Probabilistic PARAFAC2.

The Parallel Factor Analysis 2 (PARAFAC2) is a multimodal factor analysis model suitable for analyzing multi-way data when one of the modes has incomparable observation units, for example, because of differences in signal sampling or batch sizes. A fully probabilistic treatment of the PARAFAC2 is desirable to improve robustness to noise and provide a principled approach for determining the number of factors, but challenging because direct model fitting requires that factor loadings be decomposed into a shared matrix specifying how the components are consistently co-expressed across samples and sample-specific orthogonality-constrained component profiles. We develop two probabilistic formulations of the PARAFAC2 model along with variational Bayesian procedures for inference: In the first approach, the mean values of the factor loadings are orthogonal leading to closed form variational updates, and in the second, the factor loadings themselves are orthogonal using a matrix Von Mises-Fisher distribution. We contrast our probabilistic formulations to the conventional direct fitting algorithm based on maximum likelihood on synthetic data and real fluorescence spectroscopy and gas chromatography-mass spectrometry data showing that the probabilistic formulations are more robust to noise and model order misspecification. The probabilistic PARAFAC2, thus, forms a promising framework for modeling multi-way data accounting for uncertainty.

Predictive assessment of models for dynamic functional connectivity.

In neuroimaging, it has become evident that models of dynamic functional connectivity (dFC), which characterize how intrinsic brain organization changes over time, can provide a more detailed representation of brain function than traditional static analyses. Many dFC models in the literature represent functional brain networks as a meta-stable process with a discrete number of states; however, there is a lack of consensus on how to perform model selection and learn the number of states, as well as a lack of understanding of how different modeling assumptions influence the estimated state dynamics. To address these issues, we consider a predictive likelihood approach to model assessment, where models are evaluated based on their predictive performance on held-out test data. Examining several prominent models of dFC (in their probabilistic formulations) we demonstrate our framework on synthetic data, and apply it on two real-world examples: a face recognition EEG experiment and resting-state fMRI. Our results evidence that both EEG and fMRI are better characterized using dynamic modeling approaches than by their static counterparts, but we also demonstrate that one must be cautious when interpreting dFC because parameter settings and modeling assumptions, such as window lengths and emission models, can have a large impact on the estimated states and consequently on the interpretation of the brain dynamics.

Whole-Brain Exploratory Analysis of Functional Task Response Following Erythropoietin Treatment in Mood Disorders: A Supervised Machine Learning Approach.

A core symptom of mood disorders is cognitive impairment in attention, memory and executive functions. Erythropoietin (EPO) is a candidate treatment for cognitive impairment in unipolar and bipolar disorders (UD and BD) and modulates cognition-related neural activity across a fronto-temporo-parietal network. This report investigates predicting the pharmacological treatment from functional magnetic resonance imaging (fMRI) data using a supervised machine learning approach. A total of 84 patients with UD or BD were included in a randomized double-blind parallel-group study in which they received eight weekly infusions of either EPO (40 000 IU) or saline. Task fMRI data were collected before EPO/saline infusions started (baseline) and 6 weeks after last infusion (follow-up). During the scanning sessions, participants were given an n-back working memory and a picture encoding task. Linear classification models with different regularization techniques were used to predict treatment status from both cross-sectional data (at follow-up) and longitudinal data (difference between baseline and follow-up). For the n-back and picture encoding tasks, data were available and analyzed for 52 (EPO; n = 28, Saline; n = 24) and 59 patients (EPO; n = 31, Saline; n = 28), respectively. We found limited evidence that the classifiers used could predict treatment status at a reliable level of performance (≤60% accuracy) when tested using repeated cross-validation. There was no difference in using cross-sectional versus longitudinal data. Whole-brain multivariate decoding applied to pharmaco-fMRI in small to moderate samples seems to be suboptimal for exploring data driven neuronal treatment mechanisms.