Scalable Gaussian Process Regression for Biomedical Time-Series Data

• Activity Number: 265 - Stochastic Processes in Medicine and Medical Engineering: Theoretical Foundations and Applications
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Medical Devices and Diagnostics
• Author(s): Jan Graßhoff* and Philipp Rostalski
• Companies: Fraunhofer Research Institution for Individualized and Cell-Based Medical Engineering and Fraunhofer Research Institution for Individualized and Cell-Based Medical Engineering
• Keywords: stochastic processes; kernel methods; structure exploitation; biomedical signal processing

Abstract

Gaussian processes (GPs) are non-parametric Bayesian models that are widely used in machine-learning and signal processing. In this work, the application of GP regression to large biomedical datasets with temporal and spatio-temporal structure will be discussed. We particularly treat mixtures of non-stationary processes, which commonly arise in the context of biomedical source separation problems. We elaborate on several relevant applications, ranging from electrical impedance tomography to mechanical ventilation. In practice, the application of GP regression to large data sets remains challenging due to heavy memory and computational requirements. We therefore compare recent works that have demonstrated exact/near-exact solutions to the GP regression problem with quasi-linear time complexity. These methods are based on the exploitation of structure in the kernel matrix: among the most promising approaches are (1) equivalent state-space representation methods and (2) methods exploiting Toeplitz and Kronecker structure. We argue that the combination of interpretable models and scalable regression methods can lead to a multitude of new solutions in biomedical time-series processing.