diff --git a/dev/documentation/index.html b/dev/documentation/index.html index 8bf77af..40d2ed7 100644 --- a/dev/documentation/index.html +++ b/dev/documentation/index.html @@ -1,41 +1,41 @@ -Documentation · MondrianForests.jl
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Documentation

Mondrian trees

MondrianForests.MondrianTree — Type

A Mondrian tree is determined by:

  • id: a string to identify the tree
  • lambda: the non-negative lifetime parameter
  • lower: the lower coordinate of the root cell
  • upper: the upper coordinate of the root cell
  • creation_time: the time when the root cell was created during sampling
  • is_split: whether the root cell is split
  • split_axis: the direction in which the root cell is split, if any
  • split_location: the location on split_axis at which the root cell is split, if any
  • tree_left: the left child tree of the root cell, if any
  • tree_right: the right child tree of the root cell, if any
source
MondrianForests.MondrianTree — Method
MondrianTree(d::Int, lambda::Float64)

Sample a Mondrian tree $\mathcal{M}([0,1]^d, \lambda)$.

Examples

d = 2
+Documentation · MondrianForests.jl
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Documentation
Mondrian trees
MondrianForests.MondrianTree — Type
A Mondrian tree is determined by:
  • id: a string to identify the tree
  • lambda: the non-negative lifetime parameter
  • lower: the lower coordinate of the root cell
  • upper: the upper coordinate of the root cell
  • creation_time: the time when the root cell was created during sampling
  • is_split: whether the root cell is split
  • split_axis: the direction in which the root cell is split, if any
  • split_location: the location on split_axis at which the root cell is split, if any
  • tree_left: the left child tree of the root cell, if any
  • tree_right: the right child tree of the root cell, if any
source
MondrianForests.MondrianTree — Method
MondrianTree(d::Int, lambda::Float64)
Sample a Mondrian tree $\mathcal{M}([0,1]^d, \lambda)$.
Examples
d = 2
 lambda = 3.0
-tree = MondrianTree(d, lambda);
source
MondrianForests.MondrianTree — Method
MondrianTree(id::String, lambda::Float64, lower::NTuple{d,Float64},
              upper::NTuple{d,Float64}, creation_time::Float64) where {d}
Sample a Mondrian tree with a given id, lifetime, lower and upper cell coordinates, and creation time. To be used in internal construction methods.
Examples
id = ""
 lambda = 3.0
 lower = ntuple(i -> 0.2, d)
 upper = ntuple(i -> 0.7, d)
 creation_time = 0.0
-tree = MondrianTree(id, lambda, lower, upper, creation_time)
source
Base.show — Method
Base.show(tree::MondrianTree{d}) where {d}
Show the recursive structure of a Mondrian tree.
source
MondrianForests.are_in_same_leaf — Method
are_in_same_leaf(x1::NTuple{d,Float64}, x2::NTuple{d,Float64}, tree::MondrianTree)
Check if two points are in the same leaf cell of a Mondrian tree.
Examples
d = 2
+tree = MondrianTree(id, lambda, lower, upper, creation_time)
source
Base.show — Method
Base.show(tree::MondrianTree{d}) where {d}
Show the recursive structure of a Mondrian tree.
source
MondrianForests.are_in_same_leaf — Method
are_in_same_leaf(x1::NTuple{d,Float64}, x2::NTuple{d,Float64}, tree::MondrianTree)
Check if two points are in the same leaf cell of a Mondrian tree.
Examples
d = 2
 tree = MondrianTree(d, 0.0)
 x1 = ntuple(i -> 0.2, d)
 x2 = ntuple(i -> 0.7, d)
 are_in_same_leaf(x1, x2, tree)
 
 # output
-true
source
MondrianForests.count_leaves — Method
count_leaves(tree::MondrianTree{d}) where {d}
Count the leaves of a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
-count_leaves(tree)
source
MondrianForests.get_center — Method
get_center(tree::MondrianTree{d}) where {d}
Get the center point of the root cell of a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
+true
source
MondrianForests.count_leaves — Method
count_leaves(tree::MondrianTree{d}) where {d}
Count the leaves of a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
+count_leaves(tree)
source
MondrianForests.get_center — Method
get_center(tree::MondrianTree{d}) where {d}
Get the center point of the root cell of a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
 get_center(tree)
 
