GPNode: R6 Class for the nodes / leaves in the GPTree tree
In GPTreeO: Dividing Local Gaussian Processes for Online Learning Regression
GPNode R Documentation
R6 Class for the nodes / leaves in the GPTree tree
Description
The nodes contain the local GP if they are leaves (at the end of a branch). Nodes that are just nodes contain information on how the input space was split. They are responsible for computing and updating the splitting probabilities. Also, the tree interacts with the local GPs through the nodes.
Currently, GPs from the DiceKriging package (WrappedDiceKrigingGP) and mlegp package (WrappedmlegpGP) are implemented. The user can create their own wrapper using WrappedGP.
Public fields
keyA string like "0110100" to identify the node in the binary tree
x_dimDimensionality of input points. It is set once the first point is received through the GPTree method update. It needs to be specified if min_ranges should be different from default.
thetaOverlap ratio between two leafs in the split direction. The default value is 0.
split_direction_criterionA string that indicates which spitting criterion to use. The options are:
-
"max_spread": Split along the direction which has the largest data spread.
-
"min_lengthscale": split along the direction with the smallest length-scale hyperparameter from the local GP.
-
"max_spread_per_lengthscale": Split along the direction with the largest data spread relative to the corresponding GP length-scale hyperparameter.
-
"max_corr": Split along the direction where the input data is most strongly correlated with the target variable.
-
"principal_component": Split along the first principal component.
The default value is "max_spread_per_lengthscale".
split_position_criterionA string indicating how the split position along the split direction should be set. Possible values are ("mean" and "median"). The default is "mean".
shape_decayA string specifying how the probability function for a point to be assigned to the left leaf should fall off in the overlap region. The available options are a linear shape ("linear"), an exponential shape ("exponential") or a Gaussian shape ("gaussian"). Another option is to select no overlap region. This can be achieved by selecting "deterministic" or to set theta to 0. The default is "linear".
prob_min_thetaMinimum probability after which the overlap shape gets truncated (either towards 0 or 1). The default value is 0.01.
NbarMaximum number of data points for each GP in a leaf before it is split. The default value is 1000.
min_rangesSmallest allowed input data spread (per dimension) before node splitting stops. It is set to its default min_ranges = rep(0.0, x_dim) once the first point is received through the update method. x_dim needs to be specified by the user if it should be different from the default.
is_leafIf TRUE, this node a leaf, i.e the last node on its branch
wrapped_gpAn instance of the WrappedGP type
can_splitIf TRUE for a given dimension, the leaf can be split along that dimension
rotation_matrixA rotation matrix, used for transforming the data
shiftA shift, used for transforming the data
use_pc_transformTRUE if principal components transformation is used for node splitting
x_spreadVector of data spread for each dimension
split_indexIndex for the split dimension
position_splitPosition of the split along dimension split_index
width_overlapWidth of overlap region along dimension split_index
point_idsIDs of the points assigned to this node
residualsVector of residuals
pred_errsVector of prediction uncertainties
error_scalerScaling factor for the prediction error to ensure desired coverage
use_n_residualsNumber of past residuals to use in calibrating the error_scaler
Methods
Public methods
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Method new()
Create a new node object
Usage
GPNode$new(
key,
x_dim,
theta,
split_direction_criterion,
split_position_criterion,
shape_decay,
prob_min_theta,
Nbar,
wrapper,
gp_control,
retrain_buffer_length,
add_buffer_in_prediction,
min_ranges = NULL,
is_leaf = TRUE
)
Arguments
keyA string like "0110100" to identify the node in the binary tree
x_dimDimensionality of input points. It is set once the first point is received through the GPTree method update. It needs to be specified if min_ranges should be different from default.
thetaOverlap ratio between two leafs in the split direction. The default value is 0.
split_direction_criterionA string that indicates which spitting criterion to use. The options are:
-
"max_spread": Split along the direction which has the largest data spread.
-
"min_lengthscale": split along the direction with the smallest length-scale hyperparameter from the local GP.
