Semi-Supervised Factored Logistic Regression for High-Dimensional Neuroimaging Data
Imaging neuroscience links human behavior to aspects of brain biology in everincreasing datasets. Existing neuroimaging methods typically perform either discovery of unknown neural structure or testing of neural structure associated with mental tasks. However, testing hypotheses on the neural correlates underlying larger sets of mental tasks necessitates adequate representations for the observations. We therefore propose to blend representation modelling and task classification into a unified statistical learning problem. A multinomial logistic regression is introduced that is constrained by factored coefficients and coupled with an autoencoder. We show that this approach yields more accurate and interpretable neural models of psychological tasks in a reference dataset, as well as better generalization to other datasets.
The paper combines unsupervised learning on rest-state fMRI data (using a linear autoencoder) with supervised learning on task-based fMRI data (factored linear regression on task-based fMRI data). The combination is done by sharing the first matrix and using an objective which is a linear combination between reconstruction error (autoencoder) and classification error (regression).Comments:The paper reports a surprising result: The combined method obtains an out-of-sample accuracy of greater or equal than 95% whereas the best chain of independent steps for dimensionality reduction and regression achieves 87% or less. This is potentially a very interesting finding but missing information in the manuscript make it hard to understand the reason for this result.Specific comments:1) Eq. 4 is missing a closing parenthesis and, more importantly, the rationale behind this objective for regression needs to be explained. A potential problem with this objective is that it diverges to minus infinity if one class membership probability is exactly zero.2) It should be explained why \lambda = 1 is chosen for table 2 and in parts of table 3. For this setting the objective does not at all reflect reconstruction error - basically only regression performance is optimized.3) It would be good to also report the reconstruction performances achieved by the different models.