# Thresholded Partial Least Squares (TPLS) : Fast Construction of Powerful and Interpretable Whole Brain MVPA Predictor via Cross Validation

Lee, S., & Kable, J. W.

For neural predictors using fMRI data, whole-brain predictors can provide more predictive power compared to region-of-interest (ROI) or searchlight methods that only use local signals for prediction. Furthermore, they can discover relationships between different brain regions that cannot be obtained from other approaches. However, whole-brain predictions have two difficulties: 1) large number of predictive variables and 2) interpretability of the predictor. With large datasets that are becoming more common, matrix-inversions or iterative methods are too computationally expensive for thorough cross-validation. Additionally, the spatial relationship between predictor variables needs to be preserved in the final predictor in order for it to be interpretable, which is something that many existing methods such as LASSO cannot achieve. Here we propose a fast method of constructing powerful and interpretable whole-brain multivariate predictors using cross validation. We first use partial least squares (PLS) to reduce the dimensionality of the data and create a linear model. Then, we project the PLS coefficients and their p-values into the original brain space to calculate, respectively, whole-brain coefficient map and each voxel's variable importance measure. Using the voxels' importance measure, the whole-brain map can be thresholded to improve interpretability. By exploiting the orthonormality of PLS components, our method fits the model only once and the two tuning parameters (number of PLS components and voxel thresholding) can be chosen after the fact at the prediction stage. This is in stark contrast to most algorithms where the model needs to be fit for every tuning parameter combination that the user wants to test. We show that this new method, thanks to its analytical solutions, is faster, more memory-efficient, and more powerful compared to other whole-brain methods.