https://github.com/ulizesr/ift

Repo to hold my research on Information Field Theory code
https://github.com/ulizesr/ift

bayesian-inference information-theory python

Last synced: 15 days ago
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Repo to hold my research on Information Field Theory code

• Host: GitHub
• URL: https://github.com/ulizesr/ift
• Owner: UlizesR
• Created: 2024-09-24T01:34:49.000Z (4 months ago)
• Default Branch: main
• Last Pushed: 2024-12-02T03:54:56.000Z (about 2 months ago)
• Last Synced: 2024-12-02T04:30:58.708Z (about 2 months ago)
• Topics: bayesian-inference, information-theory, python
• Homepage:
• Size: 2.1 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Information Field Theory Research Repository

Welcome to the Information Field Theory (IFT) Research Repository. This repository contains our work exploring alternative methods for inferring the moments of non-Gaussian continuous random fields using techniques derived from Information Field Theory.

## Overview

In various fields like physics, astronomy, and engineering, many problems involve continuous random fields that exhibit spatial and temporal variations. While Gaussian random fields are well-understood and can be analyzed by inferring their mean and variance, non-Gaussian fields present significant challenges due to the computational complexity involved in traditional inference methods.

This project focuses on:

- **Alternative Inference Methods**: Developing and applying diagrammatic expansion techniques from Information Field Theory to compute the moments of non-Gaussian fields more efficiently.

- **Bayesian Inference Challenges**: Addressing the difficulties in calculating the evidence term in Bayes' theorem for continuous, non-parameterized fields.

- **Reducing Computational Complexity**: Providing methods that are less computationally intensive than traditional techniques like Markov Chain Monte Carlo (MCMC), especially as the number of parameters increases.

- **Application to Practical Problems**: Extending these techniques to practical cases such as linear regression models and exploring their effectiveness.

## Key Components

- **Diagrammatic Expansion Technique**: Utilizing a method that represents posterior moments as an infinite sum of diagrams, each corresponding to specific equations based on their structure.

- **Hamiltonian Formalism**: Adopting concepts from statistical mechanics, such as the Gibbs measure and partition function, to reformulate the inference problem.

- **Perturbatively Non-Gaussian Fields**: Focusing on fields that deviate slightly from Gaussian distributions, making them suitable for perturbative methods.

## Future Work

- **Higher-Dimensional Applications**: Extending the techniques to fields defined over continuous, higher-dimensional spaces.

- **Basis Functions**: Investigating the use of basis functions to improve computational efficiency and simplify calculations.

- **Broader Distribution Testing**: Exploring the applicability of these methods to other named distributions beyond the Gaussian case.

## Conclusion

This repository aims to provide valuable insights and tools for researchers dealing with the complexities of non-Gaussian continuous random fields. By leveraging Information Field Theory and diagrammatic expansions, we strive to develop more efficient and scalable inference methods that overcome the limitations of traditional computational techniques.