Bayesian inference usually focuses on the posterior parameter distribution, but in practice we care about predictions. The authors propose Self-Supervised Laplace Approximation (SSLA), which skips the parameter posterior and directly approximates the posterior predictive distribution using a self-training idea: refit the model on its own predictions. If the model assigns high likelihood to self-predicted data, those predictions are low-uncertainty, and vice versa. This yields a deterministic, sampling-free approximation. An approximate version (ASSLA) avoids expensive refitting. The modular design allows plugging in different priors for classical sensitivity analysis.
Main takeaways:
- Standard Bayesian methods focus on parameter posteriors, but predictions are often the real target
- SSLA approximates the posterior predictive by refitting the model on self-predicted data: high self-likelihood = low uncertainty
- The approach is deterministic and sampling-free, avoiding expensive MCMC
- ASSLA is an approximate version that skips expensive refitting for computational efficiency
- Experiments on regression tasks (including Bayesian neural networks) show SSLA outperforms classical Laplace approximations in predictive calibration while remaining computationally efficient