Gaussian process joint models for estimating latent dynamics of brain and behavior

For bridging implementational and algorithmic levels of analysis (Marr, 1982), Bayesian joint models (Turner et al., 2013) have been applied for investigating shared statistical constraints between neural activities and cognitive model parameters. However, the previous joint modeling approach has assumed linearity in its linking function, which might not always be ideal when dealing with complex brain dynamics. Moreover, joint models based on covariance estimation often sacrifice the temporal dynamics of cognitive processes. As a solution to these limitations, we propose a Gaussian process joint model (GPJM), a data-driven and nonparametric joint modeling framework based on hierarchical Gaussian process latent variable models (Lawrence & Moore, 2007). In the GPJM, latent Gaussian processes serve as a linking function and model temporal dynamics governing neural and behavioral observations. The GPJM can incorporate spatiotemporal covariance structures as its constraints and evaluate the relevance of each latent dimension to the process of data generation. To verify the utility of the GPJM, we tested the model performance with simulation and an application to real data. The simulation results showed that the GPJM estimates cognitive dynamics while exploiting spatiotemporal constraints. In an fMRI experiment based on a continuous motion-tracking task, the GPJM explained the neural and behavioral data appropriately and also revealed non-trivial underlying dynamics that generate the data. Cross-validation analyses demonstrated that the latent dynamics trained with complete neural data and partially observed behavioral data could predict test data reasonably. How the latent dynamics could be interpreted is an open question.