pr_tree {PRTree}

Probabilistic Regression Trees (PRTrees)

Description

Probabilistic Regression Trees (PRTrees)

Usage

pr_tree(y, X, sigma_grid = NULL, max_terminal_nodes = 15L, cp = 0.01,
  max_depth = 5L, n_min = 5L, perc_x = 0.1, p_min = 0.05)

Arguments

y

a numeric vector corresponding to the dependent variable

X

A numeric vector, matrix or dataframe corresponding to the independent variables, with the same number of observations as y.

sigma_grid

optionally, a numeric vector with candidate values for the parameter \sigma, to be passed to the grid search algorithm. If NULL, the standard deviations of the columns in X are used. The default is NULL.

max_terminal_nodes

a non-negative integer. The maximum number of regions in the output tree. The default is 15.

cp

a positive numeric value. The complexity parameter. Any split that does not decrease the MSE by a factor of cp will be ignored. The default is 0.01.

max_depth

a non-negative integer. The maximum depth of the decision tree. The depth is defined as the length of the longest path from the root to a leaf. The default is 5.

n_min

a non-negative integer, The minimum number of observations in a final node. The default is 5.

perc_x

a positive numeric value. Given a column of P, the value perc_x is the percentage of rows in this column that must have a probability higher than the threshold p_min for a splitting attempt to be made in the corresponding region. The default is 0.1.

p_min

a positive numeric value. A threshold probability that controls the splitting process. A splitting attempt is made in a given region only when the proportion of rows with probability higher than p_min, in the corresponding column of the matrix P, is equal to perc_x. The default is 0.05.

Value

yhat

the estimated values for y

P

the matrix of probabilities calculated with the observations in X for the returned tree

gamma

the values of the \gamma_j weights estimated for the returned tree

MSE

the mean squared error calculated for the returned tree

sigma

the \sigma of the returned tree

nodes_matrix_info

information related to each node of the returned tree

regions

information related to each region of the returned tree

Examples

set.seed(1234)
X = matrix(runif(200, 0, 10), ncol = 1)
eps = matrix(rnorm(200, 0, 0.05), ncol = 1)
y =  matrix(cos(X) + eps, ncol = 1)
reg = PRTree::pr_tree(y, X, max_terminal_nodes = 9)
plot(X[order(X)], reg$yhat[order(X)], xlab = 'x', ylab = 'cos(x)', col = 'blue', type = 'l')
points(X[order(X)], y[order(X)], xlab = 'x', ylab = 'cos(x)', col = 'red')