FLBI

Motivation

‍Computational Bayesian inference of parameters or summary statistics is complicated in high-dimensional parameter- or data-spaces. In that case, conventional methods, such as approximate Bayesian computation or sequential Monte Carlo versions thereof, fail to infer correct posterior distributions for a measurement which necessitates the development of efficient methods for these scenarios. A recent approach utilizes deep learning to approximate posterior distributions with neural networks, however, these approaches still do not scale well to high-dimensional data, such as time series data of the magnetic field of solar cycle.

Proposed Approach / Solution

‍For this project, we develop novel methods for high-dimensional approximate inference, both in parameter- and data-space, utilizing recent developments in neural density estimation and dimensionality reduction. We a) propose several theoretical approaches to solve high-dimensional approximate inference and b) develop high-quality Python libraries implementing these algorithms for applied researchers to use.
One of our recent methods, which we call surjective sequential neural likelihood estimation, uses dimensionality-reducing normalizing flows to more efficiently estimate probability densities which allows for increased accuracy in inferring posterior distributions. On several experimental benchmarks our method outperforms baseline methods while being more computationally efficient w.r.t. the number of trainable parameters and computational speed (Figures 1 and 2).

Impact

‍We expect of our methods to be of great value for Bayesian inference, since current methodology is not suitable for high-dimensional time series data, for instance time series observations from solar dynamos or other ODE/PDE-models.