Lilly Tech Systems
Probability for AI
Understand the probabilistic foundations of machine learning. From distributions and Bayes theorem to random variables and maximum likelihood estimation, learn how uncertainty is modeled and managed in AI systems.
What You'll Learn
By the end of this course, you'll understand how probability theory underpins all of machine learning.
Distributions
Master Gaussian, Bernoulli, Poisson, and other distributions that model real-world data and noise in ML.
Bayes Theorem
Learn Bayesian reasoning — updating beliefs with evidence — the foundation of spam filters, medical diagnosis, and more.
Random Variables
Understand expectations, variance, covariance, and how random variables model uncertainty in predictions.
MLE & MAP
Learn Maximum Likelihood and Maximum A Posteriori estimation — how models learn parameters from data.
Course Lessons
Follow the lessons in order or jump to any topic you need.
1. Introduction
Why probability matters for AI. Overview of probabilistic thinking and how ML models handle uncertainty.
2. Distributions
Probability distributions: Gaussian, Bernoulli, Uniform, Poisson, and their roles in modeling data and noise.
3. Bayes Theorem
Bayesian inference, prior and posterior distributions, conjugate priors, and applications in classification.
4. Random Variables
Expectations, variance, covariance, joint and conditional distributions, and the law of large numbers.
5. MLE / MAP
Maximum Likelihood Estimation, Maximum A Posteriori, regularization as priors, and parameter learning.
6. Best Practices
Probabilistic programming tools, common mistakes, numerical stability with probabilities, and practical tips.
Prerequisites
What you need before starting this course.
- Basic understanding of algebra
- Familiarity with calculus concepts (integrals, derivatives)
- Python with NumPy and SciPy installed
- Recommended: Complete the Calculus for ML course first