Ben Jones

Research

Research interests

Research Group

Statistics Group

Research Interests

Machine Learning, Statistics, Probability Theory, Sufficient Dimension Reduction, Hilbertian Data

Thesis

Dimension Reduction for Regression: Theoretical and Methodological Developments

Thesis

Dimension Reduction for Regression: Theoretical and Methodological Developments

In today’s environment where computer processors are powerful and computer memory is cheap, researchers are able to collect and store huge amounts of data. Analysing that data requires sophisticated statistical and computational methods when compared to classic statistical methodology, which was developed in an era where data collection was not so easy and datasets were smaller in magnitude by a large order.

Principal Components Analysis (PCA) is a commonly used method for reducing the dimension in a dataset to a few important features, called principal components. When applied in regression (i.e. prediction), the practice is controversial as the procedure does not make use of the data we have for the variable we are interested in predicting, and only uses the data for the predictor variables. One of my projects is to give probabilistic guarantees that, across a range of datasets, the higher-ranking principal components will be more informative of the response than the lower-ranking ones. Specifically, I explore this tendency for Hilbertian data and for the kernelised version of PCA.

Sufficient dimension reduction (SDR), on the other hand, is a class of methods for feature extraction in regression which requires the extracted components have the same informative power for the response as the original variables. My work in this area currently focuses on nonlinear SDR when some of the predictors are categorical variables.

Supervisors

Publications

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