CS 361 - Probability & Statistics for Computer Science

This is the primary probability and statistics class required for standalone CS majors, consisting of lectures, homeworks, exams, and a final project. Some CS + X majors allow for other prob/stat classes to take its place, but encourage CS 361. Math + CS and Stat + CS also allow STAT 400, the more classical probability and stats class offered at Illinois. If you are a standalone CS major pursuing a statistics minor, you may be allowed to take STAT400 in place of CS361 to fulfill the probability/statistics requirement for both the statistic minor and CS major.

The final project has historically involving proving properties and implementing parts of a neural net and its training.

In general, the department’s policy on interchanging CS361 and STAT400 as been inconsistent over the years. Please reach out to your advisor for the most up-to-date information.

Topics Covered

• Location and Scale Parameters
• Correlation
• Probability (Joint/Conditional Probability, Random Variables, Bayes’ Rule, Expectation, Variance)
• Law of Large numbers
• Probability Distributions (Bernoulli, Binominal, Normal, Geometric, Poisson, Exponential)
• Sample Statistics (Standard Deviation Unbiased, Standard Error, t-distribution, Confidence Interval, Bootstrap, p-test)
• MLE and MAP
• Bayesian Posterior
• Covariance and Covariance Matrix
• Classification (Decision Tree, Random Forest, SVM, Naive Bayes, Hierarchical Clustering, K-Means, Spectral Clustering)
• Markov Chains

Resources

Online office hours as hosted as specified in the syllabus. Some of the more basic content of this course largely overlaps with AP Statistics or IB Statistics.

Developer’s Commentary

The content covered in this class is very similar to STAT 400. STAT400 has a more rigorous treatment of the more pure probability and statistics content, while CS361 forgoes some rigour in exchange for some machine learning/deep learning content. At times, some topics can seem quite light on coverage as a result. There is a good amount of linear algebra used, especially in the latter half of the course. In fact, there is a little bit of content overlap, as both MATH 257and CS361 teach content like Markov chains.

Many students may find this course difficult as in general, probability and statistics is not a very intuitive field of mathematics. There are many great resources from 3Blue1Brown, StatQuest, Visually Explained The Organic Chemistry Tutor (among others).

A handful of years back, this kind person released their notes on this course. They’re quite good. Thanks anon!

As painful as probability and statistics can be, the content is foundational for a wide variety of topics, such as:

• Machine Learning
• Cryptography
• Theoretical Computer Science

If you want to investigate further into the topics above, then it’s especially important for you to have a solid understanding of the material taught in this course.

Related Courses

• STAT 400 - Statistics and Probability I: If you want a more rigorous coverage of the probability/stats material in this course, take this course.
• CS 410 - Statistics and Probability II: If you enjoyed the probability/stats material and want to learn more, take STAT410.
• CS 446 - Machine Learning: If you want to learn more about the application of probability in machine learning, take CS 446, which contains material regarding ML theory in more classical machine learning methods.
• CS 473 - Algorithms: If you want to learn more about the application of probability in algorithms, take CS 473, which covers a lot of content regarding randomized algorithms and approximation algorithms, which can involve randomized algorithms. Here are some of Professor Jeff Erickson’s notes said topic: [1] and [2].
• CS 407 - CryptographyIf you want to learn more cryptography, take this course.