Amir Bashir

Doctor of Philosophy, (Statistics)
Study Completed: 2020
College of Sciences


Thesis Title
Sparse Summaries of Complex Covariance Structures

Within statistics, studying too many variables to find meaningful relationships among them is time consuming and expensive. Reducing dimensions (the number of variables) has been widely researched. A covariance matrix Σ tells us how two variables move together. An inverse covariance matrix (Σ)^(-1) is an inverse of the covariance matrix Σ that explains the conditional independence between two variables in relation to other variables and a matrix that has most of its elements equal to zero is called a sparse matrix. The zero elements in a sparse matrix reduce the number of variables for its potential interpretability. Setting some elements of the inverse covariance matrix to exact zeros has been an active area of research. Mr Bashir worked on proposing approaches that reduce the number of variables to make interpretation easier. These proposed approaches worked well by producing new and meaningful relationships for metabolites (a substance created during metabolism), food (distinguishing between healthy and junk food), and fish (correct allocation of fish in the North and South Islands of Aotearoa New Zealand) data.

Dr Adam Smith
Distinguished Professor Marti Anderson
Dr Beatrix Jones