-
"max_spread_per_lengthscale": Split along the direction with the largest data spread relative to the corresponding GP length-scale hyperparameter.
-
"max_corr": Split along the direction where the input data is most strongly correlated with the target variable.
-
"principal_component": Split along the first principal component.
The default value is "max_spread_per_lengthscale".
split_position_criterionA string indicating how the split position along the split direction should be set. Possible values are ("mean" and "median"). The default is "mean".
shape_decayA string specifying how the probability function for a point to be assigned to the left leaf should fall off in the overlap region. The available options are a linear shape ("linear"), an exponential shape ("exponential") or a Gaussian shape ("gaussian"). Another option is to select no overlap region. This can be achieved by selecting "deterministic" or to set theta to 0. The default is "linear".
prob_min_thetaMinimum probability after which the overlap shape gets truncated (either towards 0 or 1). The default value is 0.01.
NbarMaximum number of data points for each GP in a leaf before it is split. The default value is 1000.
wrapperA string that indicates which GP implementation should be used. The current version includes wrappers for the packages "DiceKriging" and "mlegp". The default setting is "DiceKriging".
gp_controlA list of control parameter that is forwarded to the wrapper. Here, the covariance function is specified. DiceKriging allows for the following kernels, passed as string: "gauss", "matern5_2", "matern3_2", "exp", "powexp" where "matern3_2" is set as default.
retrain_buffer_lengthSize of the retrain buffer. The buffer for a each node collects data points and holds them until the buffer length is reached. Then the GP in the node is updated with the data in the buffer. For a fixed Nbar, higher values for retrain_buffer_length lead to faster run time (less frequent retraining), but the trade-off is a temporary reduced prediction accuracy. We advise that the choice for retrain_buffer_length should depend on the chosen Nbar. By default retrain_buffer_length is set equal to Nbar.
add_buffer_in_predictionIf TRUE, points in the data buffers are added to the GP before prediction. They are added into a temporarily created GP which contains the not yet included points. The GP in the node is not yet updated. The default is FALSE.
min_rangesSmallest allowed input data spread (per dimension) before node splitting stops. It is set to its default min_ranges = rep(0.0, x_dim) once the first point is received through the GPTree method update. x_dim needs to be specified by the user if it should be different from the default.
is_leafIf TRUE, this node a leaf, i.e the last node on its branch.
n_points_train_limitNumber of points at which a GP is created in the leaf
Returns
A new GPNode object. Contains the local GP in the field wrapped_gp, and information used for and related to splitting the node. If the node has been split, the local GP is removed.
Method transform()
Method to transform input data through a shift and a rotation. IS EXPECTED TO NOT BE CALLED BY THE USER
Usage
GPNode$transform(X)
Arguments
XMatrix with x points
Returns
The transformed X matrix
Method update_prob_pars()
Method to update the probability parameters (x_spread, can_split, split_index, position_split, width_overlap). IS EXPECTED TO NOT BE CALLED BY THE USER
Usage
GPNode$update_prob_pars()
Method get_prob_child_1()
Method to compute the probability that a point x should go to child 1. IS EXPECTED TO NOT BE CALLED BY THE USER
Usage
GPNode$get_prob_child_1(x)
Arguments
xSingle data point for which probability is computed; has to be a vector with length equal to x_dim
Returns
The probability that a point x should go to child 1
Method register_residual()
Method to register prediction performance
Usage
GPNode$register_residual(x, y)
Arguments
xMost recent single input data point from the data stream; has to be a vector with length equal to x_dim
yTarget variable which has to be a one-dimensional matrix or a vector; any further columns will be ignored
Method update_empirical_error_pars()
Method for updating the empirical error parameters
Usage
GPNode$update_empirical_error_pars()
Method delete_gp()
Method to delete the GP. IS EXPECTED TO NOT BE CALLED BY THE USER
Usage
GPNode$delete_gp()
Method clone()
The objects of this class are cloneable with this method.
