Sprecher
Beschreibung
Model comparison in high-dimensional Bayesian inference remains computationally challenging due to the intractability of the marginal likelihood (evidence). Variational inference offers an attractive alternative by providing a tractable lower bound to the evidence, the Evidence Lower Bound (ELBO), which can be optimized and estimated efficiently even in very large parameter spaces.
In this talk, I derive the Evidence Lower Bound (ELBO) for Metric Gaussian Variational Inference (MGVI) and its geometric extension geoVI, as implemented in the information field theory framework and the NIFTy library. The method approximates the posterior with a Gaussian in latent space whose covariance is determined by the local Fisher metric, enabling scalable Bayesian inference in extremely high-dimensional problems. I show how the ELBO can be estimated efficiently using posterior samples and analytic expectations, providing a practical tool for model comparison in high-dimensional settings.
Finally, I illustrate applications ranging from astrophysical inverse problems (e.g. imaging and lensing reconstruction) to causal inference in complex probabilistic models, where scalable evidence estimation is crucial for comparing competing generative hypotheses.