Generalized Convolution Spectral Mixture for Multi-Task Gaussian Processes

Abstract

Multi-Task Gaussian processes (MTGPs) have shown a significant progress both in expressiveness and interpretation of the relatedness between different tasks: from linear combinations of independent single-output Gaussian processes (GPs), through the direct modeling of the cross-covariances such as spectral mixture kernels with phase shift, to the design of multivariate covariance functions based on spectral mixture kernels which model delays among tasks in addition to phase differences, and which provide a parametric interpretation of the relatedness across tasks. In this paper we further extend expressiveness and interpretability of MTGPs models and introduce a new family of kernels capable to model nonlinear correlations between tasks as well as dependencies between component, including time and phase delay. Specifically, we use generalized convolution spectral mixture kernels for modeling dependencies at component level, and coupling coregionalization for discovering task level correlations. The proposed kernels for MTGP are validated on artificial data and compared with existing MTGPs methods on three real-world experiments. Results indicate the benefits of our more expressive representation with respect to performance and interpretability.

Machine Learning to Summarize and Provide Context for Sleep and Eating Schedules

“…Multi-Output Gaussian Process Toolkit (MOGPTK), our second Gaussian Process approach builds from a Python package for multi-channel data modeling using Gaussian processes (GP) [10,11]. This toolkit aims to address the need for a Multi-output Gaussian Process kernel and provides a natural way to train our model and it is based on the trained model to predict the following pattern.…”

Multioutput Convolution Spectral Mixture for Gaussian Processes

“…Recently, the generalized convolution SM (GCSM) kernel was introduced [15], [16] to model time-and phase-delay Fig. 1.…”

Generalized Convolution Spectral Mixture for Multitask Gaussian Processes

“…A more recent SM based kernel for MTGP employs generalized convolution spectral mixture of coupling coregionalization (GCSM-CC) [23]. The GCSM-CC kernel is:…”

“…MOSM has three limitations: all tasks have the same number of components, components in different tasks should be aligned, and spectral mixture level dependency within each task is ignored. Recently the generalized convolution spectral mixture of coupling coregionalization (GCSM-CC) kernel [23] explicitly extended previous works to model nonlinear correlations between tasks and dependencies between spectral mixtures and introduced coupling coregionalization to learn task level correlations. This means GCSM-CC only addresses the last mentioned limitation of MOSM, but that, as a result of using coupling coregionalization [23], tasks in GCSM-CC share the same kernel, and hyper-parameters in coregionalization terms involving task correlations are global and linear.…”