Nonlinear Functional Modeling Using Neural Networks
| Autor: | Aniruddha Rajendra Rao, Matthew Reimherr |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
Statistics and Probability
Methodology (stat.ME) FOS: Computer and information sciences Computer Science - Machine Learning Artificial Intelligence (cs.AI) Computer Science - Artificial Intelligence Statistics - Machine Learning Discrete Mathematics and Combinatorics Machine Learning (stat.ML) Statistics Probability and Uncertainty Statistics - Methodology Machine Learning (cs.LG) |
| DOI: | 10.6084/m9.figshare.21842541 |
| Popis: | We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two variations of our framework: a functional neural network with continuous hidden layers, called the Functional Direct Neural Network (FDNN), and a second version that utilizes basis expansions and continuous hidden layers, called the Functional Basis Neural Network (FBNN). Both are designed explicitly to exploit the structure inherent in functional data. To fit these models we derive a functional gradient based optimization algorithm. The effectiveness of the proposed methods in handling complex functional models is demonstrated by comprehensive simulation studies and real data examples. Comment: 3 figures, 10 tables (including supplementary material), 14 pages (including supplementary material) |
| Databáze: | OpenAIRE |
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