MLR Plugin Help

Authors: Fabrizio Esposito & Giancarlo Valente

In fMRI-based Brain Reading applications, the perceptual, cognitive or behavioral state of a subject can be either expressed in terms of discrete labels, e. g. "the subject is watching a face" or "the subject is listening to instructions", or more flexibly associated with one or more continuos variables spanning a continous range of values (e. g. ratings). In both cases, the ultimate scope of this application is to learn a functional relationship that allows predicting the unseen labels (classification) or the changes of a variable (regression) from a new data set.

The multivariate linear regression (MLR) plugin implements the linear regression variant of the multi-voxel pattern analysis (MVPA), where the class assignments are replaced by predictor variables, e. g. continous-valued time-courses sampled at the same fMRI time points (without temporal compaction), and where the output prediction will depend on a linear combination of multiple voxel time-courses whose coefficients or weights can either dampen or increase the influence of each one of them, just as in conventional univariate linear regression (GLM). The choice to perform an MVPA regression (rather than an MVPA classification) is justified in those cases where there are a few trials only of a given stimulus, but enough time points are available for the prediction, or the continous prediction itself is needed by definition (e. g. ratings, neurofeedback responses, etc...). On the other hand, MLR results can be anyway used for discrete classification in combination with a matching function applied to the prediction "post hoc".

Like in MVP-based classification, linear models are the preferred choice also for regression because they are simpler and make it easy to map voxel's relevance or sensitivity (weights) associated with a given prediction. MLR methods attempt to learn an as general and accurate as possible linear relationship between the input data and the predictors using a subset of the data (training datasets) and then use this relationship to predict the unseen changes for the same variables from a test dataset. Importantly, training and test data should be strictly separated to obtain a valid performance evaluation of the model. As performance metric, the sum of squared errors and the correlation coefficient between the predicted and true rating time-courses is usually considered for evaluating and comparing different MLR models or algorithms and different training scenarios. Pre-processing of the fMRI data sets is normally advised to reduce the effects of noise on the training.

In short, the MLR plugin operation is organized in multiple separate steps. First, features (voxels) are selected from the current anatomical space. Second, a cross-validation procedure is performed by which the data set is divided into N disjoint parts (folds) and a model is trained N times, each time leaving a different fold aside to be used as validation data set (N-fold approach). When mulitple separate fMRI runs are available, the "leave-one-run-out" approach can be used as a more convenient alternative, because the folds correspond to the runs and therefore the test data set are intrisically separated from the corresponding training data set. Third, for each "split" of the data, the fMRI dataset is transformed into a different representation using the so called kernel trick. The representation in the kernel space is more suitable for estimating the regression weights. Finally, the sum of squared errors and the correlations are reported to assess the model. 

For all details about the theoretical background or the practical usage of the MLR plugin please click on one of the following links below:

References

Valente, G., De Martino F., Esposito, F., Goebel, F., Formisano, E., 2011. Predicting subject-driven actions and sensory experience in a virtual world with Relevance Vector Machine Regression of fMRI data. Neuroimage 56, 651-661.