Learning Gaussian Process Models from Uncertain Data

Dallaire, Patrick; Besse, Camille; Chaib-draa, Brahim

doi:10.1007/978-3-642-10677-4_49

Cited by 21 publications

(16 citation statements)

References 3 publications

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“…To account for the uncertainties of the labels, we follow Dallaire et al (2009). Instead of using only point estimates, we assume that individual star labels are normally distributed around the mean valuesξ and have their own covariance matrices Σ,…”

Section: Methodsmentioning

confidence: 99%

Very Metal-poor Stars Observed by the RAVE Survey

Matijevič

2015

Proc. IAU

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Metal-poor stars trace the earliest phases in the chemical enrichment of the Universe. They give clues about the early assembly of the Galaxy as well as on the nature of the first stellar generations. Multi-object spectroscopic surveys play a key role in finding these fossil records in large volumes. Here we present a novel analysis of the metal-poor star sample in the complete Radial Velocity Experiment (RAVE) Data Release 5 catalog with the goal of identifying and characterizing all very metal-poor stars observed by the survey. Using a three-stage method, we first identified the candidate stars using only their spectra as input information. We employed an algorithm called t-SNE to construct a low-dimensional projection of the spectrum space and isolate the region containing metal-poor stars. Following this step, we measured the equivalent widths of the near-infrared Ca ii triplet lines with a method based on flexible Gaussian processes to model the correlated noise present in the spectra. In the last step, we constructed a calibration relation that converts the measured equivalent widths and the color information coming from the 2MASS and WISE surveys into metallicity and temperature estimates. We identified 877 stars with at least a 50% probability of being very metal-poor ([Fe/H] < −2 dex), out of which 43 are likely extremely metal-poor ([Fe/H] < −3 dex). The comparison of the derived values to a small subsample of stars with literature metallicity values shows that our method works reliably and correctly estimates the uncertainties, which typically have values σ [Fe/H] ≈ 0.2 dex. In addition, when compared to the metallicity results derived using the RAVE DR5 pipeline, it is evident that we achieve better accuracy than the pipeline and therefore more reliably evaluate the very metal-poor subsample. Based on the repeated observations of the same stars, our method gives very consistent results. We intend to study the identified sample further by acquiring high-resolution spectroscopic follow-up observations. The method used in this work can also easily be extended to other large-scale data sets, including to the data from the Gaia mission and the upcoming 4MOST survey.

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Section: Methodsmentioning

confidence: 99%

Very Metal-poor Stars Observed by the RAVE Survey

Matijevič

2015

Proc. IAU

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“…In the present work, the test points are assumed to be a set of Gaussian distributions, and hence, the integral is analytically tractable. It should be noted that the true scheduling variables are not observable; however, we have access to their distribution N (P * , Σ p ), where P * is the observed test point [13]. Therefore, the noise-free scheduling variables are assumed to be Gaussian distributedP * ∼ N (P * , Σ p ), whereP * = p * i , i = 1, .…”

Section: Learning With Uncertain Scheduling Variablesmentioning

confidence: 99%

A Bayesian approach for model identification of LPV systems with uncertain scheduling variables

Abbasi

Mohammadpour

Tóth

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

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This paper presents a Gaussian Process (GP) based Bayesian method that takes into account the effect of additive noise on the scheduling variables for identification of linear parameter-varying (LPV) models in input-output form. The proposed method approximates the noise-free coefficient functions by a local linear expansion on the observed scheduling variables. Therefore, additive noise on the scheduling variables is reconstructed as a corrective term added to the output noise that is proportional to the squared gradient obtained from the posterior of the Gaussian Process. An iterative procedure is given so that the obtained solution converges to the best estimation of the coefficient functions according to the given measure of fitness. Moreover, the expectation and covariance functions estimated by GP are modified for the noisy scheduling variable case to include the noise contribution on the estimated expectation and covariance functions. The model training procedure identifies noise level in the measurements including outputs and scheduling variables by estimating the noise variances, as well as other defined hyperparameters. Finally, the performance of the proposed method is compared to the standard GP approach through a numerical example.

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“…The challenge in directly applying the GP regression as described above is that the Larson-Miller parameter depends on C which we now wish to represent as an additional random variable. Fortunately, there is a analytic solution, described as a kernel function, for the statistics of Gaussian process with a radial basis (squared exponential) kernel with uncertain inputs, provided the inputs are normally distributed [16,17]. Applying this solution to Eq.…”

Section: Gaussian Process Model For Creep Rupturementioning

confidence: 99%