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Correlations in tabular data [Remote]


Term:

Fall

Department:

18: Mathematics

Faculty Supervisor:

Ankur Moitra

Faculty email:

moitra@mit.edu

Apply by:

09/05/2020

Contact:

Cole Franks: franks@mit.edu

Project Description

The matrix normal model is a statistical model used for tables of data, such as spatiotemporal data from brain magnetoencephalograms or windspeed data from multiple sites. The model is fairly well understood from a statistical and computational point of view. However, such models have limited expressive power because they assume the correlations between entries are separable, i.e., that they are the product of a row and column correlation. The “sum of Kronecker product model” is an extension which adds additional flexibility to remedy this issue. Unfortunately, it is less well understood. There are some estimators for this model, but they do not have performance guarantees akin to those in the matrix normal model. In particular, the performance of the maximum likelihood estimator is not known, and there is no efficient algorithm known to compute it. The goal of the project is to remedy the lack of understanding of the sum of Kronecker product model, including the development of and evaluation of estimators as well as efficient algorithms to compute them. The project will also involve applying the Kronecker product model to real world data to make predictions.

Pre-requisites

There are no firm prerequisites, but background in linear algebra and some experience programming in (or willingness to learn) languages with statistical packages such as R or python would be helpful. First year students are welcome.