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The promises and pitfalls of Stochastic Gradient Langevin Dynamics
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use control variates centered at the posterior mode | SGLD · Bayesian logistic regression, Covertype | test negative loglikelihood | Helped |
| Use control variates centered at the posterior mode | SGLD · Covertype | stochastic gradient variance scaling with N: 2 -> 1 | Helped |
| Use constant step size γ = η/N with plain stochastic gradients | SGLD · Bayesian linear regression | Wasserstein distance to posterior: Ω(1) | Hurt |
| Replace full gradients with minibatch stochastic gradients | LMC · Bayesian posterior sampling | Wasserstein distance between invariant measure and posterior: √(d) O(N^-1/2) for SGLD and SGD distance; Ω(1) for SGLD-to-posterior in linear regression | Hurt |
| Center minibatch gradients at the posterior mode, canceling their additive noise component | SGLDFP · Bayesian posterior sampling | Wasserstein distance to LMC: √(d η) O(N^-1/2) | Helped |
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