 # output
-(0.5, 0.5)
source
MondrianForests.get_common_refinement — Method
get_common_refinement(trees::Vector{MondrianTree{d}}) where {d}
Get the common refinement of several Mondrian trees, whose leaf cells are the intersections of all leaf cells in trees. Preserves the split times and returns a new equivalent MondrianTree.
Examples
trees = [MondrianTree(2, 3.0) for _ in 1:3]
-refined_tree = get_common_refinement(trees)
source
MondrianForests.get_common_refinement — Method
get_common_refinement(trees::Vector{MondrianTree{d}}) where {d}
Get the common refinement of several Mondrian trees, whose leaf cells are the intersections of all leaf cells in trees. Preserves the split times and returns a new equivalent MondrianTree.
Examples
trees = [MondrianTree(2, 3.0) for _ in 1:3]
+refined_tree = get_common_refinement(trees)
source
MondrianForests.get_leaf_containing — Method
get_leaf_containing(x::NTuple{d,Float64}, tree::MondrianTree{d}) where {d}
Get the leaf of a Mondrian tree containing a point x.
Examples
d = 2
 x = ntuple(i -> 0.2, d)
 tree = MondrianTree(d, 3.0)
-get_leaf_containing(x, tree)
source
MondrianForests.get_leaves — Method
get_leaves(tree::MondrianTree{d}) where {d}
Get a list of the leaves in a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
-get_leaves(tree)
source
MondrianForests.get_subtrees — Method
get_subtrees(tree::MondrianTree{d}) where {d}
Get a list of the subtrees contained in a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
-get_subtrees(tree)
source
MondrianForests.get_volume — Method
get_volume(tree::MondrianTree{d}) where {d}
Get the d-dimensional volume of the root cell of a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
+get_leaf_containing(x, tree)
source
MondrianForests.get_leaves — Method
get_leaves(tree::MondrianTree{d}) where {d}
Get a list of the leaves in a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
+get_leaves(tree)
source
MondrianForests.get_subtrees — Method
get_subtrees(tree::MondrianTree{d}) where {d}
Get a list of the subtrees contained in a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
+get_subtrees(tree)
source
MondrianForests.get_volume — Method
get_volume(tree::MondrianTree{d}) where {d}
Get the d-dimensional volume of the root cell of a Mondrian tree.
Examples
tree = MondrianTree(2, 3.0)
 get_volume(tree)
 
 # output
-1.0
source
MondrianForests.is_in — Method
is_in(x::NTuple{d,Float64}, tree::MondrianTree{d}) where {d}
Check if a point x is contained in the root cell of a Mondrian tree.
Examples
x = ntuple(i -> 0.2, 2)
+1.0
source
MondrianForests.is_in — Method
is_in(x::NTuple{d,Float64}, tree::MondrianTree{d}) where {d}
Check if a point x is contained in the root cell of a Mondrian tree.
Examples
x = ntuple(i -> 0.2, 2)
 tree = MondrianTree(2, 3.0)
 is_in(x, tree)
 
