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Grades
Grades
Final project, 50%: The final project should involve reading one or more research papers related to the course, identifying an open research problem, and making progress towards resolving the problem. Around the middle of the semester, a project proposal consisting of one page describing the problem and all references will be due.
Homework, 40%: There will be 3 homework sets throughout the semester. You are encouraged to work together with others on the problems, but you have to write down the solutions on your own.
Scribing, 5%: Part of the grade will consist of typing up the lecture notes of two or three lectures so that they can be posted on the course website. Here is the latex template for these.
Participation, 5%: Since student-teacher interaction is much harder in an online class, the participants are strongly encouraged to ask and answer questions and bring up ideas.
Tentative List of Topics
Tentative List of Topics
Course Overview and Motivating Examples
CP decomposition - definition and properties
CP decomposition - properties continued
CP decomposition - properties continued
Examples of CP decomposition - latent variable models, parallel factors
Examples of CP decomposition - blind source separation, ICA, the method of moments
Examples of CP decomposition - Gaussian mixture models, neural networks
Algorithms for CP decomposition - alternating least squares
Algorithms for CP decomposition - Jennrich’s algorithm, tensor power method and eigenvectors of tensors
Eigenvectors of tensors, the tensor power method, orthogonally decomposable tensors
Overcomplete symmetric CP decompositions - the subspace power method
Atomic norm minimization and the tensor nuclear norm
Tensor network decompositions - motivation from quantum physics
Tensor network decompositions - Tucker, MPS (aka Tensor Train), PEPS, MERA
Graphical models - undirected, Markov properties
Correspondence between tensor networks and graphical models
Nonnegative matrix decompositions - nonnegative rank, properties, examples
Nonnegative matrix decompositions - alternating least squares, EM, other algorithms
Nonnegative matrix decompositions - geometric description
Nonnegative tensor decompositions - properties, examples, algorithms
Total positivity - properties and relationship to nonnegative tensor decomposition
Graphical models - directed acyclic, Markov properties, equivalence classes
Linear structural equation models - Gaussian vs. non-Gaussian; learning non-Gaussian LSEMs via ICA
Presentations
Presentations
Presentations
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