A new adaptive response surface method for reliability analysis

Response surface method is a convenient tool to assess reliability for a wide range of structural mechanical problems. More specifically, adaptive schemes which consist in iteratively refine the experimental design close to the limit state have received much attention. However, it is generally difficult to take into account a lot of variables and to well handle approximation error. The method, proposed in this paper, addresses these points using sparse response surface and a relevant criterion for results accuracy. For this purpose, a response surface is built from an initial Latin Hypercube Sampling (LHS) where the most significant terms are chosen from statistical criteria and cross-validation method. At each step, LHS is refined in a region of interest defined with respect to an importance level on probability density in the design point. Two convergence criteria are used in the procedure: The first one concerns localization of the region and the second one the response surface quality. Finally, a bootstrap method is used to determine the influence of the response error on the estimated probability of failure. This method is applied to several examples and results are discussed

Multiple-Description Coding by Dithered Delta-Sigma Quantization

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has been fixed. Accepted for publication in the IEEE Transactions on Information Theor

Heteroscedastic Gaussian processes for uncertainty modeling in large-scale crowdsourced traffic data

Accurately modeling traffic speeds is a fundamental part of efficient intelligent transportation systems. Nowadays, with the widespread deployment of GPS-enabled devices, it has become possible to crowdsource the collection of speed information to road users (e.g. through mobile applications or dedicated in-vehicle devices). Despite its rather wide spatial coverage, crowdsourced speed data also brings very important challenges, such as the highly variable measurement noise in the data due to a variety of driving behaviors and sample sizes. When not properly accounted for, this noise can severely compromise any application that relies on accurate traffic data. In this article, we propose the use of heteroscedastic Gaussian processes (HGP) to model the time-varying uncertainty in large-scale crowdsourced traffic data. Furthermore, we develop a HGP conditioned on sample size and traffic regime (SRC-HGP), which makes use of sample size information (probe vehicles per minute) as well as previous observed speeds, in order to more accurately model the uncertainty in observed speeds. Using 6 months of crowdsourced traffic data from Copenhagen, we empirically show that the proposed heteroscedastic models produce significantly better predictive distributions when compared to current state-of-the-art methods for both speed imputation and short-term forecasting tasks.Comment: 22 pages, Transportation Research Part C: Emerging Technologies (Elsevier

Node harvest

When choosing a suitable technique for regression and classification with multivariate predictor variables, one is often faced with a tradeoff between interpretability and high predictive accuracy. To give a classical example, classification and regression trees are easy to understand and interpret. Tree ensembles like Random Forests provide usually more accurate predictions. Yet tree ensembles are also more difficult to analyze than single trees and are often criticized, perhaps unfairly, as `black box' predictors. Node harvest is trying to reconcile the two aims of interpretability and predictive accuracy by combining positive aspects of trees and tree ensembles. Results are very sparse and interpretable and predictive accuracy is extremely competitive, especially for low signal-to-noise data. The procedure is simple: an initial set of a few thousand nodes is generated randomly. If a new observation falls into just a single node, its prediction is the mean response of all training observation within this node, identical to a tree-like prediction. A new observation falls typically into several nodes and its prediction is then the weighted average of the mean responses across all these nodes. The only role of node harvest is to `pick' the right nodes from the initial large ensemble of nodes by choosing node weights, which amounts in the proposed algorithm to a quadratic programming problem with linear inequality constraints. The solution is sparse in the sense that only very few nodes are selected with a nonzero weight. This sparsity is not explicitly enforced. Maybe surprisingly, it is not necessary to select a tuning parameter for optimal predictive accuracy. Node harvest can handle mixed data and missing values and is shown to be simple to interpret and competitive in predictive accuracy on a variety of data sets.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS367 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org