Project

The goal of the project is investigating a specific application of mathematics to data science.

Logistics

The project can be carried out in groups of two. Submitting a project used for another course is not allowed.

Proposal

The proposal must be one page long. It should include the following information (each point will be evaluated separately):

• A description of a specific question that you want to explore. The question can be experimental, i.e. whether a certain technique works for a particular application, or theoretical, whether a certain theoretical tool can be used to analyze a data-analysis method. Be as concrete as you can.

• Context for your topic, including relevant bibliographic references.

• An outline of what you plan to do and a precise justification of how it relates to the question that you are studying. For experimental projects, this includes a description of the dataset you plan to use.

Project report

The project should be written in Latex and be no more than 5 pages (not including references).

It should include the following sections, which will be evaluated separately:

• Introduction: What question have you been studying? Why should anyone care?

• State of the art: Provide context, with relevant bibliographic references.

• Methodology: How did you tackle the question? How did you modify existing methods? What datasets did you use? What theoretical tools did you apply? If you deviated from your original plan, explain why.

• Results: What results did you obtain? Do they make sense? Provide a thorough analysis. Negative results are completely fine (they can be very valuable!).

• Discussion: What did you find out? Do the results suggest any other interesting questions to explore?

Presentation

Projects will be presented in class. Presentations will last 5 minutes (strict limit).

Possible topics

You may find some topics of interest among the talks of the Math and Data seminar. In addition, below is a list of papers on topics relevant to the course.

• Random design analysis of ridge regression

• High-dimensional covariance estimation

• Probabilistic algorithms for constructing approximate matrix decompositions

• Compressed sensing in MRI

• Scattering transform

• Finite rate of innovation

• Matrix completion using alternating minimization

• Graphical lasso

• Mixed regression

• Super-resolution microscopy

• Best subset selection for sparse regression

• Phase retrieval via Wirtinger flow

• Transform Invariant Low-rank Textures

• Video magnification

• Latent variable graphical model selection via convex optimization

• Sparse fast Fourier transform

• Analysis of gradient descent for randomized nonconvex problems

• Curvelets

Research projects

We will be happy to suggest more concrete research-oriented applied or theoretical topics related to the areas below. If you are interested in one of them, book an appointment to discuss it with us in person during the first four weeks of class. Please read the relevant references carefully before the meeting.

• Super-resolution of point sources

• Magnetic-resonance fingerprinting

• Machine learning for compressed sensing

• Learning-based image restoration