# Geometric Variational Inference

@article{Frank2021GeometricVI, title={Geometric Variational Inference}, author={Philipp Frank and Reimar H. Leike and Torsten A. Ensslin}, journal={Entropy}, year={2021}, volume={23} }

Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize the geometric properties of continuous probability distributions to increase their efficiency have been proposed, VI methods rarely use the geometry. This…

## 8 Citations

### Geometric Variational Inference and Its Application to Bayesian Imaging

- 2022

Computer Science, Mathematics

MaxEnt 2022

GeoVI has recently been introduced as an accurate Variational Inference technique for nonlinear unimodal probability distributions that enables its application to real-world astrophysical imaging problems in millions of dimensions.

### Information Field Theory and Artificial Intelligence

- 2022

Computer Science

Entropy

This paper reformulated the process of inference in IFT in terms of GNN training, suggesting that IFT is well suited to address many problems in AI and ML research and application.

### Butterfly Transforms for Efficient Representation of Spatially Variant Point Spread Functions in Bayesian Imaging

- 2023

Computer Science

Entropy

This work combines butterfly transforms in several ways into butterfly networks, compares the different architectures with respect to their performance and identifies a representation that is suitable for the efficient representation of a synthetic spatially variant point spread function up to a 1% error.

### Reconstructing the universe with variational self-boosted sampling

- 2023

Computer Science

Journal of Cosmology and Astroparticle Physics

A hybrid scheme, called variational self-boosted sampling (VBS) is developed to mitigate the drawbacks of both these algorithms by learning a variational approximation for the proposal distribution of Monte Carlo sampling and combine it with HMC.

### Efficient Representations of Spatially Variant Point Spread Functions with Butterfly Transforms in Bayesian Imaging Algorithms

- 2022

Computer Science

MaxEnt 2022

This work discusses the application of butterﬂy transforms, which are linear neural network structures whose sizes scale subquadratically with the number of data points whose shapes are inspired by the structure of the Cooley–Tukey Fast Fourier transform.

### Sparse Kernel Gaussian Processes through Iterative Charted Refinement (ICR)

- 2022

Computer Science

ArXiv

A new, generative method named Iterative Charted Reﬁnement (ICR) is presented to model GPs on nearly arbitrarily spaced points in O ( N ) time for decaying kernels without nested optimizations and its accuracy is comparable to state-of-the-art GP methods.

### Probabilistic Autoencoder Using Fisher Information

- 2021

Computer Science

Entropy

In this work, an extension to the autoencoder architecture is introduced, the FisherNet, which has advantages from a theoretical point of view as it provides a direct uncertainty quantification derived from the model and also accounts for uncertainty cross-correlations.

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