A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings
This work addresses the challenge of capturing complex dependencies in multi-output data, such as EEG signals, for applications in fields like neuroscience, though it appears incremental as it builds on existing Gaussian process and kernel methods.
The authors tackled the problem of modeling input-dependent couplings across multiple latent processes by introducing a novel kernel and a latent correlation Gaussian process (LCGP) model, achieving state-of-the-art performance in recovering correlations between latent signals on several datasets.
We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent correlation Gaussian process (LCGP) model combines these non-stationary latent components into multiple outputs by an input-dependent mixing matrix. Probit classification and support for multiple observation sets are derived by Variational Bayesian inference. Results on several datasets indicate that the LCGP model can recover the correlations between latent signals while simultaneously achieving state-of-the-art performance. We highlight the latent covariances with an EEG classification dataset where latent brain processes and their couplings simultaneously emerge from the model.