Gaussian Processes
The determination of periodicities using Gaussian Processes has been getting somewhat trendy as of recent years. In the area of astrophysical time series analysis, it’s been used with varying degrees of success to study stellar magnetic cycles (timescale of years) and stellar rotation (timescale of days), none of which are strictly periodic processes.
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class
periodicity.gp.
BrownianGP
(signal, err, init_period=None, period_ppf=None) Bases:
periodicity.gp.CeleriteModeler
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prior_transform
(u)
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class
periodicity.gp.
BrownianTheanoGP
(signal, err, init_period=None, predict_at=None, psd_at=None) Bases:
periodicity.gp.TheanoModeler
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class
periodicity.gp.
CeleriteModeler
(signal, err, init_period=None, period_ppf=None) Bases:
object
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get_kernel
(tau, gp)
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get_prediction
(time, gp)
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get_psd
(frequency, gp)
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log_prob
(u, gp)
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mcmc
(n_walkers=50, n_steps=1000, burn=0, use_prior=False, random_seed=None) Samples the posterior probability distribution with a Markov Chain Monte Carlo simulation.
- Parameters
n_walkers (int, optional) – Number of walkers (the default is 50).
n_steps (int, optional) – Number of steps taken by each walker (the default is 1000).
burn (int, optional) – Number of burn-in samples to remove from the beginning of the simulation (the default is 0).
use_prior (bool, optional) – Whether to start walkers by sampling from the prior distribution. The default is False, in which case a ball centered at the MLE hyperparameter vector is used.
- Returns
trace (dict) – Samples of the posterior hyperparameter distribution.
tau (ndarray) – Estimated autocorrelation time of MCMC chain for each parameter.
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minimize
(gp, **kwargs) Gradient-based optimization of the objective function within the unit hypercube.
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nll
(u, gp) Objective function based on the Negative Log-Likelihood.
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prior_transform
(u)
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set_params
(params, gp)
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class
periodicity.gp.
GeorgeModeler
(signal, err, init_period=None, period_prior=None, bounds=None, constraints=None) Bases:
object
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get_kernel
(tau, gp)
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get_prediction
(time, gp)
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grad_nll
(theta, gp)
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log_prior
(theta)
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log_prob
(theta, gp) Posterior distribution over the hyperparameters.
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mcmc
(n_walkers=50, n_steps=1000, burn=0, random_seed=None) Samples the posterior probability distribution with a Markov Chain Monte Carlo simulation.
- Parameters
n_walkers (int, optional) – Number of walkers (the default is 50).
n_steps (int, optional) – Number of steps taken by each walker (the default is 1000).
burn (int, optional) – Number of burn-in samples to remove from the beginning of the simulation (the default is 0).
use_prior (bool, optional) – Whether to start walkers by sampling from the prior distribution. The default is False, in which case a ball centered at the MLE hyperparameter vector is used.
- Returns
samples – Samples of the posterior hyperparameter distribution.
- Return type
ndarray[n_dim, n_walkers * (n_steps - burn)]
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minimize
(gp, grad=False, **kwargs) Gradient-based optimization of the objective function within the unit hypercube.
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nll
(theta, gp) Objective function based on the Negative Log-Likelihood.
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set_params
(theta, gp)
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class
periodicity.gp.
HarmonicGP
(signal, err, init_period=None, period_ppf=None) Bases:
periodicity.gp.CeleriteModeler
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prior_transform
(u)
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class
periodicity.gp.
HarmonicTheanoGP
(signal, err, init_period=None, predict_at=None, psd_at=None) Bases:
periodicity.gp.TheanoModeler
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class
periodicity.gp.
QuasiPeriodicGP
(signal, err, init_period=None, period_prior=None, bounds=None, constraints=None) Bases:
periodicity.gp.GeorgeModeler
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log_prior
(theta)
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class
periodicity.gp.
TheanoModeler
(signal, err, init_period=None) Bases:
object
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mcmc
(n_walkers=1, n_steps=2000, burn=1000, cores=1)
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