Dimensionality reduction for survival data via the Gaussian process latent variable model

The analysis of high dimensional survival data is challenging, primarily due to the problem of overfitting which occurs when spurious relationships are inferred from data that subsequently fail to exist in test data. Here we propose a novel method of extracting a low dimensional rep- resentation of survival data by combining the popular Gaussian Process Latent Variable Model (GPLVM) with a Weibull Proportional Hazards Model (WPHM). The model offers a flexible non-linear probabilistic method of detecting and extracting any intrinsic lower dimensional structure from high dimensional data. In addition we can simultaneously combine information from multiple data sources. We present results from several simulation studies that illustrate a reduction in overfitting and an increase in predictive performance, as well as successful detection of intrinsic dimensionality.