536 research outputs found

    Global consensus Monte Carlo

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    To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples

    Multiplex Decomposition of Non-Markovian Dynamics and the Hidden Layer Reconstruction Problem

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    Elements composing complex systems usually interact in several different ways and as such the interaction architecture is well modelled by a multiplex network. However often this architecture is hidden, as one usually only has experimental access to an aggregated projection. A fundamental challenge is thus to determine whether the hidden underlying architecture of complex systems is better modelled as a single interaction layer or results from the aggregation and interplay of multiple layers. Here we show that using local information provided by a random walker navigating the aggregated network one can decide in a robust way if the underlying structure is a multiplex or not and, in the former case, to determine the most probable number of hidden layers. As a byproduct, we show that the mathematical formalism also provides a principled solution for the optimal decomposition and projection of complex, non-Markovian dynamics into a Markov switching combination of diffusive modes. We validate the proposed methodology with numerical simulations of both (i) random walks navigating hidden multiplex networks (thereby reconstructing the true hidden architecture) and (ii) Markovian and non-Markovian continuous stochastic processes (thereby reconstructing an effective multiplex decomposition where each layer accounts for a different diffusive mode). We also state and prove two existence theorems guaranteeing that an exact reconstruction of the dynamics in terms of these hidden jump-Markov models is always possible for arbitrary finite-order Markovian and fully non-Markovian processes. Finally, we showcase the applicability of the method to experimental recordings from (i) the mobility dynamics of human players in an online multiplayer game and (ii) the dynamics of RNA polymerases at the single-molecule level.Comment: 40 pages, 24 figure

    Long memory or shifting means? A new approach and application to realised volatility

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    It is now recognised that long memory and structural change can be confused because the statistical properties of times series of lengths typical of financial and econometric series are similar for both models. We propose a new set of methods aimed at distinguishing between long memory and structural change. The approach, which utilises the computational efficient methods based upon Atheoretical Regression Trees (ART), establishes through simulation the bivariate distribution of the fractional integration parameter, d, with regime length for simulated fractionally integrated series. This bivariate distribution is then compared with the data for the time series. We also combine ART with the established goodness of fit test for long memory series due to Beran. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average. We show that in these series the value of the fractional integration parameter is not constant with time. The mathematical consequence of this is that the definition of H self-similarity is violated. We present evidence that these series have structural breaks.Long-range dependence; Strong dependence; Global dependence; Hurst phenomena

    Analytical modeling of spatial dependencies and calibration techniques for stochastic traffic simulators

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    Thesis (S.M. in Transportation)--Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 79-82).Exact numerical evaluation of the stationary joint queue-length distribution of a Markovian finite capacity network with arbitrary size and topology can be obtained numerically. Nonetheless, the main challenge to such an approach remains the dimensionality of the joint distribution, which is exponential in the number of queues. This thesis proposes an analytical approximation of the joint distribution with a dimension that is linear in the number of queues. The method decomposes the network into overlapping subnetworks. The state of each subnetwork is described aggregately, i.e. in terms of a reduced state space, while ensuring consistency with the disaggregate, i.e., full state space, distribution. This aggregation-disaggregation technique is proposed for the analysis of Markovian tandem finite capacity queueing networks. The model is validated. We present its use to address an urban traffic control problem, and show the added value of accounting for higher-order spatial between-queue dependency information in the control of congested networks. A second, distinct goal of this thesis is to examine the calibration of route choice parameters in microscopic traffic simulators. Automatically calibrating simulators using traffic counts requires describing the relationship between route choice and traffic flows. This thesis proposes an analytical finite capacity queueing model that accounts for the relationship between route choice and traffic flows. The method is embedded in a simulation-based optimization framework and applied to a calibration problem.by Carter Wang.S.M.in Transportatio

    Streaming Probabilistic PCA for Missing Data with Heteroscedastic Noise

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    Streaming principal component analysis (PCA) is an integral tool in large-scale machine learning for rapidly estimating low-dimensional subspaces of very high dimensional and high arrival-rate data with missing entries and corrupting noise. However, modern trends increasingly combine data from a variety of sources, meaning they may exhibit heterogeneous quality across samples. Since standard streaming PCA algorithms do not account for non-uniform noise, their subspace estimates can quickly degrade. On the other hand, the recently proposed Heteroscedastic Probabilistic PCA Technique (HePPCAT) addresses this heterogeneity, but it was not designed to handle missing entries and streaming data, nor does it adapt to non-stationary behavior in time series data. This paper proposes the Streaming HeteroscedASTic Algorithm for PCA (SHASTA-PCA) to bridge this divide. SHASTA-PCA employs a stochastic alternating expectation maximization approach that jointly learns the low-rank latent factors and the unknown noise variances from streaming data that may have missing entries and heteroscedastic noise, all while maintaining a low memory and computational footprint. Numerical experiments validate the superior subspace estimation of our method compared to state-of-the-art streaming PCA algorithms in the heteroscedastic setting. Finally, we illustrate SHASTA-PCA applied to highly-heterogeneous real data from astronomy.Comment: 19 pages, 6 figure

    Leveraging deep reinforcement learning in the smart grid environment

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    L’apprentissage statistique moderne démontre des résultats impressionnants, où les or- dinateurs viennent à atteindre ou même à excéder les standards humains dans certaines applications telles que la vision par ordinateur ou les jeux de stratégie. Pourtant, malgré ces avancées, force est de constater que les applications fiables en déploiement en sont encore à leur état embryonnaire en comparaison aux opportunités qu’elles pourraient apporter. C’est dans cette perspective, avec une emphase mise sur la théorie de décision séquentielle et sur les recherches récentes en apprentissage automatique, que nous démontrons l’applica- tion efficace de ces méthodes sur des cas liés au réseau électrique et à l’optimisation de ses acteurs. Nous considérons ainsi des instances impliquant des unités d’emmagasinement éner- gétique ou des voitures électriques, jusqu’aux contrôles thermiques des bâtiments intelligents. Nous concluons finalement en introduisant une nouvelle approche hybride qui combine les performances modernes de l’apprentissage profond et de l’apprentissage par renforcement au cadre d’application éprouvé de la recherche opérationnelle classique, dans le but de faciliter l’intégration de nouvelles méthodes d’apprentissage statistique sur différentes applications concrètes.While modern statistical learning is achieving impressive results, as computers start exceeding human baselines in some applications like computer vision, or even beating pro- fessional human players at strategy games without any prior knowledge, reliable deployed applications are still in their infancy compared to what these new opportunities could fathom. In this perspective, with a keen focus on sequential decision theory and recent statistical learning research, we demonstrate efficient application of such methods on instances involving the energy grid and the optimization of its actors, from energy storage and electric cars to smart buildings and thermal controls. We conclude by introducing a new hybrid approach combining the modern performance of deep learning and reinforcement learning with the proven application framework of operations research, in the objective of facilitating seamlessly the integration of new statistical learning-oriented methodologies in concrete applications
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