Tools

- Source code is hosted here: https://github.com/filipzz/applied-stochastics/
- To run the scripts you can use Jupyter
- or you can run it on Google Colaboratory (and then go: File->Open notebook->GitHub and search for filipzz/applied-stochastics (you need to be signed in)

L1: Motivations

Google Page Rank, Machine learning, Cryptography

L2: Simple Markov chains

- Basics of Markov chainscode

Hypothesis testing and Risk Limiting Audits. . (https://github.com/filipzz/applied-stochastics/blob/master/05_rla/1_rla_intro.ipynb)

Rate of convergence. Coupling. Strong Stationary Times

Markov Chain Monte Carlo. Metropolis algorithm

Linear cryptanalysis tutorial

Problem set 1 (for developing intuition, so informal)

Use 3 examples from: code sample and modify the code.

- How can you get uniform distibution? You can modify initial distribution for each example.
- How can you get uniform distibution? You can modify only one row of transition matrix.
- Every plot seems to be constant from some point. How can you measure distance between the distrinution at time n and its "stationary distribution"?
- How would you define stationary distribution? The process is defined by its transition matrix P but it can have any initial distribution.

Problems

Project

Final grade is based on homeworks see here and a final project.

A final project is a problem that will be assigned to a student individually. You need to (1) solve a problem, (2) write down the solution e.g., in a Jupyter notebook, describing the steps leading to the solution, (3) present your solution during a video call. You may be asked additional questions related to (but not limited) to your project.
The list of projects will be announced soon. You will be given 2 weeks to submit your solution.