that convergence of the ERM principle is guaranteed when LPSs are employed as training sets for the learning procedure, yielding up to a superlinear convergence rate under some regularity hypotheses on the involved functions. Preliminary simulation results are also provided. [ABSTRACT FROM AUTHOR]

The general problem of reconstructing an unknown function from a finite collection of samples is considered, in case the position of each input vector in the training set is not flied beforehand but is part of the learning process. In particular, the consistency of the empirical risk minimization (ERM) principle is analyzed, when the points in the input space are generated by employing a purely deterministic algorithm (deterministic learning). When the output generation is not subject to noise, classical number-theoretic results, involving discrepancy and variation, enable the establishment of a sufficient condition for the consistency of the ERM principle. In addition, the adoption of low-discrepancy sequences enables the achievement of a learning rate of O(1/L), with L being the size of the training set. An extension to the noisy case is provided, which Shows that the good properties of deterministic learning are preserved, if the level of noise at the output is not high. Simulation results confirm the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

The need for extracting a small sample from a large amount of real data, possibly streaming, arises routinely in learning problems, e.g., for storage, to cope with computational limitations, obtain good training/test/validation sets, and select minibatches for stochastic gradient neural network training. Unless we have reasons to select the samples in an active way dictated by the specific task and/or model at hand, it is important that the distribution of the selected points is as similar as possible to the original data. This is obvious for unsupervised learning problems, where the goal is to gain insights on the distribution of the data, but it is also relevant for supervised problems, where the theory explains how the training set distribution influences the generalization error. In this paper, we analyze the technique of stratified sampling from the point of view of distances between probabilities. This allows us to introduce an algorithm, based on recursive binary partition of the input space, aimed at obtaining samples that are distributed as much as possible as the original data. A theoretical analysis is proposed, proving the (greedy) optimality of the procedure together with explicit error bounds. An adaptive version of the algorithm is also introduced to cope with streaming data. Simulation tests on various data sets and different learning tasks are also provided.

In this paper, we address the problem of generating efficient state sample points for the solution of continuous-state finite-horizon Markovian decision problems through approximate dynamic programming. It is known that the selection of sampling points at which the value function is observed is a key factor when such function is approximated by a model based on a finite number of evaluations. A standard approach consists in generating these points through a random or deterministic procedure, aiming at a balanced covering of the state space. Yet, this solution may not be efficient if the state trajectories are not uniformly distributed. Here, we propose to exploit F -discrepancy, a quantity that measures how closely a set of random points represents a probability distribution, and introduce an example of an algorithm based on such concept to automatically select point sets that are efficient with respect to the underlying Markovian process. An error analysis of the approximate solution is provided, showing how the proposed algorithm enables convergence under suitable regularity hypotheses. Then, simulation results are provided concerning an inventory forecasting test problem. The tests confirm in general the important role of F -discrepancy, and show how the proposed algorithm is able to yield better results than uniform sampling, using sets even 50 times smaller.

The traditional extreme learning machine (ELM) approach is based on a random assignment of the hidden weight values, while the linear coefficients of the output layer are determined analytically. This brief presents an analysis based on geometric properties of the sampling points used to assign the weight values, investigating the replacement of random generation of such values with low-discrepancy sequences (LDSs). Such sequences are a family of sampling methods commonly employed for numerical integration, yielding a more efficient covering of multidimensional sets with respect to random sequences, without the need for any computationally intensive procedure. In particular, we prove that the universal approximation property of the ELM is guaranteed when LDSs are employed, and how an efficient covering affects the convergence positively. Furthermore, since LDSs are generated deterministically, the results do not have a probabilistic nature. Simulation results confirm, in practice, the good theoretical properties given by the combination of ELM with LDSs.

Local linear regression models, a kind of nonparametric structures that locally perform a linear estimation of the target function, are analyzed in the context of empirical risk minimization (ERM) for function learning. The analysis is carried out with emphasis on geometric properties of the available data. In particular, the discrepancy of the observation points used both to build the local regression models and compute the empirical risk is considered. This allows to treat indifferently the case in which the samples come from a random external source and the one in which the input space can be freely explored. Both consistency of the ERM procedure and approximating capabilities of the estimator are analyzed, proving conditions to ensure convergence. Since the theoretical analysis shows that the estimation improves as the discrepancy of the observation points becomes smaller, low-discrepancy sequences, a family of sampling methods commonly employed for efficient numerical integration, are also analyzed. Simulation results involving two different examples of function learning are provided.

This brief presents an analysis of the performance of kernel smoothing models used to estimate an unknown target function, addressing the case where the choice of the training set is part of the learning process. In particular, we consider a choice of the points at which the function is observed based on low-discrepancy sequences, which is a family of sampling methods commonly employed for efficient numerical integration. We prove that, under suitable regularity assumptions, consistency of the empirical risk minimization is guaranteed with a good rate of convergence of the estimation error, as well as the convergence of the approximation error. Simulation results confirm, in practice, the good theoretical properties given by the combination of kernel smoothing models with low-discrepancy sampling.