# Part-A: A brief and selective review of applications of RMT; Part B: Estimation of rectangular random matrices: Applications to high-dimensional biological data (- in person)

Dates: | 4 October 2023 |
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Times: | 14:30 - 14:30 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

Speaker: | Madhuchhanda Bhattacharjee, |

Madhuchhanda Bhattacharjee, Reader in Statistics in the Department of Mathematics, University of Manchester.

Title: Part-A: A brief and selective review of applications of RMT; Part B: Estimation of rectangular random matrices: Applications to high-dimensional biological data

Abstract: Part-A: A brief and selective review of applications of RMT

Random Matrices have been encountered in Statistics, Mathematics, Physics, and other disciplines for nearly a century now. Literature on the theoretic developments in this field has grown substantially since then. With that there have been wide range of applications of such theories. We discuss a few examples involving, the more popular, square random matrices and a few where the matrix is rectangular.

Part B: Estimation of rectangular random matrices: Applications to high-dimensional biological data

It is commonly thought that for a high-dimensional data one of the key objectives would be to study it at a lower dimensional level. Contrary to this, there are many examples in real life where it might be necessary to study it at a latent finer (or further higher dimensional) level.

Consider such an observed (random) vector, say Y. then the task would be to explain Y by means of a collection of random vectors, say presented in a rectangular random matrix X, where X is not observed.

In the two applications we consider here, we have a partially observed (random) binary matrix, say B, and a completely unobserved (random) “signal” matrix, say S, such that X can be viewed as a (Hadamard) product of B and S. Our two examples are from neural coding and genomics respectively, where one of the dimensions of X is in millions or at least hundreds of thousands. The other dimension, in both of our examples, is unknown. It is evident that the problem is ill posed and has many feasible solutions. Our first objective would be to propose a model that captures the desired higher dimensional understanding, which we do by using domain knowledge as far as possible. Next is to obtain estimate of the random components and parameters involved. For which we use an Estimation-Maximization (EM) type algorithm for one and the Bayesian hierarchical modelling for the other example

Venue: G.114 Alan Turing Building Manchester M13 9PL

### Speakers

Madhuchhanda Bhattacharjee

Role: Reader

Organisation: University of Manchester