# CS 761 Project: Spectral Methods for Latent Variable Models

One of my courses this past semester was CS761, “Advanced Machine Learning”. The idea of the course was to present some of the mathematical and statistical theory underlying machine learning. It was taught by Dr. Xiaojin (Jerry) Zhu.

One of the things we had to do was a course project. Since CS761 was a
theory course, the project needed to be of a theoretical nature. Rather than
merely *applying* machine learning to some problem, we were expected to peruse the
theoretical machine learning literature and try making some contribution to the
research.

Three weeks before the semester ended—after much procrastination—I
finally buckled down and got to work. I teamed up with
Parikshit Sharma; we had
both, independently, stumbled on the topic of *spectral methods* for
latent variable models, and decided to pursue possibilities in that area.

The main idea is that we can sometimes learn the parameters of
a Bayesian network by computing a *spectral decomposition*
of certain *empirical moment* tensors obtained from the data.
Parikshit and I tried to do this for new kinds of Bayesian networks.
We were not ultimately successful; however, the project was still
an instructive exercise, and I feel like I got pretty familiar with
the subject matter.

I felt kind of proud of our work. And it got a decent score. So I’ve decided to post it here.

Here’s a link to our completed project.

\( \blacksquare\)