syllabus // machine learning and statistics
See the schedule for topics by week and links to slides.
Applied Mathematics III: Machine Learning and Statistics
This is a draft syllabus, subject to change.
Goals: Students completing this course should be able to deploy modern methods in computational inference and feedforward and recurrent neural networks, and develop familiarity with underlying theory and assumptions. The students will be able to design and train efficiently neural networks using supervised, unsupervised and reinforcement learning algorithm.
Topics: information theory, statistical inference, generative models, mean field theory, feedforward and recurrent neural networks, supervised/unsupervised
Calculus, linear algebra, probability, python, as presented in the Fall and Winter courses. The course will include recap of information theory and statistical mechanics.
- Week 1: Recap of probability theory. Statistical inference.
- Week 2-4: Supervised learning. Error backpropagation.
- Weeks 5: Unsupervised learning.
- Weeks 6-8: Stat mech. Hopfield network. Boltzmann machines.
- Weeks 9-10: Backpropagation through time. Reinforcement learning.
Homework and assessment:
Weekly homeworks will consist of a mix of pen-and-paper problems and computational exercises. Computational homework will be turned in as jupyter notebooks, allowing integration of programming, simulation results, and LaTeX into a single document. There will be a final exam, which will be taken in-class, on paper - we will assess understanding of computational methods by asking for written descriptions of algorithms (for instance).
We will not follow a single text, but students who would like additional reading might find these useful:
- Hertz, Krogh & Palmer, Introduction to the theory of neural computation.
- David MacKay, Information Theory, Inference, and Learning Algorithms.
- Mezard, Parisi & Virasoro, Spin glass theory and beyond. Classic statistical mechanics book for the theory of spin glasses and the Hopfield network.
- Abbott & Dayan, Theoretical neuroscience.
- Dalvit et al., Problems on statistical mechanics.
Exhaustive lecture notes for the class are available here.
Inclusion and accessibility
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