Regression on the basis of nonstationary Gaussian processes with Bayesian regularization

Ustyuzhanin

et al. 2017

J. Phys.: Conf. Ser.

Abstract. The SHiP experiment is designed to search for very weakly interacting particles beyond the Standard Model which are produced in a 400 GeV/c proton beam dump at the CERN SPS. The critical challenge for this experiment is to keep the Standard Model background level negligible. In the beam dump, around 10 11 muons will be produced per second. The muon rate in the spectrometer has to be reduced by at least four orders of magnitude to avoid muoninduced backgrounds. It is demonstrated that new improved active muon shield may be used to magnetically deflect the muons out of the acceptance of the spectrometer.

Section: Theoremmentioning

confidence: 99%

Optimising the Active Muon Shield for the SHiP Experiment at CERN

Baranov

Ustyuzhanin

et al. 2017

J. Phys.: Conf. Ser.

“…Maximum likelihood estimation of a Gaussian process regression model sometimes provides degenerate results -a phenomenon closely connected to overfitting [65,68,48,51]. To regularize the problem and avoid inversion of large ill-conditioned matrices, one can impose a prior distribution on a Gaussian process regression model and then use Bayesian MAP (Maximum A Posteriory) estimates [20,23,11]. In particular in this paper we adopted the approach described in [20]: we impose prior distributions on all parameters of the covariance function and additional hyperprior distributions on parameters of the prior distributions.…”

Section: Gaussian Process Regression For Single Fidelity Datamentioning

confidence: 99%

“…To regularize the problem and avoid inversion of large ill-conditioned matrices, one can impose a prior distribution on a Gaussian process regression model and then use Bayesian MAP (Maximum A Posteriory) estimates [20,23,11]. In particular in this paper we adopted the approach described in [20]: we impose prior distributions on all parameters of the covariance function and additional hyperprior distributions on parameters of the prior distributions. Experiments confirm that such approach allows to avoid ill-conditioned and degenerate cases, that can occur even more often when processing variable fidelity data.…”

Section: Gaussian Process Regression For Single Fidelity Datamentioning

confidence: 99%

Large scale variable fidelity surrogate modeling

Zaytsev

2017

Ann Math Artif Intell

Engineers widely use Gaussian process regression framework to construct surrogate models aimed to replace computationally expensive physical models while exploring design space. Thanks to Gaussian process properties we can use both samples generated by a high fidelity function (an expensive and accurate representation of a physical phenomenon) and a low fidelity function (a cheap and coarse approximation of the same physical phenomenon) while constructing a surrogate model. However, if samples sizes are more than few thousands of points, computational costs of the Gaussian process regression become prohibitive both in case of learning and in case of prediction calculation. We propose two approaches to circumvent this computational burden: one approach is based on the Nyström approximation of sample covariance matrices and another is based on an intelligent usage of a blackbox that can evaluate a low fidelity function on the fly at any point of a design space. We examine performance of the proposed approaches using a number of artificial and real problems, including engineering optimization of a rotating disk shape.

“…Yet, GPs have found success on various applications. They are in use on a wide range of fields and use cases ranging from surrogate modeling, experiment design, mining and geo-spatial data to battery health [3], [71], [87], [11], [33], [32], [8], [10], [5], [6], [9]. On techniques for demand forecasting in the FMCG sector, there has been little academic research and not enough efforts to expose practitioners to them.…”

Section: Introductionmentioning

confidence: 99%

Forecasting of Commercial Sales with Large Scale Gaussian Processes

Rivera¹,

2017 IEEE International Conference on Data Mining Workshops (ICDMW)

2017

This paper argues that there has not been enough discussion in the field of applications of Gaussian Process for the fast moving consumer goods industry. Yet, this technique can be important as it e.g., can provide automatic feature relevance determination and the posterior mean can unlock insights on the data. Significant challenges are the large size and high dimensionality of commercial data at a point of sale. The study reviews approaches in the Gaussian Processes modeling for large data sets, evaluates their performance on commercial sales and shows value of this type of models as a decision-making tool for management.