A0661
Title: Multi-object regression: A linear framework using partial least squares
Authors: Robert Cantwell - University of Cambridge (United Kingdom) [presenting]
John Aston - University of Cambridge (United Kingdom)
Abstract: Modern statistical problems regularly involve data collected with more structure than simple scalars, for example, functional or image data. Accompanying these more exotic data types has been the generalization of statistical methods to analyze data that take values in almost arbitrary Hilbert spaces. However, to date, nearly all regression approaches treat a single, often specific, data type within a single Hilbert space. A linear framework for statistical analysis of data objects naturally represented in a variety of Hilbert spaces, using latent space projections, is considered. In particular, the method of partial least squares are generalized, and significance testing of different data objects is discussed to conduct model selection, a challenge often raised in applications where complicated data objects can be costly to collect and practitioners use statistical modeling to understand the relative importance of each object.
