ABSTRACT
So far, we have discussed Gaussian process regression models for a single curve (which can also be regarded as a batch with only one realization). We now turn our attention to consider batch data or data with repeated curves. A typical example of batch data is the paraplegia data discussed in Section 1.3.1, in which we want to model a standing-up maneuver. The response variable is the vertical trajectory of the body’s COM that is a continuous functional variable, but there are two types of covariates. One type of covariate is for functional variables such as forces and torques under the patient’s feet in the period of standing-up maneuver, and the other type is for scalar variables such as the patient’s weight and height. The data collected from repeated experiments form what we call batch data. This is a typical functional regression problem with functional response variable as described in Section 1.1.2.
