https://github.com/edserranoc/inverse_problems_course
Inverse Problems Course.
https://github.com/edserranoc/inverse_problems_course
bayesian-inference mcmc-sampling regularization-methods variational-inference
Last synced: 10 months ago
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Inverse Problems Course.
- Host: GitHub
- URL: https://github.com/edserranoc/inverse_problems_course
- Owner: edserranoc
- License: gpl-3.0
- Created: 2025-03-21T23:39:16.000Z (10 months ago)
- Default Branch: main
- Last Pushed: 2025-03-22T01:14:42.000Z (10 months ago)
- Last Synced: 2025-03-22T01:21:51.513Z (10 months ago)
- Topics: bayesian-inference, mcmc-sampling, regularization-methods, variational-inference
- Language: Jupyter Notebook
- Homepage:
- Size: 2.73 MB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Inverse-Problems
This repository contains the assignments and final project for the "Inverse Problems" taught by Dr. [Marcos Aurelio Capistrán Ocampo](https://salud.conahcyt.mx/coronavirus/investigacion/investigadores/maco.html) at CIMAT (Centro de Investigación en Matemáticas), developed in the Python programming language. The code is written in Spanish.
## Final Project
### Review of Stein Variational Gradient Descend Method
Reviewed PyTorch implementations of Stein variational methods, analyzed algorithms, and conducted sampling simulations. The code is based on the notebook provided in [[4](https://github.com/activatedgeek/svgd)], with some modifications.
**Mixture of Six Gaussians**
**Banana-shaped distribution:**
## Assigments
### Metropolis-Hastings Algorithm
### Landweber and Kaczmarz Method
### TSVD and Tikhonov Regularizations
## Reference
1. Kaipio, J., & Somersalo, E. (2006). Statistical and computational inverse problems (Vol. 160). Springer Science & Business Media.
2. Vogel, C. R. (2002). Computational methods for inverse problems. Society for Industrial and Applied Mathematics.
3. Liu, Q., & Wang, D. (2016). Stein variational gradient descent: A general purpose bayesian inference algorithm. Advances in neural information processing systems, 29.
4. PyTorch implementation of Stein Variational Gradient Descent. https://github.com/activatedgeek/svgd
5. Anzengruber, S. W., & Ramlau, R. (2009). Morozov's discrepancy principle for Tikhonov-type functionals with nonlinear operators. Inverse Problems, 26(2), 025001.
## License
This project is licensed under the GPL-3.0 license. See the LICENSE file for details.