Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
PAC-Bayesian Theory Meets Bayesian Inference
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the PAC-Bayes bound with lambda=1/n (instead of lambda=sqrt(n)) for the Gibbs posterior on the synthetic regression task | Bayesian linear regression bound · Synthetic linear regression, n from 10 to 10^6 | NLL generalization bound value | Mixed |
| Select model by minimizing sub-gamma PAC-Bayes bound (equivalently maximizing marginal likelihood) | Polynomial model selection · Toy sin(x) regression, degrees 1-7 | selected degree | No clear effect |
| Replace classical [0,1]-bounded PAC-Bayes with sub-gamma PAC-Bayes bound for unbounded NLL | Bayesian linear regression bound · Synthetic linear regression, n up to 10^6 | bound tightness vs bounded-loss bounds | Helped |
| Use model averaging (sum of evidences) instead of selecting single best model in the PAC-Bayes bound | Model selection bound · Theoretical comparison over L models | bound value | Helped |
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