Discrete Distributions in JAX: A Foundations Guide

Probability distributions are the mathematical foundation of modern deep learning, generative modeling, and reinforcement learning. To write efficient, hardware-accelerated machine learning code, you must understand how to represent these statistical concepts computationally. This course provides a clear, step-by-step introduction to discrete probability distributions using JAX, the powerful framework for high-performance numerical computing. You will transition from theoretical probability concepts to clean, functional JAX code, mastering how to simulate, evaluate, and utilize discrete distributions in your machine learning pipelines. What you'll learn: - Understand foundational probability concepts including probability mass functions (PMFs) and cumulative distribution functions (CDFs) - Configure and manipulate Bernoulli and Binomial distributions for binary and multi-trial classification scenarios - Apply Poisson and Geometric distributions to model count data and event frequencies - Practice pseudo-random number generation (PRNG) using JAX's unique, stateless random key design - Implement efficient sampling techniques and calculate statistical properties like mean, variance, and entropy - Explore modern probabilistic programming patterns and how JAX accelerates gradient calculations for distribution parameters The course begins with essential mathematical terminology and foundational statistics before moving into hands-on JAX implementations. You will read clear explanations, study structured code examples, and practice translating statistical formulas into functional pythonic code. This course is designed for beginners in probabilistic machine learning, data scientists, and developers looking to build a strong theoretical and practical foundation in JAX without complex prerequisites. Start reading today to unlock the power of probabilistic modeling in JAX.