Bayesian Importance Sampling (and Normalizing Flows)

Supervisor: Scott Schwartz

Yichen Ji, Eric Jiang, Haining Tan, Ryan Wang

Current Experiments:

Yichen:

• Conditional Density/Regression

Eric:

• learning rate experiments with swag

Haining:

• NF with SWAG on one moon data (Karpathy/nflows); SWAG vs gold standard on MVN

• Grid Heatmap

Ryan:

• Importance sampling to improve SWAG posterior uncertainty approximations of non-Gaussian posterior over parameters of a normalizing flow
  • Current issues: IS weighting only very minutely improves uncertainty characterization in log densities (using KS-distance as a metric)
• Linear regression, non-linear regression, variational regression?
  • Current issues: None atm; IS mean estimator uncertainty almost identitical with SWAG mean estimator; How to quantify uncertainty?
• Characterizing uncertainty in the two moons dataset
  • Current issues: No ground truth to compare SWAG and IS weighted
• MNIST SWAG + IS
  • Current issues: None atm; IS actually did end up improving accuracy :O (only after exponentiating the loss); How to quantify uncertainty here?