Finding Nonlinear Relationships in Functional Magnetic Resonance Imaging Data with Genetic Programming

The human brain is a complex, nonlinear dynamic chaotic system that is poorly understood. When faced with these difficult to understand systems, it is common to observe the system and develop models such that the underlying system might be deciphered. When observing neurological activity within the brain with functional magnetic resonance imaging (fMRI), it is common to develop linear models of functional connectivity; however, these models are incapable of describing the nonlinearities we know to exist within the system. A genetic programming (GP) system was developed to perform symbolic regression on recorded fMRI data. Symbolic regression makes fewer assumptions than traditional linear tools and can describe nonlinearities within the system. Although GP is a powerful form of machine learning that has many drawbacks (computational cost, overfitting, stochastic), it may provide new insights into the underlying system being studied. The contents of this thesis are presented in an integrated article format. For all articles, data from the Human Connectome Project were used. In the first article, nonlinear models for 507 subjects performing a motor task were created. These nonlinear models generated by GP contained fewer ROI than what would be found with traditional, linear tools. It was found that the generated nonlinear models would not fit the data as well as the linear models; however, when compared to linear models containing a similar number of ROI, the nonlinear models performed better. Ten subjects performing 7 tasks were studied in article two. After improvements to the GP system, the generated nonlinear models outperformed the linear models in many cases and were never significantly worse than the linear models. Forty subjects performing 7 tasks were studied in article three. Newly generated nonlinear models were applied to unseen data from the same subject performing the same task (intrasubject generalization) and many nonlinear models generalized to unseen data better than the linear models. The nonlinear models were applied to unseen data from other subjects performing the same task (intersubject generalization) and were not capable of generalizing as well as the linear

Discovering Causal Relations and Equations from Data

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.Comment: 137 page

Typical and aberrant functional brain flexibility: lifespan development and aberrant organization in traumatic brain injury and dyslexia

Intrinsic functional connectivity networks derived from different neuroimaging methods and connectivity estimators have revealed robust developmental trends linked to behavioural and cognitive maturation. The present study employed a dynamic functional connectivity approach to determine dominant intrinsic coupling modes in resting-state neuromagnetic data from 178 healthy participants aged 8–60 years. Results revealed significant developmental trends in three types of dominant intra- and inter-hemispheric neuronal population interactions (amplitude envelope, phase coupling, and phase-amplitude synchronization) involving frontal, temporal, and parieto-occipital regions. Multi-class support vector machines achieved 89% correct classification of participants according to their chronological age using dynamic functional connectivity indices. Moreover, systematic temporal variability in functional connectivity profiles, which was used to empirically derive a composite flexibility index, displayed an inverse U-shaped curve among healthy participants. Lower flexibility values were found among age-matched children with reading disability and adults who had suffered mild traumatic brain injury. The importance of these results for normal and abnormal brain development are discussed in light of the recently proposed role of cross-frequency interactions in the fine-grained coordination of neuronal population activity

Broad Learning for Healthcare

A broad spectrum of data from different modalities are generated in the healthcare domain every day, including scalar data (e.g., clinical measures collected at hospitals), tensor data (e.g., neuroimages analyzed by research institutes), graph data (e.g., brain connectivity networks), and sequence data (e.g., digital footprints recorded on smart sensors). Capability for modeling information from these heterogeneous data sources is potentially transformative for investigating disease mechanisms and for informing therapeutic interventions. Our works in this thesis attempt to facilitate healthcare applications in the setting of broad learning which focuses on fusing heterogeneous data sources for a variety of synergistic knowledge discovery and machine learning tasks. We are generally interested in computer-aided diagnosis, precision medicine, and mobile health by creating accurate user profiles which include important biomarkers, brain connectivity patterns, and latent representations. In particular, our works involve four different data mining problems with application to the healthcare domain: multi-view feature selection, subgraph pattern mining, brain network embedding, and multi-view sequence prediction.Comment: PhD Thesis, University of Illinois at Chicago, March 201

The role of the left intraparietal sulcus in the relationship between symbolic number processing and children\u27s arithmetic competence

The neural foundations of arithmetic learning are not well understood. While behavioral studies have revealed relationships between symbolic number processing and individual differences in children\u27s arithmetic performance, the neurocognitive mechanisms that bind symbolic number processing and arithmetic are unknown. The current fMRI study investigated the relationship between children\u27s brain activation during symbolic number comparison (Arabic digits) and individual differences in arithmetic fluency. A significant correlation was found between the numerical ratio effect on reaction times and accuracy and children\u27s arithmetic scores. Furthermore, children with a stronger neural ratio effect in the left intraparietal sulcus (IPS) during symbolic number processing exhibited higher arithmetic scores. Previous research has demonstrated that activation of the IPS during numerical magnitude processing increases over the course of development, and that the left IPS plays an important role in symbolic number processing. The present findings extend this knowledge to show that children with more mature response modulation of the IPS during symbolic number processing exhibit higher arithmetic competence. These results suggest that the left IPS is a key neural substrate for the relationship between the relative of precision of the representation of numerical magnitude and school-level arithmetic competence. © 2012 Elsevier Ltd

The role of the left intraparietal sulcus in the relationship between symbolic number processing and children\u27s arithmetic competence

The neural foundations of arithmetic learning are not well understood. While behavioral studies have revealed relationships between symbolic number processing and individual differences in children\u27s arithmetic performance, the neurocognitive mechanisms that bind symbolic number processing and arithmetic are unknown. The current fMRI study investigated the relationship between children\u27s brain activation during symbolic number comparison (Arabic digits) and individual differences in arithmetic fluency. A significant correlation was found between the numerical ratio effect on reaction times and accuracy and children\u27s arithmetic scores. Furthermore, children with a stronger neural ratio effect in the left intraparietal sulcus (IPS) during symbolic number processing exhibited higher arithmetic scores. Previous research has demonstrated that activation of the IPS during numerical magnitude processing increases over the course of development, and that the left IPS plays an important role in symbolic number processing. The present findings extend this knowledge to show that children with more mature response modulation of the IPS during symbolic number processing exhibit higher arithmetic competence. These results suggest that the left IPS is a key neural substrate for the relationship between the relative of precision of the representation of numerical magnitude and school-level arithmetic competence. © 2012 Elsevier Ltd