 # output
-true
source
MondrianForests.restrict — Method
restrict(tree::MondrianTree{d}, time::Float64) where {d}
Restrict a Mondrian tree to a stopping time.
Examples
tree = MondrianTree(2, 3.0)
-restrict(tree, 2.0)
source
Mondrian random forests
MondrianForests.MondrianForest — Type
A Mondrian random forest is determined by:
  • lambda: the non-negative lifetime parameter
  • n_trees: the number of Mondrian trees in the forest
  • n_data: the number of data points
  • n_evals: the number of evaluation points
  • x_evals: the evaluation points
  • significance_level: the significance level for confidence intervals
  • X_data: the covariate data
  • Y_data: the response data
  • trees: a list of the trees used in the forest
  • mu_hat: the estimated regression function
  • sigma2_hat: the estimated residual variance function
  • Sigma_hat: the estimated forest variance function
  • confidence_band: a confidence band for the regression function
source
MondrianForests.restrict — Method
restrict(tree::MondrianTree{d}, time::Float64) where {d}
Restrict a Mondrian tree to a stopping time.
Examples
tree = MondrianTree(2, 3.0)
+restrict(tree, 2.0)
source
Mondrian random forests
MondrianForests.MondrianForest — Type
A Mondrian random forest is determined by:
  • lambda: the non-negative lifetime parameter
  • n_trees: the number of Mondrian trees in the forest
  • n_data: the number of data points
  • n_evals: the number of evaluation points
  • x_evals: the evaluation points
  • significance_level: the significance level for confidence intervals
  • X_data: the covariate data
  • Y_data: the response data
  • trees: a list of the trees used in the forest
  • mu_hat: the estimated regression function
  • sigma2_hat: the estimated residual variance function
  • Sigma_hat: the estimated forest variance function
  • confidence_band: a confidence band for the regression function
source
MondrianForests.MondrianForest — Method
MondrianForest(lambda::Float64, n_trees::Int, x_evals::Vector{NTuple{d,Float64}},
                X_data::Vector{NTuple{d,Float64}}, Y_data::Vector{Float64},
                estimate_var::Bool=false, significance_level::Float64=0.05) where {d}
Fit a Mondrian random forest to data. If estimate_var is false, do not estimate the variance or construct confidence bands. This can speed up computation significantly.
Examples
lambda = 3.0
 n_trees = 20
@@ -46,7 +46,7 @@
 estimate_var = true
 significance_level = 0.05
 forest = MondrianForest(lambda, n_trees, x_evals, X_data, Y_data,
-                        estimate_var, significance_level)
source
Base.show — Method
Base.show(forest::MondrianForest{d}) where {d}
Show a Mondrian random forest.
source
Debiased Mondrian random forests
MondrianForests.DebiasedMondrianForest — Type
A debiased Mondrian random forest is determined by:
  • lambda: the non-negative lifetime parameter
  • n_trees: the number of Mondrian trees in the forest
  • n_data: the number of data points
  • n_evals: the number of evaluation points
  • x_evals: the evaluation points
  • debias_order: the order of debiasing to apply
  • significance_level: the significance level for confidence intervals
  • X_data: the covariate data
  • Y_data: the response data
  • debias_scaling: the lifetime scaling values
  • debias_coeffs: the debiasing coefficients
  • trees: a list of the trees used in the forest
  • mu_hat: the estimated regression function
  • sigma2_hat: the estimated residual variance function
  • Sigma_hat: the estimated forest variance function
  • confidence_band: a confidence band for the regression function
source
Base.show — Method
Base.show(forest::MondrianForest{d}) where {d}
Show a Mondrian random forest.
source
Debiased Mondrian random forests
MondrianForests.DebiasedMondrianForest — Type
A debiased Mondrian random forest is determined by:
  • lambda: the non-negative lifetime parameter
  • n_trees: the number of Mondrian trees in the forest
  • n_data: the number of data points
  • n_evals: the number of evaluation points
  • x_evals: the evaluation points
  • debias_order: the order of debiasing to apply
  • significance_level: the significance level for confidence intervals
