Workflow:Pyro ppl Pyro Bayesian Regression
| Knowledge Sources | |
|---|---|
| Domains | Probabilistic_Programming, Bayesian_Modeling, Regression |
| Last Updated | 2026-02-09 09:00 GMT |
Overview
End-to-end process for building and fitting a Bayesian regression model in Pyro using automatic guide construction, covering prior specification, model definition, inference via SVI or MCMC, and posterior predictive analysis.
Description
This workflow describes the standard procedure for Bayesian regression analysis using Pyro. It covers specifying prior distributions over regression coefficients and noise parameters, defining the likelihood function, automatically constructing a variational guide using Pyro's AutoGuide machinery, and performing inference. The workflow supports both SVI-based approximate inference (fast, scalable) and MCMC-based exact inference (accurate, calibrated). After fitting, the posterior is used to quantify parameter uncertainty, make predictions with uncertainty bands, and perform model comparison. This pattern generalizes to hierarchical models, generalized linear models, and models with regularization priors for feature selection.
Usage
Execute this workflow when you have a regression problem and want principled uncertainty quantification over model parameters and predictions. This is appropriate when you need credible intervals on coefficients, predictive uncertainty bands, model comparison via marginal likelihood, or regularization through informative priors. Use cases include scientific data analysis, hierarchical and multilevel modeling, sparse feature selection with shrinkage priors, and any regression setting where point estimates are insufficient.
Execution Steps
Step 1: Prepare Data and Define Priors
Load and preprocess the dataset, separating covariates from the response variable. Choose prior distributions that encode domain knowledge about the regression coefficients (e.g., Normal for weakly informative, HalfCauchy or Horseshoe for sparsity). Consider the scale of the data when setting prior hyperparameters. Standardizing covariates often improves inference efficiency.
Key considerations:
- Standardize covariates for better sampling/optimization geometry
- Normal priors are weakly informative defaults for coefficients
- HalfCauchy or HalfNormal priors work well for scale parameters
- Horseshoe priors enable automatic sparse feature selection
- Consider hierarchical priors for grouped data
Step 2: Define the Regression Model
Write a model function that samples regression coefficients from their priors, computes the linear predictor, and scores observations against the likelihood. Use pyro.sample for all Bayesian parameters, pyro.plate for the observation dimension, and pyro.deterministic for derived quantities. For generalized linear models, apply the appropriate link function (logit, log, etc.) to the linear predictor.
Key considerations:
- Sample each coefficient and noise parameter with pyro.sample
- Use pyro.plate for the observation dimension
- Linear predictor: mu = X @ beta + intercept
- Choose likelihood matching the data: Normal for continuous, Bernoulli for binary, Poisson for counts
- pyro.deterministic tracks derived quantities in the posterior
Step 3: Construct the Guide Automatically
Use Pyro's AutoGuide classes to automatically build a variational approximation from the model structure. AutoNormal creates independent Normal posteriors for each parameter. AutoMultivariateNormal captures posterior correlations. AutoDelta produces MAP point estimates. AutoDiagonalNormal is equivalent to AutoNormal. Configure initialization strategies (init_to_median, init_to_feasible) for stable optimization starting points.
Key considerations:
- AutoNormal is the default for fast mean-field approximation
- AutoMultivariateNormal captures correlations but scales quadratically
- AutoDelta provides MAP estimation (no uncertainty)
- init_to_median or init_to_feasible prevents initialization failures
- For MCMC, no guide is needed — skip this step
Step 4: Perform Inference
For SVI: create an SVI instance with Trace_ELBO, optimizer, model, and guide, then run the training loop. For MCMC: create a NUTS kernel and MCMC sampler, then call mcmc.run(). Both approaches produce posterior samples or parameter estimates for the regression coefficients.
Key considerations:
- SVI is faster for large datasets; MCMC is more accurate for small datasets
- SVI: monitor ELBO convergence over iterations
- MCMC: check R-hat, effective sample size, and divergent transitions
- For MCMC, consider reparameterization (centered vs. non-centered) for hierarchical models
- Multiple MCMC chains enable convergence assessment
Step 5: Analyze Posterior and Generate Predictions
Extract posterior samples and compute summary statistics (means, credible intervals) for each coefficient. Use the Predictive utility to generate posterior predictive distributions on new data. Compare model predictions to held-out observations. Visualize posterior distributions, coefficient estimates with uncertainty, and prediction intervals.
Key considerations:
- Predictive class wraps model and guide/posterior for forward sampling
- 89% or 95% credible intervals from posterior quantiles
- Posterior predictive checks validate model fit
- Compare multiple models via ELBO or WAIC
- Coefficient posterior distributions reveal which features are important