Implementation:Pyro ppl Pyro GP TimeSeries

Property	Value
Implementation Type	Pattern Doc
Source File	examples/contrib/timeseries/gp_models.py
Module	pyro.contrib.timeseries
Pyro Features	pyro.contrib.timeseries.IndependentMaternGP, pyro.contrib.timeseries.LinearlyCoupledMaternGP, maximum likelihood training, one-step and multi-step forecasting
Dataset	EEG Eye State (UCI Machine Learning Repository)

Overview

This file demonstrates Pyro's time series GP models for multivariate time series forecasting. It compares two Gaussian Process models on EEG (electroencephalography) data:

• IndependentMaternGP (IMGP): Models each output dimension independently with a Matern-1.5 kernel. Forecasts are independent across dimensions.
• LinearlyCoupledMaternGP (LCMGP): Uses a linear mixing model where multiple latent GPs are linearly combined to produce correlated output dimensions. This captures cross-channel correlations.

The training procedure:

• Maximize the log marginal likelihood gp.log_prob(data) using Adam with exponential learning rate decay
• Perform one-step-ahead forecasting using a rolling window
• Perform multi-step forecasting from a fixed conditioning set

Code Reference

def main(args):
    # Set up model
    if args.model == "imgp":
        gp = IndependentMaternGP(nu=1.5, obs_dim=obs_dim,
            length_scale_init=1.5 * torch.ones(obs_dim)).double()
    elif args.model == "lcmgp":
        num_gps = 9
        gp = LinearlyCoupledMaternGP(nu=1.5, obs_dim=obs_dim, num_gps=num_gps,
            length_scale_init=1.5 * torch.ones(num_gps)).double()

    # Training loop - maximize log marginal likelihood
    adam = torch.optim.Adam(gp.parameters(), lr=args.init_learning_rate)
    for step in range(args.num_steps):
        loss = -gp.log_prob(data[0:T_train, :]).sum() / T_train
        loss.backward()
        adam.step()

    # One-step-ahead forecasting
    for t in range(T_onestep):
        dts = torch.tensor([1.0]).double()
        pred_dist = gp.forecast(data[0:T_train+t, :], dts)

    # Multi-step forecasting
    dts = (1 + torch.arange(T_multistep)).double()
    pred_dist = gp.forecast(data[0:T_train+T_onestep, :], dts)

I/O Contract

Parameter	Type	Description
-m / --model	str	Model type: "imgp" or "lcmgp"
-n / --num-steps	int	Training steps (default: 300)
-ilr / --init-learning-rate	float	Initial learning rate (default: 0.01)
-flr / --final-learning-rate	float	Final learning rate (default: 0.0003)
--test	flag	Use synthetic data for testing
--plot	flag	Generate forecast plots

Output:

• Training loss per step
• Forecast means and confidence intervals for selected channels
• PDF plot showing one-step and multi-step predictions

Usage Examples

# Independent Matern GP on EEG data
# python gp_models.py -m imgp -n 300 --plot

# Linearly Coupled Matern GP
# python gp_models.py -m lcmgp -n 300 --plot

# Quick test with synthetic data
# python gp_models.py --test -m imgp -n 50

Related Pages

• Pyro_ppl_Pyro_SV_DKL - Deep kernel learning combining GP with CNN
• Pyro_ppl_Pyro_GP_BayesOpt - GP-based Bayesian optimization
• Pyro_ppl_Pyro_BART_Forecast - Forecasting with ForecastingModel framework