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Stochastic Gradient Richardson-Romberg Markov Chain Monte Carlo
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply Richardson-Romberg extrapolation to SGLD (two chains with step sizes γ and γ/2, correlated Brownian motions) | SGLD · Linear Gaussian model (d=1) | bias of estimated posterior variance: bias reduced from ≈10^-2 to ≈10^-4 | Helped |
| Apply Richardson-Romberg extrapolation to SGLD | SGLD · Large-scale matrix factorization (MovieLens-1M/10M/20M) | test RMSE vs wall-clock time: SGRRLD reaches SGLD's ≈400 s accuracy in ≈200 s on ML-1M | Helped |
| Apply Richardson-Romberg extrapolation to SGHMC | SGHMC · Linear Gaussian model (d=1), step size sweep | bias and MSE of estimated variance | Helped |
| Apply Richardson-Romberg extrapolation to SGLD | SGLD · Linear Gaussian model, MSE vs dimension d | MSE of posterior covariance | Helped |
| Use fully correlated Brownian increments (Sigma = Id) in the RR scheme versus less correlated choices | SGRRLD · Theory (CLT variance) | asymptotic variance of RR estimator | No clear effect |
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