543 research outputs found
Forecasting Time Series with VARMA Recursions on Graphs
Graph-based techniques emerged as a choice to deal with the dimensionality
issues in modeling multivariate time series. However, there is yet no complete
understanding of how the underlying structure could be exploited to ease this
task. This work provides contributions in this direction by considering the
forecasting of a process evolving over a graph. We make use of the
(approximate) time-vertex stationarity assumption, i.e., timevarying graph
signals whose first and second order statistical moments are invariant over
time and correlated to a known graph topology. The latter is combined with VAR
and VARMA models to tackle the dimensionality issues present in predicting the
temporal evolution of multivariate time series. We find out that by projecting
the data to the graph spectral domain: (i) the multivariate model estimation
reduces to that of fitting a number of uncorrelated univariate ARMA models and
(ii) an optimal low-rank data representation can be exploited so as to further
reduce the estimation costs. In the case that the multivariate process can be
observed at a subset of nodes, the proposed models extend naturally to Kalman
filtering on graphs allowing for optimal tracking. Numerical experiments with
both synthetic and real data validate the proposed approach and highlight its
benefits over state-of-the-art alternatives.Comment: submitted to the IEEE Transactions on Signal Processin
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
Calibrating the sqHIMMELI v1.0 wetland methane emission model with hierarchical modeling and adaptive MCMC
Estimating methane (CH4) emissions from natural wetlands is complex, and the estimates contain large uncertainties. The models used for the task are typically heavily parameterized and the parameter values are not well known. In this study, we perform a Bayesian model calibration for a new wetland CH4 emission model to improve the quality of the predictions and to understand the limitations of such models. The detailed process model that we analyze contains descriptions for CH4 production from anaerobic respiration, CH4 oxidation, and gas transportation by diffusion, ebullition, and the aerenchyma cells of vascular plants. The processes are controlled by several tunable parameters. We use a hierarchical statistical model to describe the parameters and obtain the posterior distributions of the parameters and uncertainties in the processes with adaptive Markov chain Monte Carlo (MCMC), importance resampling, and time series analysis techniques. For the estimation, the analysis utilizes measurement data from the Siikaneva flux measurement site in southern Finland. The uncertainties related to the parameters and the modeled processes are described quantitatively. At the process level, the flux measurement data are able to constrain the CH4 production processes, methane oxidation, and the different gas transport processes. The posterior covariance structures explain how the parameters and the processes are related. Additionally, the flux and flux component uncertain-ties are analyzed both at the annual and daily levels. The parameter posterior densities obtained provide information regarding importance of the different processes, which is also useful for development of wetland methane emission models other than the square root HelsinkI Model of MEthane buiLd- up and emIssion for peatlands (sqHIMMELI). The hierarchical modeling allows us to assess the effects of some of the parameters on an annual basis. The results of the calibration and the cross validation suggest that the early spring net primary production could be used to predict parameters affecting the annual methane production. Even though the calibration is specific to the Siikaneva site, the hierarchical modeling approach is well suited for larger-scale studies and the results of the estimation pave way for a regional or global- scale Bayesian calibration of wetland emission models.Peer reviewe
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