C茅dric Beaulac (Universit茅 du Qu茅bec 脿 Montr茅al)
Title: Neural network architectures for functional data analysis
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Abstract:
Functional data is defined as any random variables that assume values in an infinite precision domain, such as time or space. In applications, this data is usually discretely observed at some regularly or irregularly-spaced points over the domain. In this talk, we discuss ways to adapt modern neural network architectures for the analysis of functional data. To do so, we design new neural network layers in order to process functional data either as input, output or both. First, we propose the functional output layer, which can be used to solve a multitude of function-on-scalar regression problems in a non-linear way. The proposed layer provides a smooth representation of the output and we demonstrate how to regularize such a layer during the network training phase. Second, we propose a concept for functional weights that project functional data to a scalar representation, leading to a novel formulation for a functional input layer. We demonstrate how to combine both of these proposed functional layers to create a functional autoencoder. This model takes as input the data in the form it is usually collected, as discrete points over the domain, and can be used for feature extraction and functional data smoothing. We demonstrate the benefits of the proposed architectures with various experiments on simulated data and real data applications. We conclude with a brief discussion of ongoing work in the design of a functional convolution layer that bridges the gap between the discrete convolution operation and its continuous counterpart.
Speaker
C茅dric Beaulac is a professor of Statistics at the Universit茅 du Qu茅bec 脿 Montr茅al. He completed a postdoctoral fellowship at Simon Fraser University and at the University of Victoria under the supervision of Farouk Nathou, Jiguo Cao and Mirza Faisal Beg and completed a Ph.D. in Statistical Sciences at the University of Toronto under the supervision of Jeffrey S. Rosenthal. His research interests are at the intersection of machine learning and statistics. His research focuses on the development of new models for image analysis and image generation by integrating machine learning models to functional data analysis.
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Meeting ID: 897 6116 5882
Passcode: None
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