Gaussianprocessderivatives

A Python package for smoothing data and estimating first- and second-order derivatives and their errors. Covariance functions can be linear, squared exponential, squared exponential with a linear trend, twice-differentiable Matern, periodic, and locally periodic.

Example

An example workflow to smooth data (x, y), where the columns of y are replicates, is

>>> import gaussianprocessderivatives as gp
>>> g = gp.maternGP({0: (-4, 4), 1: (-4, 4), 2: (-4, -2)}, x, y)

The dictionary sets bounds on the hyperparameters, so that 0: (-4, 4) means that the bounds on the first hyperparameter are 1e-4 and 1e4.

The amplitude and measurement-error hyperparameters are variances of y, so their bounds depend on the magnitude of the data. Passing scale_y=True divides y by its root mean square before fitting while restoring the units of the data in every prediction and sample, so that one set of bounds serves data of most scales. The hyperparameters are relative to the root-mean-square scale.

>>> g.info()

explains what each hyperparameter does.

Once g is instantiated,

>>> g.findhyperparameters()
>>> g.results()
>>> g.predict(x, derivs=2)

optimises the hyperparameters, determines a smoothed version of the data, and estimates the derivatives.

The results can be visualised by

>>> import matplotlib.pylab as plt
>>> plt.figure()
>>> plt.subplot(2, 1, 1)
>>> g.sketch('.')
>>> plt.subplot(2, 1, 2)
>>> g.sketch('.', derivs=1)
>>> plt.show()

and are available as g.f and g.fvar (smoothed data and error), g.df and g.dfvar (estimate of dy/dx), and g.ddf and g.ddfvar (estimate of d2y/dx2).

Citation

If you find the software useful, please consider citing:

Swain, P. S., Stevenson, K., Leary, A., Montano-Gutierrez, L. F., Clark, I. B. N., Vogel, J., & Pilizota, T. (2016). Inferring time derivatives including cell growth rates using Gaussian processes. Nature Communications, 7, 13766.

Development history

• v0.2.0: Each covariance function became a class of its own; only for python 3.11; warnings from the Gaussian process are optional.
• v0.3.0: scale_y introduced; the random-number generator now belongs to the instance, not to the module; a pytest suite added.