Abstract:
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The use of functional variables as predictors is an important tool in functional data analysis. The classical approach involves functional linear regression where one uses standard inner product to design linear predictors for scalar response variables. We are focused on situations where the functional data contains certain phase variability that can adversely affect the prediction performance. This situation arises, for example, when using bio-signals for predicting a patient's disease level, and where measurements across subjects are seldom registered. One solution is to use some functional alignment tool as a pre-processing step and then perform functional linear regression. Our solution is to perform elastic functional regression, where the alignment is performed at the same time as estimation of the regression coefficients. This is based on choosing the Fisher-Rao inner product, rather than the L2- inner product, to exploit its invariance properties. Estimated coefficients are then used to predict the response variable for future predictor values. We demonstrate these techniques using a number of datasets involving gait signals and certain cognition diseases such as Alzheimers
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