Computational Probability and Inference

 with  George H. Chen, Polina Golland, Gregory W. Wornell and Lizhong Zheng

Probability and inference are used everywhere. For example, they help us figure out which of your emails are spam, what results to show you when you search on Google, how a self-driving car should navigate its environment, or even how a computer can beat the best Jeopardy and Go players! What do all of these examples have in common? They are all situations in which a computer program can carry out inferences in the face of uncertainty at a speed and accuracy that far exceed what we could do in our heads or on a piece of paper.

In this data analysis and computer programming course, you will learn the principles of probability and inference. We will put these mathematical concepts to work in code that solves problems people care about. You will learn about different data structures for storing probability distributions, such as probabilistic graphical models, and build efficient algorithms for reasoning with these data structures.

By the end of this course, you will know how to model real-world problems with probability, and how to use the resulting models for inference.

You don’t need to have prior experience in either probability or inference, but you should be comfortable with basic Python programming and calculus.


“I love that you can do so much with the material, from programming a robot to move in an unfamiliar environment, to segmenting foreground/background of an image, to classifying tweets on Twitter—all homework examples taken from the class!” – Previous Student in the residential version of this new online course.


Week 1: Introduction to probability and computation
A first look at basic discrete probability, how to interpret it, what probability spaces and random variables are, and how to code these up and do basic simulations and visualizations.

Week 2: Incorporating observations
Incorporating observations using jointly distributed random variables and using events. Three classic probability puzzles are presented to help elucidate how to interpret probability: Simpson’s paradox, Monty Hall, boy or girl paradox.

Week 3: Introduction to inference, and to structure in distributions
The product rule and inference with Bayes' theorem. Independence-A structure in distributions. Measures of randomness: entropy and information divergence. Mini-project: movie recommendations.

Week 4: Expectations, and driving to infinity in modeling uncertainty
Expected values of random variables. Classic puzzle: the two envelope problem. Probability spaces and random variables that take on a countably infinite number of values and inference with these random variables.

Week 5: Efficient representations of probability distributions on a computer
Introduction to undirected graphical models as a data structure for representing probability distributions and the benefits/drawbacks of these graphical models. Incorporating observations with graphical models.

Week 6: Inference with graphical models, part I
Computing marginal distributions with graphical models in undirected graphical models including hidden Markov models. Mini-project: robot localization, part I.

Week 7: Inference with graphical models, part II
Computing most probable configurations with graphical models including hidden Markov models. Mini-project: robot localization, part II.

Week 8: Introduction to learning probability distributions
Learning an underlying unknown probability distribution from observations using maximum likelihood. Three examples: estimating the bias of a coin, the German tank problem, and email spam detection.

Week 9: Parameter estimation in graphical models
Given the graph structure of an undirected graphical model, we examine how to estimate all the tables associated with the graphical model.

Week 10: Model selection with information theory
Learning both the graph structure and the tables of an undirected graphical model with the help of information theory. Mutual information of random variables.

Week 11: Final project part I
Mystery project

Week 12: Final project part II
Mystery project, cont’d

3 Student
Cost Free Online Course
Pace Self Paced
Provider edX
Language English
Hours 4-6 hours a week
Calendar 14 weeks long
+ Add to My Courses
Learn Data Analysis

Learn to become a Data Analyst. Job offer guaranteed or get a full refund.

75+ Hour Free Coding Course

Get started with Ruby & JS curriculum online with all-day instructor help.

FAQ View All
What are MOOCs?
MOOCs stand for Massive Open Online Courses. These are free online courses from universities around the world (eg. Stanford Harvard MIT) offered to anyone with an internet connection.
How do I register?
To register for a course, click on "Go to Class" button on the course page. This will take you to the providers website where you can register for the course.
How do these MOOCs or free online courses work?
MOOCs are designed for an online audience, teaching primarily through short (5-20 min.) pre recorded video lectures, that you watch on weekly schedule when convenient for you.  They also have student discussion forums, homework/assignments, and online quizzes or exams.

3 reviews

Write a review
4 months ago
profile picture
Anonymous is taking this course right now.
This is an excellent course with very clear lecture videos and comprehensive class notes. The instructors have a high degree of mastery of the subject and are able to communicate clearly and concisely. Numerous, interesting problem sets range from straightforward to challenging. This is a high-quality MOOC. Looking forward to the second part of the course -- 6.008.2x -- when it becomes available.
Was this review helpful to you? YES | NO
4 months ago
profile picture
Anonymous partially completed this course.
The course is super-cool. The subject is hard but the instructors have a deep knowledge of the subject. Teaching style is great and it combines a great accuracy with clear examples. I would definitely recommend it to anyone who is interested in learning Probability.
Was this review helpful to you? YES | NO
5 months ago
Brian Page partially completed this course.
Was this review helpful to you? YES | NO

Write a review

How would you rate this course? *
How much of the course did you finish? *
Create Review