Usage
GPNode$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
See Also
GPTree() for the main methods
GPTreeO documentation built on Oct. 16, 2024, 5:08 p.m.
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| GPNode | R Documentation |
R6 Class for the nodes / leaves in the GPTree tree
Description
The nodes contain the local GP if they are leaves (at the end of a branch). Nodes that are just nodes contain information on how the input space was split. They are responsible for computing and updating the splitting probabilities. Also, the tree interacts with the local GPs through the nodes.
Currently, GPs from the DiceKriging package (WrappedDiceKrigingGP) and mlegp package (WrappedmlegpGP) are implemented. The user can create their own wrapper using WrappedGP.
Public fields
keyA string like "0110100" to identify the node in the binary tree
x_dimDimensionality of input points. It is set once the first point is received through the GPTree method
update. It needs to be specified ifmin_rangesshould be different from default.thetaOverlap ratio between two leafs in the split direction. The default value is 0.
split_direction_criterionA string that indicates which spitting criterion to use. The options are:
-
"max_spread": Split along the direction which has the largest data spread. -
"min_lengthscale": split along the direction with the smallest length-scale hyperparameter from the local GP. -
"max_spread_per_lengthscale": Split along the direction with the largest data spread relative to the corresponding GP length-scale hyperparameter. -
"max_corr": Split along the direction where the input data is most strongly correlated with the target variable. -
"principal_component": Split along the first principal component.
The default value is
"max_spread_per_lengthscale".-
split_position_criterionA string indicating how the split position along the split direction should be set. Possible values are (
"mean"and"median"). The default is"mean".shape_decayA string specifying how the probability function for a point to be assigned to the left leaf should fall off in the overlap region. The available options are a linear shape (
"linear"), an exponential shape ("exponential") or a Gaussian shape ("gaussian"). Another option is to select no overlap region. This can be achieved by selecting"deterministic"or to setthetato 0. The default is"linear".prob_min_thetaMinimum probability after which the overlap shape gets truncated (either towards 0 or 1). The default value is 0.01.
NbarMaximum number of data points for each GP in a leaf before it is split. The default value is 1000.
min_rangesSmallest allowed input data spread (per dimension) before node splitting stops. It is set to its default
min_ranges = rep(0.0, x_dim)once the first point is received through theupdatemethod.x_dimneeds to be specified by the user if it should be different from the default.is_leafIf TRUE, this node a leaf, i.e the last node on its branch
wrapped_gpAn instance of the WrappedGP type
can_splitIf TRUE for a given dimension, the leaf can be split along that dimension
rotation_matrixA rotation matrix, used for transforming the data
shiftA shift, used for transforming the data
use_pc_transformTRUE if principal components transformation is used for node splitting
x_spreadVector of data spread for each dimension
split_indexIndex for the split dimension
position_splitPosition of the split along dimension split_index
width_overlapWidth of overlap region along dimension split_index
point_idsIDs of the points assigned to this node
residualsVector of residuals
pred_errsVector of prediction uncertainties
error_scalerScaling factor for the prediction error to ensure desired coverage
use_n_residualsNumber of past residuals to use in calibrating the
error_scaler
Methods
Public methods
Method new()
Create a new node object
Usage
GPNode$new( key, x_dim, theta, split_direction_criterion, split_position_criterion, shape_decay, prob_min_theta, Nbar, wrapper, gp_control, retrain_buffer_length, add_buffer_in_prediction, min_ranges = NULL, is_leaf = TRUE )
Arguments
keyA string like "0110100" to identify the node in the binary tree
x_dimDimensionality of input points. It is set once the first point is received through the GPTree method
update. It needs to be specified ifmin_rangesshould be different from default.thetaOverlap ratio between two leafs in the split direction. The default value is 0.
split_direction_criterionA string that indicates which spitting criterion to use. The options are:
-
"max_spread": Split along the direction which has the largest data spread. -
"min_lengthscale": split along the direction with the smallest length-scale hyperparameter from the local GP. -
"max_spread_per_lengthscale": Split along the direction with the largest data spread relative to the corresponding GP length-scale hyperparameter. -
"max_corr": Split along the direction where the input data is most strongly correlated with the target variable. -
"principal_component": Split along the first principal component.
