| # Stochastic Processes | |
| ## Assignments | |
| - [Stationary Stochastic Process](Assignments/HW2-Stationary-Stochastic-Process.pdf) | |
| - [LTI & Ergodicity](Assignments/HW3-LTI-Ergodicity.pdf) | |
| - [Point Process & Gaussian Process](Assignments/HW4-Point-Process-Gaussian-Process.pdf) | |
| - [Estimation Theory](Assignments/HW5-Estimation-Theory.pdf) | |
| - [Markov Chain](Assignments/HW6-Markov-Chain.pdf) | |
| ## Implementations of Stochastic Processes | |
| [Link to notebook](SP-Code/visualization.ipynb) | |
| This notebook includes implementations to generate stochastic processes: | |
| Example: | |
| - A very pretty gaussian distribution: | |
| <p align="center"> | |
| <img src="SP-Code/sample-plots/gaussian.png" width="500"> | |
| </p> | |
| - Gaussian process with RBF kernel: | |
| <p align="center"> | |
| <img src="SP-Code/sample-plots/g-rbf.png" width="500" > | |
| </p> | |
| - Brownian motion: | |
| <p align="center"> | |
| <img src="SP-Code/sample-plots/g-brownian.png" width="500"> | |
| </p> | |
| - Poisson process: | |
| <p align="center"> | |
| <img src="SP-Code/sample-plots/point.png" width="500" > | |
| </p> | |
| - Hawkes process: | |
| <p align="center"> | |
| <img src="SP-Code/sample-plots/hawkes.png" width="500"> | |
| </p> | |
| ## Markov Chain | |
| ### Part 1 | |
| [Link to notebook](Project/Markov-Chain/hmm-final-part1.ipynb) | |
| "Baum-Welch" algorithm is implemented to train a Hidden Markov Model parameters from | |
| sequences of observed data. | |
| ### Part 2 | |
| [Link to notebook](Project/Markov-Chain/hmm-final-part2.ipynb) | |
| Hidden Markov Model parameters is trained using counting from sequence of observed | |
| data and states. | |
| "Viterbi" algorithm is implemented to find the most probable sequence of states from | |
| observations | |
| ## Gibbs Sampling | |
| [Link to notebook](Project/Gibbs-Sampling/gibbs.ipynb) | |
| Implemented Gibbs sampling to denoise an image. | |
| Example: | |
| <p align="center"> | |
| <img src="Gibbs-Sampling/initial_img.png" width="300" title="noisy image"> | |
| <img src="Gibbs-Sampling/new_image.png" width="300" title="denoised image"> | |
| </p> | |
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