Functional Regression via Deep Neural Networks

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Functional Data Regression Model

• : fixed vector of length d for the j-th observational point
• : scalar random variable for the i-th subject and j-th observational point
• : error random process with measurement error for the i-th subject and j-th observational point
• : sample size
• : number of observational points
• : true function to estimate

Deep Neural Network Model input and output

• Input:
• Output:

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Deep Neural Network Hyperparameters and Structures

• L: number of layers
• p: neurons per layer (uniform for all layers)
• s: l1 penalty parameter
• Loss function: square loss
• Batch size: data dependent
• Epoch number: data dependent
• Activation function: ReLU
• Optimizer: Adam

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Function descriptions

• Main function is in "FDADNN.R".
• 2D and 3D examples are in "example.R".
• The package is under "master" branch. Download and install the r package. Use "help" for more function details and examples.

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