The default value is
"max_spread_per_lengthscale".-
split_position_criterionA string indicating how the split position along the split direction should be set. Possible values are (
"mean"and"median"). The default is"mean".shape_decayA string specifying how the probability function for a point to be assigned to the left leaf should fall off in the overlap region. The available options are a linear shape (
"linear"), an exponential shape ("exponential") or a Gaussian shape ("gaussian"). Another option is to select no overlap region. This can be achieved by selecting"deterministic"or to setthetato 0. The default is"linear".prob_min_thetaMinimum probability after which the overlap shape gets truncated (either towards 0 or 1). The default value is 0.01.
NbarMaximum number of data points for each GP in a leaf before it is split. The default value is 1000.
wrapperA string that indicates which GP implementation should be used. The current version includes wrappers for the packages
"DiceKriging"and"mlegp". The default setting is"DiceKriging".gp_controlA
listof control parameter that is forwarded to the wrapper. Here, the covariance function is specified.DiceKrigingallows for the following kernels, passed as string:"gauss","matern5_2","matern3_2","exp","powexp"where"matern3_2"is set as default.retrain_buffer_lengthSize of the retrain buffer. The buffer for a each node collects data points and holds them until the buffer length is reached. Then the GP in the node is updated with the data in the buffer. For a fixed
Nbar, higher values forretrain_buffer_lengthlead to faster run time (less frequent retraining), but the trade-off is a temporary reduced prediction accuracy. We advise that the choice forretrain_buffer_lengthshould depend on the chosenNbar. By defaultretrain_buffer_lengthis set equal toNbar.add_buffer_in_predictionIf TRUE, points in the data buffers are added to the GP before prediction. They are added into a temporarily created GP which contains the not yet included points. The GP in the node is not yet updated. The default is
FALSE.min_rangesSmallest allowed input data spread (per dimension) before node splitting stops. It is set to its default
min_ranges = rep(0.0, x_dim)once the first point is received through the GPTree methodupdate.x_dimneeds to be specified by the user if it should be different from the default.is_leafIf TRUE, this node a leaf, i.e the last node on its branch.
n_points_train_limitNumber of points at which a GP is created in the leaf
Returns
A new GPNode object. Contains the local GP in the field wrapped_gp, and information used for and related to splitting the node. If the node has been split, the local GP is removed.
Method transform()
Method to transform input data through a shift and a rotation. IS EXPECTED TO NOT BE CALLED BY THE USER
Usage
GPNode$transform(X)
Arguments
XMatrix with x points
Returns
The transformed X matrix
Method update_prob_pars()
Method to update the probability parameters (x_spread, can_split, split_index, position_split, width_overlap). IS EXPECTED TO NOT BE CALLED BY THE USER
Usage
GPNode$update_prob_pars()
Method get_prob_child_1()
Method to compute the probability that a point x should go to child 1. IS EXPECTED TO NOT BE CALLED BY THE USER
Usage
GPNode$get_prob_child_1(x)
Arguments
xSingle data point for which probability is computed; has to be a vector with length equal to x_dim
Returns
The probability that a point x should go to child 1
Method register_residual()
Method to register prediction performance
Usage
GPNode$register_residual(x, y)
Arguments
xMost recent single input data point from the data stream; has to be a vector with length equal to x_dim
yTarget variable which has to be a one-dimensional matrix or a vector; any further columns will be ignored
Method update_empirical_error_pars()
Method for updating the empirical error parameters
Usage
GPNode$update_empirical_error_pars()
Method delete_gp()
Method to delete the GP. IS EXPECTED TO NOT BE CALLED BY THE USER
Usage
GPNode$delete_gp()
Method clone()
The objects of this class are cloneable with this method.
Usage
GPNode$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
See Also
GPTree() for the main methods
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