Abstract

In the last century, a huge multi-disciplinary scientific endeavor is devoted to answer the historical questions in understanding the brain functions. Among the statistical methods used for this purpose, brain decoding provides a tool to predict the mental state of a human subject based on the recorded brain signal. Brain decoding is widely applied in the contexts of brain-computer interfacing, medical diagnosis, and multivariate hypothesis testing on neuroimaging data. In the latest case, linear classifiers are generally employed to discriminate between experimental conditions. Then, the derived weights are visualized in the form of brain maps to further study the spatio-temporal patterns of the underlying neurophysiological activity. It is well known that the brain maps derived from weights of linear classifiers are hard to interpret because of high correlations between predictors, low signal-to-noise ratio, across-subject variability, and the high dimensionality of the neuroimaging data. Therefore, improving the interpretability of brain decoding approaches is of primary interest in many neuroimaging studies. Despite extensive studies of this type, at present, there is no formal definition for interpretability of multivariate brain maps. As a consequence, there is no quantitative measure for evaluating the interpretability of different brain decoding methods. In this thesis, as the primary contribution, we propose a theoretical definition of interpretability in linear brain decoding; we show that the interpretability of multivariate brain maps can be decomposed into their reproducibility and representativeness. As an application of the proposed definition, we exemplify a heuristic for approximating the interpretability in multivariate analysis of evoked magnetoencephalography (MEG) responses. We propose to combine the approximated interpretability and the generalization performance of the model into a new multi-objective criterion for model selection. Our results, for the simulated and real MEG data, show that optimizing the hyper-parameters of the regularized linear classifier based on the proposed criterion results in more informative multivariate brain maps. More importantly, the presented definition provides the theoretical background for quantitative evaluation of interpretability, and hence, facilitates the development of more effective brain decoding algorithms in the future. As the secondary contribution, we present an application of multi-task joint feature learning for group-level multivariate pattern recovery in single-trial MEG decoding. The proposed method allows for recovering sparse yet consistent patterns across different subjects, and therefore enhances the interpretability of the decoding model. We evaluated the performance of the multi-task joint feature learning in terms of generalization, reproducibility, and quality of pattern recovery against traditional single-subject and pooling approaches on both simulated and real MEG datasets. Our experimental results demonstrate that the multi-task joint feature learning framework is capable of recovering meaningful patterns of varying spatio-temporally distributed brain activity across individuals while still maintaining excellent generalization performance. The presented methodology facilitates the application of brain decoding for characterizing the fine-level distinctive patterns of brain activity in group-level inference on neuroimaging data.