Comparison of Gaussian process modeling software

Gaussian process fitting, or kriging, is often used to create a model from a set of data. Many available software packages do this, but we show that very different results can be obtained from different packages even when using the same data and model. We describe the parameterization, features, and optimization used by eight different fitting packages that run on four different platforms. We then compare these eight packages using various data functions and data sets, revealing that there are stark differences between the packages. In addition to comparing the prediction accuracy, the predictive variance--which is important for evaluating precision of predictions and is often used in stopping criteria--is also evaluated

Forecasting of commercial sales with large scale Gaussian Processes

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.Comment: 1o pages, 5 figure

An Extended Laplace Approximation Method for Bayesian Inference of Self-Exciting Spatial-Temporal Models of Count Data

Self-Exciting models are statistical models of count data where the probability of an event occurring is influenced by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as temporal self-excitation. For large spatial or temporal regions, however, the model leads to an intractable likelihood. An increasingly common method for dealing with large spatio-temporal models is by using Laplace approximations (LA). This method is convenient as it can easily be applied and is quickly implemented. However, as we will demonstrate in this manuscript, when applied to self-exciting Poisson spatial-temporal models, Laplace Approximations result in a significant bias in estimating some parameters. Due to this bias, we propose using up to sixth-order corrections to the LA for fitting these models. We will demonstrate how to do this in a Bayesian setting for Self-Exciting Spatio-Temporal models. We will further show there is a limited parameter space where the extended LA method still has bias. In these uncommon instances we will demonstrate how a more computationally intensive fully Bayesian approach using the Stan software program is possible in those rare instances. The performance of the extended LA method is illustrated with both simulation and real-world data

Physiological Gaussian Process Priors for the Hemodynamics in fMRI Analysis

Background: Inference from fMRI data faces the challenge that the hemodynamic system that relates neural activity to the observed BOLD fMRI signal is unknown. New Method: We propose a new Bayesian model for task fMRI data with the following features: (i) joint estimation of brain activity and the underlying hemodynamics, (ii) the hemodynamics is modeled nonparametrically with a Gaussian process (GP) prior guided by physiological information and (iii) the predicted BOLD is not necessarily generated by a linear time-invariant (LTI) system. We place a GP prior directly on the predicted BOLD response, rather than on the hemodynamic response function as in previous literature. This allows us to incorporate physiological information via the GP prior mean in a flexible way, and simultaneously gives us the nonparametric flexibility of the GP. Results: Results on simulated data show that the proposed model is able to discriminate between active and non-active voxels also when the GP prior deviates from the true hemodynamics. Our model finds time varying dynamics when applied to real fMRI data. Comparison with Existing Method(s): The proposed model is better at detecting activity in simulated data than standard models, without inflating the false positive rate. When applied to real fMRI data, our GP model in several cases finds brain activity where previously proposed LTI models does not. Conclusions: We have proposed a new non-linear model for the hemodynamics in task fMRI, that is able to detect active voxels, and gives the opportunity to ask new kinds of questions related to hemodynamics.Comment: 18 pages, 14 figure