aleatory.processes.GPSquaredExponential

class aleatory.processes.GPSquaredExponential(length_scale=1.0, sigma=1.0, T=1.0, rng=None)

Gaussian Process with Squared Exponential Kernel

This process is identical to the Gaussian Process with RBF kernel, as the Squared Exponential kernel is just another name for the RBF kernel. The covariance function is given by

\[K(t, s) = \sigma^2 \exp\left(-\frac{(t - s)^2}{2l^2}\right) \ \ \ \ \ t, s \in [0,T]\]

__init__(length_scale=1.0, sigma=1.0, T=1.0, rng=None)

Methods

__init__([length_scale, sigma, T, rng])
covariance_function(times)
draw(n, N[, T, marginal, envelope, type, title])	Simulates and plots paths/trajectories from the instanced stochastic process.
estimate_covariances([times])
estimate_expectations()
estimate_quantiles(q)
estimate_stds()
estimate_variances()
get_marginal(time)
make_widget([cmap, matrix_shape])
marginal_expectation([times])
marginal_stds([times])
marginal_variance([times])
plot(n, N[, T, title, suptitle])	Simulates and plots paths/trajectories from the instanced stochastic process.
plot_covariance([times, colormap, ...])
plot_kernel([times, colormap, matrix_shape, ...])
plot_kernel3d([times, title])
plot_mean_function([T, n])
plot_mean_variance([times])
plot_paths_and_kernel(n, N[, T, cmap, ...])	Plots the paths of the process and the covariance kernel.
process_covariance([times])
process_expectation()
process_stds()
process_variance()
sample(n[, T])
sample_at(times)
simulate(n, N[, T])	Simulate paths/trajectories from the instanced stochastic process.
variance_function(times)

Attributes

T	End time of the process.
rng