Neuroscientists are increasingly collecting multimodal data during experiments and observational studies. Different data modalities-such as EEG, fMRI, LFP, and spike trains-offer different views of the complex systems contributing to neural phenomena. Here, we focus on joint modeling of LFP and spike train data, and present a novel Bayesian method for neural decoding to infer behavioral and experimental conditions. This model performs supervised dual-dimensionality reduction: it learns low-dimensional representations of two different sources of information that not only explain variation in the input data itself, but also predict extra-neuronal outcomes. Despite being one probabilistic unit, the model consists of multiple modules: exponential PCA and wavelet PCA are used for dimensionality reduction in the spike train and LFP modules, respectively; these modules simultaneously interface with a Bayesian binary regression module. We demonstrate how this model may be used for prediction, parametric inference, and identification of influential predictors. In prediction, the hierarchical model outperforms other models trained on LFP alone, spike train alone, and combined LFP and spike train data. We compare two methods for modeling the loading matrix and find them to perform similarly. Finally, model parameters and their posterior distributions yield scientific insights.
Keywords: Bayesian methods; discrimination; high dimensional data; statistical learning.