Tensor Regression with Applications in Neuroimaging Data Analysis

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data.Comment: 27 pages, 4 figure

Generalized sparse regularization with application to fmri brain decoding

Abstract. Many current medical image analysis problems involve learning thousands or even millions of model parameters from extremely few samples. Employing sparse models provides an effective means for handling the curse of dimensionality, but other propitious properties beyond sparsity are typically not modeled. In this paper, we propose a simple approach, generalized sparse regularization (GSR), for incorporating domain-specific knowledge into a wide range of sparse linear models, such as the LASSO and group LASSO regression models. We demonstrate the power of GSR by building anatomically-informed sparse classifiers that additionally model the intrinsic spatiotemporal characteristics of brain activity for fMRI classification. We validate on real data and show how prior-informed sparse classifiers outperform standard classifiers, such as SVM and a number of sparse linear classifiers, both in terms of prediction accuracy and result interpretability. Our results illustrate the addedvalue in facilitating flexible integration of prior knowledge beyond sparsity in large-scale model learning problems

Model-based feature construction for multivariate decoding

Conventional decoding methods in neuroscience aim to predict discrete brain states from multivariate correlates of neural activity. This approach faces two important challenges. First, a small number of examples are typically represented by a much larger number of features, making it hard to select the few informative features that allow for accurate predictions. Second, accuracy estimates and information maps often remain descriptive and can be hard to interpret. In this paper, we propose a model-based decoding approach that addresses both challenges from a new angle. Our method involves (i) inverting a dynamic causal model of neurophysiological data in a trial-by-trial fashion; (ii) training and testing a discriminative classifier on a strongly reduced feature space derived from trial-wise estimates of the model parameters; and (iii) reconstructing the separating hyperplane. Since the approach is model-based, it provides a principled dimensionality reduction of the feature space; in addition, if the model is neurobiologically plausible, decoding results may offer a mechanistically meaningful interpretation. The proposed method can be used in conjunction with a variety of modelling approaches and brain data, and supports decoding of either trial or subject labels. Moreover, it can supplement evidence-based approaches for model-based decoding and enable structural model selection in cases where Bayesian model selection cannot be applied. Here, we illustrate its application using dynamic causal modelling (DCM) of electrophysiological recordings in rodents. We demonstrate that the approach achieves significant above-chance performance and, at the same time, allows for a neurobiological interpretation of the results