Probit Latent Variables Estimation for a Gaussian Process Classifier: Application to the Detection of High-Voltage Spindles

The Deep Brain Stimulation (DBS) is a surgical procedure efficient to relieve symptoms of some neurodegenerative disease like the Parkinson’s disease (PD). However, apply permanently the deep brain stimulation due to the lack of possible control lead to several side effects. Recent studies shown the detection of High-Voltage Spindles (HVS) in local field potentials is an interesting way to predict the arrival of symptoms in PD people. The complexity of signals and the short time lag between the apparition of HVS and the arrival of symptoms make it necessary to have a fast and robust model to classify the presence of HVS (\(Y=1\)) or not (\(Y=-1\)) and to apply the DBS only when needed. In this paper, we focus on a Gaussian process model. It consists to estimate the latent variable f of the probit model: \({\text {Pr}}(Y=1|input) = \varPhi (f(input))\) with \(\varPhi \) the distribution function of the standard normal distribution.