Summary

Recent advances in Machine Learning and Artificial Intelligence have result in a great deal of attention and interest in these two areas of Computer Science and Mathematics. Most of these advances and developments have relied in stochastic and probabilistic models, requiring a deep understanding of Probability Theory and how to apply it to each specific situation

In this lecture we will cover in a hands-on and incremental fashion the theoretical foundations of probability theory and recent applications such as Markov Chains, Bayesian Analysis and A/B testing that are commonly used in practical applications in both industry and academia

Program

Basic Definitions and Intuition
- Understand what is a probability
- Calculate the probability of different outcomes
- Generate numbers following a specific probability distribution
- Estimate Population sizes from a sample
Random Walks and Markov Chains
- Simulate a random walk in 1D
- Understand random walks on networks
- Define Markov Chains
- Implement PageRank
Bayesian Statistics
- Understand conditional Probabilities
- Derive Bayes Theorem
- Understand how to Update a Belief
A/B Testing
- Understand Hypothesis Testing
- Measure p-values
- Compare the likelihood of two outcomes.