Full Bayesian multi-task learning for multi-output brain decoding and accommodating missing data

Multi-task learning (MTL) has recently been demonstrated to be highly promising for decoding multiple target variables from neuroimaging data. Its primary advantage is that it makes more efficient use of the data than existing decoding models, leading to improved accuracy. In this work, we propose a novel Bayesian MTL approach, motivated by problems such as clinical applications where accurate quantification of uncertainty is crucial. We present a Markov chain Monte Carlo approach to perform inference in the model and demonstrate the approach using a publicly available neuroimaging dataset. We study the conditions where MTL is likely to improve performance: we first evaluate MTL as an approach for accommodating missing data, which is an important problem that has received little attention from the neuroimaging community. We then examine whether it is beneficial to include classification and regression tasks in the same model. We relate our conclusions to results from geostatistics, where MTL methods were pioneered, and make recommendations for neuroimaging practitioners using MTL.