Early cancer detection can change lives. If cancer can be detected early in its development, while a patient is still asymptomatic, it is easier and less expensive to treat. Volatile organic compounds, as measured by field asymmetric ion mobility spectrometry (FAIMS), are a novel class of biomarkers which have shown promise as a low-cost early screening test for a range of cancers. However, FAIMS data is high-dimensional, difficult to interpret, and can be subject to a range of subtle data quality problems. Additionally, in the current literature many researchers use linear methods for analysing FAIMS data. We believe improved results could be achieved by applying modern machine learning techniques to the problem.

In this thesis, we investigate using modern machine learning techniques and best practices for FAIMS analysis, and develop corresponding software. We found that FAIMS has a moderate ability to detect cancer in an at-risk population, and that FAIMS could be used for the pre-symptomatic detection of other diseases with excellent results, achieving an AUC of 0.91 for the pre-symptomatic detection of anastomotic leakage after surgical resection to treat cancer.

We present a novel Bayesian dimensionality reduction technique, the structured Gaussian process latent variable model (SGPLVM), which extends GPLVM to exploit structured correlations between variables, as are seen in FAIMS data. We also present a stochastic optimization algorithm and a number of extensions based on stochastic gradient descent variants. We explore the properties of SGPLVM, which we found to outperform GPLVM at recovering a latent representation of data which meet the model assumptions. We also demonstrate SGPLVM’s robustness to partially observed data.

Finally, we present software packages for GPLVM, SGPLVM, and GP regression with a novel method of specifying and automatically selecting compound kernel functions.