Implementation:Pyro ppl Pyro BART Forecast

Property	Value
Implementation Type	Pattern Doc
Source File	examples/contrib/forecast/bart.py
Module	pyro.contrib.forecast
Pyro Features	pyro.contrib.forecast.ForecastingModel, backtest, GaussianHMM, LKJCholesky, seasonal modeling, periodic_cumsum, periodic_repeat
Dataset	BART (Bay Area Rapid Transit) origin-destination ridership data

Overview

This file demonstrates Pyro's forecasting framework by modeling hourly arrivals and departures at the Embarcadero BART station. The model subclasses ForecastingModel and implements a .model() method that defines a bivariate time series model with:

• Seasonal component: Weekly seasonality (period = 24 hours x 7 days = 168) with an initial seasonal pattern and slow drift via periodic_cumsum.
• Noise model: A GaussianHMM with correlated bivariate transitions, modeling autocorrelated noise with LKJ-distributed correlation matrices.
• Global parameters: Noise scale, transition timescale, transition location, transition scale and correlation, observation scale and correlation.

The model is evaluated using backtesting via the backtest() function, which automatically trains on sliding windows and evaluates on held-out test windows.

Code Reference

class Model(ForecastingModel):
    def model(self, zero_data, covariates):
        period = 24 * 7
        duration, dim = zero_data.shape[-2:]

        noise_scale = pyro.sample("noise_scale",
            dist.LogNormal(torch.full((dim,), -3.0), 1.0).to_event(1))
        trans_timescale = pyro.sample("trans_timescale",
            dist.LogNormal(torch.zeros(dim), 1).to_event(1))
        # ... more global parameters ...

        with pyro.plate("season_plate", period, dim=-1):
            season_init = pyro.sample("season_init",
                dist.Normal(torch.zeros(dim), 1).to_event(1))

        with self.time_plate:
            season_noise = pyro.sample("season_noise",
                dist.Normal(0, noise_scale).to_event(1))

        prediction = periodic_repeat(season_init, duration, dim=-2) + \
                     periodic_cumsum(season_noise, period, dim=-2)

        noise_model = dist.GaussianHMM(init_dist, trans_mat, trans_dist,
                                        obs_mat, obs_dist, duration=duration)
        self.predict(noise_model, prediction)

I/O Contract

Parameter	Type	Description
--train-window	int	Training window size in hours (default: 2160)
--test-window	int	Test window size in hours (default: 336)
--stride	int	Stride between backtest windows (default: 168)
-n / --num-steps	int	SVI optimization steps (default: 501)
--num-samples	int	Forecast samples (default: 100)
--dct	flag	Use DCT gradients

Output:

• Backtest metrics: MAE, RMSE, CRPS (mean +/- std across windows)
• Data shape: bivariate (arrivals, departures) hourly counts

Usage Examples

# Run backtesting with default parameters
# python bart.py -n 501 -lr 0.01 --num-samples 100

# With DCT gradients for faster training
# python bart.py --dct -n 501

Related Pages

• Pyro_ppl_Pyro_GP_TimeSeries - GP-based time series models