Assessing Steady-State, Multivariate Experimental Data Using Gaussian Processes: The GPExp Open-Source Library

Experimental data are subject to different sources of disturbance and errors, whose importance should be assessed. The level of noise, the presence of outliers or a measure of the “explainability” of the key variables with respect to the externally-imposed operating condition are important indicators, but are not straightforward to obtain, especially if the data are sparse and multivariate. This paper proposes a methodology and a suite of tools implementing Gaussian processes for quality assessment of steady-state experimental data. The aim of the proposed tool is to: (1) provide a smooth (de-noised) multivariate operating map of the measured variable with respect to the inputs; (2) determine which inputs are relevant to predict a selected output; (3) provide a sensitivity analysis of the measured variables with respect to the inputs; (4) provide a measure of the accuracy (confidence intervals) for the prediction of the data; (5) detect the observations that are likely to be outliers. We show that Gaussian processes regression provides insightful numerical indicators for these purposes and that the obtained performance is higher or comparable to alternative modeling techniques. Finally, the datasets and tools developed in this work are provided within the GPExp open-source package

Assessing the Quality of Experimental Data with Gaussian Processes: Example with an Injection Scroll Compressor

This paper describes an experimental study carried out on a refrigeration scroll compressor with and without vapour injection. The test rig designed for that purposed allows evaluating the performance over a wide range of operating conditions, by varying the supply pressure, the injection pressure, the exhaust pressure, the supply superheating and the injection superheating. 97 Steady-state points are measured, with a maximum isentropic efficiency of 64.1% and a maximum consumed electrical power of 13.1 kW. A critical analysis of the experimental results is then carried out to evaluate the quality of the data using a machine learning method. This method based on Gaussian Processes regression, is used to build a statistical operating map of the compressor as a function of the different inputs. This statistical operating map can then be compared to the experimental data points to evaluate their accuracy

Interpreting weight maps in terms of cognitive or clinical neuroscience: nonsense?

Since machine learning models have been applied to neuroimaging data, researchers have drawn conclusions from the derived weight maps. In particular, weight maps of classifiers between two conditions are often described as a proxy for the underlying signal differences between the conditions. Recent studies have however suggested that such weight maps could not reliably recover the source of the neural signals and even led to false positives (FP). In this work, we used semi-simulated data from ElectroCorticoGraphy (ECoG) to investigate how the signal-to-noise ratio and sparsity of the neural signal affect the similarity between signal and weights. We show that not all cases produce FP and that it is unlikely for FP features to have a high weight in most cases.Comment: conference articl

Decoding Semi-Constrained Brain Activity from fMRI Using Support Vector Machines and Gaussian Processes

Predicting a particular cognitive state from a specific pattern of fMRI voxel values is still a methodological challenge. Decoding brain activity is usually performed in highly controlled experimental paradigms characterized by a series of distinct states induced by a temporally constrained experimental design. In more realistic conditions, the number, sequence and duration of mental states are unpredictably generated by the individual, resulting in complex and imbalanced fMRI data sets. This study tests the classification of brain activity, acquired on 16 volunteers using fMRI, during mental imagery, a condition in which the number and duration of mental events were not externally imposed but self-generated. To deal with these issues, two classification techniques were considered (Support Vector Machines, SVM, and Gaussian Processes, GP), as well as different feature extraction methods (General Linear Model, GLM and SVM). These techniques were combined in order to identify the procedures leading to the highest accuracy measures. Our results showed that 12 data sets out of 16 could be significantly modeled by either SVM or GP. Model accuracies tended to be related to the degree of imbalance between classes and to task performance of the volunteers. We also conclude that the GP technique tends to be more robust than SVM to model unbalanced data sets

Mapping human temporal and parietal neuronal population activity and functional coupling during mathematical cognition

Brain areas within the lateral parietal cortex (LPC) and ventral temporal cortex (VTC) have been shown to code for abstract quantity representations and for symbolic numerical representations, respectively. To explore the fast dynamics of activity within each region and the interaction between them, we used electrocorticography recordings from 16 neurosurgical subjects implanted with grids of electrodes over these two regions and tracked the activity within and between the regions as subjects performed three different numerical tasks. Although our results reconfirm the presence of math-selective hubs within the VTC and LPC, we report here a remarkable heterogeneity of neural responses within each region at both millimeter and millisecond scales. Moreover, we show that the heterogeneity of response profiles within each hub mirrors the distinct patterns of functional coupling between them. Our results support the existence of multiple bidirectional functional loops operating between discrete populations of neurons within the VTC and LPC during the visual processing of numerals and the performance of arithmetic functions. These findings reveal information about the dynamics of numerical processing in the brain and also provide insight into the fine-grained functional architecture and connectivity within the human brain

ABCD Neurocognitive Prediction Challenge 2019: Predicting individual residual fluid intelligence scores from cortical grey matter morphology

We predicted residual fluid intelligence scores from T1-weighted MRI data available as part of the ABCD NP Challenge 2019, using morphological similarity of grey-matter regions across the cortex. Individual structural covariance networks (SCN) were abstracted into graph-theory metrics averaged over nodes across the brain and in data-driven communities/modules. Metrics included degree, path length, clustering coefficient, centrality, rich club coefficient, and small-worldness. These features derived from the training set were used to build various regression models for predicting residual fluid intelligence scores, with performance evaluated both using cross-validation within the training set and using the held-out validation set. Our predictions on the test set were generated with a support vector regression model trained on the training set. We found minimal improvement over predicting a zero residual fluid intelligence score across the sample population, implying that structural covariance networks calculated from T1-weighted MR imaging data provide little information about residual fluid intelligence.Comment: 8 pages plus references, 3 figures, 2 tables. Submission to the ABCD Neurocognitive Prediction Challenge at MICCAI 201

ABCD Neurocognitive Prediction Challenge 2019: Predicting individual fluid intelligence scores from structural MRI using probabilistic segmentation and kernel ridge regression

We applied several regression and deep learning methods to predict fluid intelligence scores from T1-weighted MRI scans as part of the ABCD Neurocognitive Prediction Challenge (ABCD-NP-Challenge) 2019. We used voxel intensities and probabilistic tissue-type labels derived from these as features to train the models. The best predictive performance (lowest mean-squared error) came from Kernel Ridge Regression (KRR; $\lambda=10$), which produced a mean-squared error of 69.7204 on the validation set and 92.1298 on the test set. This placed our group in the fifth position on the validation leader board and first place on the final (test) leader board.Comment: Winning entry in the ABCD Neurocognitive Prediction Challenge at MICCAI 2019. 7 pages plus references, 3 figures, 1 tabl

Improving SNR and reducing training time of classifiers in large datasets via kernel averaging

Kernel methods are of growing importance in neuroscience research. As an elegant extension of linear methods, they are able to model complex non-linear relationships. However, since the kernel matrix grows with data size, the training of classifiers is computationally demanding in large datasets. Here, a technique developed for linear classifiers is extended to kernel methods: In linearly separable data, replacing sets of instances by their averages improves signal-to-noise ratio (SNR) and reduces data size. In kernel methods, data is linearly non-separable in input space, but linearly separable in the high-dimensional feature space that kernel methods implicitly operate in. It is shown that a classifier can be efficiently trained on instances averaged in feature space by averaging entries in the kernel matrix. Using artificial and publicly available data, it is shown that kernel averaging improves classification performance substantially and reduces training time, even in non-linearly separable data