MeanFunction: Mean Function Class
In duckmayr/gpmss: Gaussian Process Models for Social Science
Description
Details
Public fields
Methods
Description
This provides a parent class for all mean function classes for gpmss.
Details
"A Gaussian process is completely specified by its mean function and
covariance function" (Rasmussen and Williams 2006, 13). The mean
function gives the prior mean for function output given input values.
We implement the following mean functions:
- MeanZero
A zero mean; for any set of inputs, the GP's prior
mean is zero.
- MeanLinear
A linear mean; the GP's prior mean is a vector of
coefficients multiplied by the predictors, plus (optionally) an
intercept.
Users may also define their own mean functions for use with gpmss
functions. A mean function class must provide a mean() method,
a parameter_derivative() method, and a input_derivative()
method. It must have data members hypers and name.
The mean() method is used to actually call the mean function.
The first argument should be X, the first set of inputs.
The second argument should be hypers, a numeric vector giving all the
hyperparameters of the mean function; its default value should be
NULL, in which case, the data member hypers is utilized.
(We allow passing different hypers for convenience in hyperparameter
optimization).
The parameter_derivative() method is used to obtain the partial
derivatives of the mean function with respect to each of its
hyperparameters. (This is useful for optimization). Its arguments should be
the same as the mean() method, with one additional argument,
param, giving the index of hypers of the parameter with
respect to which the derivative should be taken.
The input_derivative() method is used to obtain the partial
derivatives of the mean function with respect to its inputs.
(This is useful for obtaining marginal effects). Its arguments should be
the same as the mean() method, with an additional argument:
dimension, an integer vector of length one giving the dimension of X
with respect to which the derivative is being taken.
Its constructor should take at least one argument, hypers,
which will be stored as the data member hypers.
This should have a sane default, as many users may pass the class generator
to the constructor for a GPModel without explicitly
specifying hyperparameters. This should not cause much difficulty if the
user optimizes the hyperparameters, but a sane default should be provided
nonetheless.
The data member hypers should be a public member so that it can be
accessed and modified directly.
The data member name should be hard-coded within the class definition;
it is used for printing purposes (potentially in other functions). It should
be a public member so that it can be accessed directly.
Public fields
nameA character vector of length one giving the mean
function's name
hypersA numeric vector giving the mean function's
hyperparameters
Methods
Public methods
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Method mean()
Compute function prior mean
Usage
MeanFunction$mean(X, hypers = NULL)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the
mean function. If NULL (the default), the hypers data
member is used.
Method parameter_derivative()
Compute partial derivatives of mean function with respect to
its hyperparameters
Usage
MeanFunction$parameter_derivative(X, hypers = NULL, param = 1)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the
mean function. If NULL (the default), the hypers data
member is used.
paramAn integer vector of length one; which element of
hypers should the derivative be taken with respect to?
The default is 1
Method input_derivative()
Compute partial derivatives of mean function with respect to
its inputs
Usage
MeanFunction$input_derivative(X, hypers = NULL, dimension = 1)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the
mean function. If NULL (the default), the hypers data
member is used.
dimensionan integer vector of length one giving the dimension
of X with respect to which the derivative is being taken; the
default is 1
Method new()
Create a new MeanFunction object
Usage
MeanFunction$new(hypers = numeric())
Arguments
hypersA numeric vector giving hyperparameters for the
mean function.
Method clone()
The objects of this class are cloneable with this method.
Usage
MeanFunction$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
duckmayr/gpmss documentation built on Nov. 8, 2021, 5:48 a.m.
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Description Details Public fields Methods
Description
This provides a parent class for all mean function classes for gpmss.
Details
"A Gaussian process is completely specified by its mean function and covariance function" (Rasmussen and Williams 2006, 13). The mean function gives the prior mean for function output given input values.
We implement the following mean functions:
- MeanZero
A zero mean; for any set of inputs, the GP's prior mean is zero.
- MeanLinear
A linear mean; the GP's prior mean is a vector of coefficients multiplied by the predictors, plus (optionally) an intercept.
Users may also define their own mean functions for use with gpmss
functions. A mean function class must provide a mean() method,
a parameter_derivative() method, and a input_derivative()
method. It must have data members hypers and name.
The mean() method is used to actually call the mean function.
The first argument should be X, the first set of inputs.
The second argument should be hypers, a numeric vector giving all the
hyperparameters of the mean function; its default value should be
NULL, in which case, the data member hypers is utilized.
(We allow passing different hypers for convenience in hyperparameter
optimization).
The parameter_derivative() method is used to obtain the partial
derivatives of the mean function with respect to each of its
hyperparameters. (This is useful for optimization). Its arguments should be
the same as the mean() method, with one additional argument,
param, giving the index of hypers of the parameter with
respect to which the derivative should be taken.
The input_derivative() method is used to obtain the partial
derivatives of the mean function with respect to its inputs.
(This is useful for obtaining marginal effects). Its arguments should be
the same as the mean() method, with an additional argument:
dimension, an integer vector of length one giving the dimension of X
with respect to which the derivative is being taken.
Its constructor should take at least one argument, hypers,
which will be stored as the data member hypers.
This should have a sane default, as many users may pass the class generator
to the constructor for a GPModel without explicitly
specifying hyperparameters. This should not cause much difficulty if the
user optimizes the hyperparameters, but a sane default should be provided
nonetheless.
The data member hypers should be a public member so that it can be
accessed and modified directly.
The data member name should be hard-coded within the class definition;
it is used for printing purposes (potentially in other functions). It should
be a public member so that it can be accessed directly.
Public fields
nameA character vector of length one giving the mean function's name
hypersA numeric vector giving the mean function's hyperparameters
Methods
Public methods
Method mean()
Compute function prior mean
Usage
MeanFunction$mean(X, hypers = NULL)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the mean function. If NULL (the default), the hypers data member is used.
Method parameter_derivative()
Compute partial derivatives of mean function with respect to its hyperparameters
Usage
MeanFunction$parameter_derivative(X, hypers = NULL, param = 1)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the mean function. If NULL (the default), the hypers data member is used.
paramAn integer vector of length one; which element of
hypersshould the derivative be taken with respect to? The default is 1
Method input_derivative()
Compute partial derivatives of mean function with respect to its inputs
Usage
MeanFunction$input_derivative(X, hypers = NULL, dimension = 1)
Arguments
XThe input values (should be a numeric matrix)
hypersA numeric vector giving hyperparameters for the mean function. If NULL (the default), the hypers data member is used.
dimensionan integer vector of length one giving the dimension of X with respect to which the derivative is being taken; the default is 1
Method new()
Create a new MeanFunction object
Usage
MeanFunction$new(hypers = numeric())
Arguments
hypersA numeric vector giving hyperparameters for the mean function.
Method clone()
The objects of this class are cloneable with this method.
Usage
MeanFunction$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
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