6,875 research outputs found
Parallelized Particle and Gaussian Sum Particle Filters for Large Scale Freeway Traffic Systems
Large scale traffic systems require techniques able to: 1) deal with high amounts of data and heterogenous data coming from different types of sensors, 2) provide robustness in the presence of sparse sensor data, 3) incorporate different models that can deal with various traffic regimes, 4) cope with multimodal conditional probability density functions for the states. Often centralized architectures face challenges due to high communication demands. This paper develops new estimation techniques able to cope with these problems of large traffic network systems. These are Parallelized Particle Filters (PPFs) and a Parallelized Gaussian Sum Particle Filter (PGSPF) that are suitable for on-line traffic management. We show how complex probability density functions of the high dimensional trafc state can be decomposed into functions with simpler forms and the whole estimation problem solved in an efcient way. The proposed approach is general, with limited interactions which reduces the computational time and provides high estimation accuracy. The efciency of the PPFs and PGSPFs is evaluated in terms of accuracy, complexity and communication demands and compared with the case where all processing is centralized
An efficient surrogate model for emulation and physics extraction of large eddy simulations
In the quest for advanced propulsion and power-generation systems,
high-fidelity simulations are too computationally expensive to survey the
desired design space, and a new design methodology is needed that combines
engineering physics, computer simulations and statistical modeling. In this
paper, we propose a new surrogate model that provides efficient prediction and
uncertainty quantification of turbulent flows in swirl injectors with varying
geometries, devices commonly used in many engineering applications. The novelty
of the proposed method lies in the incorporation of known physical properties
of the fluid flow as {simplifying assumptions} for the statistical model. In
view of the massive simulation data at hand, which is on the order of hundreds
of gigabytes, these assumptions allow for accurate flow predictions in around
an hour of computation time. To contrast, existing flow emulators which forgo
such simplications may require more computation time for training and
prediction than is needed for conducting the simulation itself. Moreover, by
accounting for coupling mechanisms between flow variables, the proposed model
can jointly reduce prediction uncertainty and extract useful flow physics,
which can then be used to guide further investigations.Comment: Submitted to JASA A&C
Balancing the Communication Load of Asynchronously Parallelized Machine Learning Algorithms
Stochastic Gradient Descent (SGD) is the standard numerical method used to
solve the core optimization problem for the vast majority of machine learning
(ML) algorithms. In the context of large scale learning, as utilized by many
Big Data applications, efficient parallelization of SGD is in the focus of
active research. Recently, we were able to show that the asynchronous
communication paradigm can be applied to achieve a fast and scalable
parallelization of SGD. Asynchronous Stochastic Gradient Descent (ASGD)
outperforms other, mostly MapReduce based, parallel algorithms solving large
scale machine learning problems. In this paper, we investigate the impact of
asynchronous communication frequency and message size on the performance of
ASGD applied to large scale ML on HTC cluster and cloud environments. We
introduce a novel algorithm for the automatic balancing of the asynchronous
communication load, which allows to adapt ASGD to changing network bandwidths
and latencies.Comment: arXiv admin note: substantial text overlap with arXiv:1505.0495
Practical Bayesian Optimization of Machine Learning Algorithms
Machine learning algorithms frequently require careful tuning of model
hyperparameters, regularization terms, and optimization parameters.
Unfortunately, this tuning is often a "black art" that requires expert
experience, unwritten rules of thumb, or sometimes brute-force search. Much
more appealing is the idea of developing automatic approaches which can
optimize the performance of a given learning algorithm to the task at hand. In
this work, we consider the automatic tuning problem within the framework of
Bayesian optimization, in which a learning algorithm's generalization
performance is modeled as a sample from a Gaussian process (GP). The tractable
posterior distribution induced by the GP leads to efficient use of the
information gathered by previous experiments, enabling optimal choices about
what parameters to try next. Here we show how the effects of the Gaussian
process prior and the associated inference procedure can have a large impact on
the success or failure of Bayesian optimization. We show that thoughtful
choices can lead to results that exceed expert-level performance in tuning
machine learning algorithms. We also describe new algorithms that take into
account the variable cost (duration) of learning experiments and that can
leverage the presence of multiple cores for parallel experimentation. We show
that these proposed algorithms improve on previous automatic procedures and can
reach or surpass human expert-level optimization on a diverse set of
contemporary algorithms including latent Dirichlet allocation, structured SVMs
and convolutional neural networks
Solving, Estimating and Selecting Nonlinear Dynamic Models without the Curse of Dimensionality
We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids. TheSmolyak operator underlying the sparse grids approach frees global approximation from the curse of dimensionality and we apply it to a Chebyshev approximation of the model solution. The operator also eliminates the curse from Gaussian quadrature and we use it for the integrals arising from rational expectations and in three new nonlinear state space filters. The filters substantially decrease the computational burden compared to the sequential importance resampling particle filter. The posterior of the structural parameters is estimated by a new Metropolis-Hastings algorithm with mixing parallel sequences. The parallel extension improves the global maximization property of the algorithm, simplifies the choice of the innovation variances, allows for unbiased convergence diagnostics and for a simple implementation of the estimation on parallel computers. Finally, we provide all algorithms in the open source software JBendge4 for the solution and estimation of a general class of models.Dynamic Stochastic General Equilibrium (DSGE) Models, Bayesian Time Series Econometrics, Curse of Dimensionality
Regularized brain reading with shrinkage and smoothing
Functional neuroimaging measures how the brain responds to complex stimuli.
However, sample sizes are modest, noise is substantial, and stimuli are high
dimensional. Hence, direct estimates are inherently imprecise and call for
regularization. We compare a suite of approaches which regularize via
shrinkage: ridge regression, the elastic net (a generalization of ridge
regression and the lasso), and a hierarchical Bayesian model based on small
area estimation (SAE). We contrast regularization with spatial smoothing and
combinations of smoothing and shrinkage. All methods are tested on functional
magnetic resonance imaging (fMRI) data from multiple subjects participating in
two different experiments related to reading, for both predicting neural
response to stimuli and decoding stimuli from responses. Interestingly, when
the regularization parameters are chosen by cross-validation independently for
every voxel, low/high regularization is chosen in voxels where the
classification accuracy is high/low, indicating that the regularization
intensity is a good tool for identification of relevant voxels for the
cognitive task. Surprisingly, all the regularization methods work about equally
well, suggesting that beating basic smoothing and shrinkage will take not only
clever methods, but also careful modeling.Comment: Published at http://dx.doi.org/10.1214/15-AOAS837 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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