Principle:Sktime Pytorch forecasting Probabilistic Prediction
| Knowledge Sources | |
|---|---|
| Domains | Time_Series, Probabilistic_Forecasting, Model_Evaluation |
| Last Updated | 2026-02-08 07:00 GMT |
Overview
Technique for generating probabilistic forecasts from trained autoregressive models by sampling from learned output distributions and computing prediction intervals.
Description
Probabilistic Prediction extends point forecasting by producing full predictive distributions. For autoregressive models like DeepAR, predictions are generated by sampling from the learned distribution at each time step and feeding samples back as inputs for subsequent steps. Multiple samples (typically 100) are drawn to approximate the predictive distribution, from which quantiles and prediction intervals can be computed. The predict method supports multiple output modes: point predictions (median), quantile predictions, raw distribution parameters, or full sample sets. This enables downstream applications like risk-aware decision making and inventory optimization.
Usage
Use this principle after training a DeepAR or other distributional model to generate forecasts on validation or test data. The n_samples parameter controls the quality of the distribution approximation. Higher values give smoother quantile estimates but increase computation.
Theoretical Basis
Autoregressive sampling:
# Abstract autoregressive prediction
for step in range(prediction_length):
distribution_params = model.forward(history)
for sample_idx in range(n_samples):
sample = distribution.sample(distribution_params)
samples[sample_idx, step] = sample
history = append(history, median(samples[:, step]))
Output modes:
- prediction — point forecast (median of distribution)
- quantiles — quantile forecasts (e.g., 10th, 50th, 90th percentiles)
- samples — raw Monte Carlo samples from the predictive distribution
- raw — distribution parameters (mean, variance) before sampling
Prediction interval from samples:
Where is the q-th quantile of the samples.