Models of input dependent covariances between multiple responses
Andrew Wilson, doctoral candidate at University of Cambridge, Cambridge, U.K
Accounting for input dependent covariances between multiple responses can greatly improve statistical inferences. For example, if we wish to predict the expression level of a gene (response) at a particular time (input), it helps to consider the expression levels of correlated genes, and how these correlations depend on time. I will discuss three new models I have introduced for input dependent covariances: the Gaussian process regression network (Wilson et. al, 2012), generalised Wishart processes (Wilson and Ghahramani 2011), and copula processes (Wilson and Ghahramani, 2010). I will describe the connections between these models, and the high level ideas that can be applied to regression and classification in general, to improve predictive performance. I apply these models to problems in econometrics, geostatistics, and large-scale gene expression. The models prove to be scalable with greatly enhanced predictive performance over alternatives: the extra structure being learned is an important part of a wide range of real data.