Abstract

Neural Processes (NPs) are a class of regression models that learn a map from a set of input-output pairs to a distribution over functions. NPs are computationally tractable and provide a number of benefits over traditional nonlinear regression models. Despite these benefits, there are two main domains where NPs fail. This thesis is focused on presenting extensions of the Neural Process to these two areas. The first of these is the extension of Neural Processes graph and network data which we call Graph Neural Processes (GNP). A Graph Neural Process is defined as a Neural Process that operates on graph data. It takes spectral information from the graph Laplacian as inputs and then outputs a distribution over values. We demonstrate Graph Neural Processes in edge value imputation and discuss benefits and drawbacks of the method for other application areas. The second extension of Neural Processes comes in the fundamental training mechanism. NPs are traditionally trained using maximum likelihood, a probabilistic technique. We show that there are desirable classes of problems where NPs fail to learn. We also show that this drawback is solved by using approximations of the Wasserstein distance. We give experimental justification for our method and demonstrate its performance. These Wasserstein Neural Processes (WNPs) maintain the benefits of traditional NPs while being able to approximate new classes of function mappings.

Degree

MS

College and Department

Physical and Mathematical Sciences

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2020-05-18

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd11146

Keywords

optimal transport, neural processes, graph laplacian, non-linear regression

Language

English

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