Solving nonlinear rational expectations models by eigenvalue-eigenvector decompositions

We provide a summarized presentation of solution methods for rational expectations models, based on eigenvalue/eigenvector decompositions. These methods solve systems of stochastic linear difference equations by relying on the use of stability conditions derived from the eigenvectors associated to unstable eigenvalues of the coefficient matrices in the system. For nonlinear models, a linear approximation must be obtained, and the stability conditions are approximate, This is however, the only source of approximation error, since the nonlinear structure of the original model is used to produce the numerical solution. After applying the method to a baseline stochastic growth model, we explain how it can be used: i) to salve some identification problems that may arise in standard growth models, and ii) to solve endogenous growth models

Domain-Adversarial Training of Neural Networks

We introduce a new representation learning approach for domain adaptation, in which data at training and test time come from similar but different distributions. Our approach is directly inspired by the theory on domain adaptation suggesting that, for effective domain transfer to be achieved, predictions must be made based on features that cannot discriminate between the training (source) and test (target) domains. The approach implements this idea in the context of neural network architectures that are trained on labeled data from the source domain and unlabeled data from the target domain (no labeled target-domain data is necessary). As the training progresses, the approach promotes the emergence of features that are (i) discriminative for the main learning task on the source domain and (ii) indiscriminate with respect to the shift between the domains. We show that this adaptation behaviour can be achieved in almost any feed-forward model by augmenting it with few standard layers and a new gradient reversal layer. The resulting augmented architecture can be trained using standard backpropagation and stochastic gradient descent, and can thus be implemented with little effort using any of the deep learning packages. We demonstrate the success of our approach for two distinct classification problems (document sentiment analysis and image classification), where state-of-the-art domain adaptation performance on standard benchmarks is achieved. We also validate the approach for descriptor learning task in the context of person re-identification application.Comment: Published in JMLR: http://jmlr.org/papers/v17/15-239.htm

Event Reconstruction for Atmospheric Releases Employing Urban Puff Model UDM with Stochastic Inversion Methodology

The rapid identification of contaminant plume sources and their characteristics in urban environments can greatly enhance emergency response efforts. Source identification based on downwind concentration measurements is complicated by the presence of building obstacles that can cause flow diversion and entrainment. While high-resolution computational fluid dynamics (CFD) simulations are available for predicting plume evolution in complex urban geometries, such simulations require large computational effort. We make use of an urban puff model, the Defence Science Technology Laboratory's (Dstl) Urban Dispersion Model (UDM), which employs empirically based puff splitting techniques. UDM enables rapid urban dispersion simulations by combining traditional Gaussian puff modeling with empirically deduced mixing and entrainment approximations. Here we demonstrate the preliminary reconstruction of an atmospheric release event using stochastic sampling algorithms and Bayesian inference together with the rapid UDM urban puff model based on point measurements of concentration. We consider source inversions for both a prototype isolated building and for observations and flow conditions taken during the Joint URBAN 2003 field campaign at Oklahoma City. The Markov Chain Monte Carlo (MCMC) stochastic sampling method is used to determine likely source term parameters and considers both measurement and forward model errors. It should be noted that the stochastic methodology is general and can be used for time-varying release rates and flow conditions as well as nonlinear dispersion problems. The results of inversion indicate the probability of a source being at a particular location with a particular release rate. Uncertainty in observed data, or lack of sufficient data, is inherently reflected in the shape and size of the probability distribution of source term parameters. Although developed and used independently, source inversion with both UDM and a finite-element CFD code can be complementary in determining proper emergency response to an urban release. Ideally, the urban puff model is used to approximate the source location and strength. The more accurate CFD model can then be used to refine the solution

A graph-based factor screening method for synchronous data flow simulation models

This thesis develops a method for identifying important input factors in large system dynamics models from an analysis based on those models\u27 underlying structures. The identification of important input factors is commonly called factor screening and is a key step in the analysis of simulation models with many input parameters. Models under investigation are system dynamics models implemented as synchronous data flow programs, a model of computation that requires encoding the model components\u27 dependencies in a graph format. The developed method views this graph as a stochastic process and attempts to rank the importance of inputs, or source nodes, with respect to an output, or non-source node. This ranking is accomplished primarily through the use of weighted random-walks through the graph. A comparison is made against other factor screening techniques, including fractional factorial experiments. The presented structure-based method is found to be comparably accurate to statistical factor screen experiments at magnitude order ranking. Run time of the developed method compared against a resolution III fractional factorial design is found to be similar for small models, and significantly faster for large models