Academic literature on the topic 'Multi-output gaussian processes'

Deterministic nuclear reactor simulators employing the prevalent two-step scheme often generate a substantial amount of intermediate data at the interface of their two subcodes, which can impede the overall performance of the software. The bulk of this data comprises “few-groups homogenized cross-sections” or HXS, which are stored as tabulated multivariate functions and interpolated inside the core simulator. A number of mathematical tools have been studied for this interpolation purpose over the years, but few meet all the challenging requirements of neutronics computation chains: extreme accuracy, low memory footprint, fast predictions… We here present a new framework to tackle this task, based on multi-outputs gaussian processes (MOGP). This machine learning model enables us to interpolate HXS’s with improved accuracy compared to the current multilinear standard, using only a fraction of its training data – meaning that the amount of required precomputation is reduced by a factor of several dozens. It also necessitates an even smaller fraction of its storage requirements, preserves its reconstruction speed, and unlocks new functionalities such as adaptive sampling and facilitated uncertainty quantification. We demonstrate the efficiency of this approach on a rich test case reproducing the VERA benchmark, proving in particular its scalability to datasets of millions of HXS.

Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution propagation within the hierarchy. Recently, it was pointed out that the hierarchical structure of DGP well suited modeling the multi-fidelity regression, in which one is provided sparse observations with high precision and plenty of low fidelity observations. We propose the conditional DGP model in which the latent GPs are directly supported by the fixed lower fidelity data. Then the moment matching method is applied to approximate the marginal prior of conditional DGP with a GP. The obtained effective kernels are implicit functions of the lower-fidelity data, manifesting the expressivity contributed by distribution propagation within the hierarchy. The hyperparameters are learned via optimizing the approximate marginal likelihood. Experiments with synthetic and high dimensional data show comparable performance against other multi-fidelity regression methods, variational inference, and multi-output GP. We conclude that, with the low fidelity data and the hierarchical DGP structure, the effective kernel encodes the inductive bias for true function allowing the compositional freedom.

The study of brain electrical activity (BEA) from different cognitive conditions has attracted a lot of interest in the last decade due to the high number of possible applications that could be generated from it. In this work, a discriminative framework for BEA via electroencephalography (EEG) is proposed based on multi-output Gaussian Processes (MOGPs) with a specialized spectral kernel. First, a signal segmentation stage is executed, and the channels from the EEG are used as the model outputs. Then, a novel covariance function within the MOGP known as the multispectral mixture kernel (MOSM) allows us to find and quantify the relationships between different channels. Several MOGPs are trained from different conditions grouped in bi-class problems, and the discrimination is performed based on the likelihood score of the test signals against all the models. Finally, the mean likelihood is computed to predict the correspondence of new inputs with each class’s existing models. Results show that this framework allows us to model the EEG signals adequately using generative models and allows analyzing the relationships between channels of the EEG for a particular condition. At the same time, the set of trained MOGPs is well suited to discriminate new input data.