3.1.1. 64 ms Light Curves

To obtain counts recorded at identical times relative to the trigger time for each light curve, BATSE and *Swift*/BAT light curves were modelled and resampled onto an identical grid using Gaussian Process Regression (GPR), a machine learning method that uses the input data to infer the function and explain the observations [82]. Gaussian processes model observations function as joint multivariate normal distributions, which can be fully specified by a mean function and covariance matrix. GPR determines the mean function and the entries of the covariance matrix using a user-specified covariance function (kernel). Hyperparameters of the kernel were optimised to maximise the marginal likelihood of the data under the Gaussian process prior.

The Gaussian Process model was implemented using the GPFlow library in Python [83], which originates from GPy but is built on TensorFlow [84]. A heteroscedastic regression model was used, which incorporates uncertainty in each point into the interpolation process by applying less weight to points with greater uncertainty. The radial-basis function

kernel (also known as squared exponential kernel) was used, as it is infinitely differentiable and produces smooth functions. The Adam and natural gradient optimisers were used to converge to the best-fit hyperparameters. The resulting equally spaced, evenly sampled 64 ms light curves were zero-padded beyond T<sup>100</sup> to ensure noise was discarded. The T<sup>100</sup> interval was extracted from the GRB catalogues. The four-band light curves were concatenated together and input to the feature extraction algorithm depicted in Figure 1.