  • X_data: the covariate data
  • Y_data: the response data
  • debias_scaling: the lifetime scaling values
  • debias_coeffs: the debiasing coefficients
  • trees: a list of the trees used in the forest
  • mu_hat: the estimated regression function
  • sigma2_hat: the estimated residual variance function
  • Sigma_hat: the estimated forest variance function
  • confidence_band: a confidence band for the regression function
source
MondrianForests.DebiasedMondrianForest — Method
DebiasedMondrianForest(lambda::Float64, n_trees::Int, x_evals::Vector{NTuple{d,Float64}},
                        debias_order::Int,
                        X_data::Vector{NTuple{d,Float64}}, Y_data::Vector{Float64},
                        estimate_var::Bool=false,
@@ -60,12 +60,12 @@
 estimate_var = true
 significance_level = 0.05
 forest = DebiasedMondrianForest(lambda, n_trees, x_evals, debias_order, X_data, Y_data,
-                                estimate_var, significance_level)
source
Base.show — Method
Base.show(forest::DebiasedMondrianForest{d}) where {d}
Show a debiased Mondrian random forest.
source
Lifetime parameter selection
Base.show — Method
Base.show(forest::DebiasedMondrianForest{d}) where {d}
Show a debiased Mondrian random forest.
source
Lifetime parameter selection
MondrianForests.select_lifetime_polynomial — Method
select_lifetime_polynomial(X_data::Vector{NTuple{d,Float64}}, Y_data::Vector{Float64},
                            debias_order::Int=0) where {d}
Select the lifetime parameter for a (debiased) Mondrian random forest using polynomial estimation.
Examples
data = generate_uniform_data_uniform_errors(2, 50)
 X_data = data["X"]
 Y_data= data["Y"]
 debias_order = 0
-lambda = select_lifetime_polynomial(X_data, Y_data, debias_order)
source
MondrianForests.get_gcv — Method
get_gcv(lambda::Float64, n_trees::Int,
+lambda = select_lifetime_polynomial(X_data, Y_data, debias_order)
source
MondrianForests.get_gcv — Method
get_gcv(lambda::Float64, n_trees::Int,
         X_data::Vector{NTuple{d,Float64}}, Y_data::Vector{Float64},
         debias_order::Int, n_subsample::Int) where {d}
Get the generalized cross-validation score of a lifetime parameter lambda.
Examples
lambda = 3.0
 n_trees = 20
@@ -74,7 +74,7 @@
 data = generate_uniform_data_uniform_errors(2, 50)
 X_data = data["X"]
 Y_data= data["Y"]
-lambda = get_gcv(lambdas, n_trees, X_data, Y_data, debias_order, n_subsample)
source
MondrianForests.select_lifetime_gcv — Method
select_lifetime_gcv(lambdas::Vector{Float64}, n_trees::Int,
                     X_data::Vector{NTuple{d,Float64}}, Y_data::Vector{Float64},
                     debias_order::Int, n_subsample::Int) where {d}
Select the lifetime parameter for a (debiased) Mondrian random forest using generalized cross-validation.
Examples
lambdas = collect(range(0.5, 10.0, step=0.5))
 n_trees = 20
@@ -83,14 +83,14 @@
 data = generate_uniform_data_uniform_errors(2, 50)
 X_data = data["X"]
 Y_data= data["Y"]
-lambda = select_lifetime_gcv(lambdas, n_trees, X_data, Y_data, debias_order, n_subsample)
source
Data generation
MondrianForests.generate_data — Method
generate_data(n::Int, X_dist::Distribution, eps_dist::Distribution,
+lambda = select_lifetime_gcv(lambdas, n_trees, X_data, Y_data, debias_order, n_subsample)
source
Data generation
MondrianForests.generate_data — Method
generate_data(n::Int, X_dist::Distribution, eps_dist::Distribution,
               mu::Function, sigma2::Function)
Generate sample data for Mondrian forest estimation.
Draws n independent samples from $Y = \mu(X) + \sigma(X) \varepsilon$, with $X \sim$ X_dist and $\varepsilon \sim$ eps_dist.
Examples
n = 20
 X_dist = product_distribution([Uniform(0, 1) for _ in 1:2])
 eps_dist = Uniform(-1, 1)
 mu = (x -> x[1]^2)
 sigma2 = (x -> 1 + x[2]^4)
-generate_data(n, X_dist, eps_dist, mu, sigma2)
source
MondrianForests.generate_uniform_data_normal_errors — Method
generate_uniform_data_normal_errors(d::Int, n::Int)
Generate uniform sample data with normal errors for Mondrian forest estimation.
Draws n independent samples from $Y = \varepsilon$, with $X \sim \mathcal{U}[0, 1]$ and $\varepsilon \sim \mathcal{N}(0, 1)$.
Examples
d = 3
+generate_data(n, X_dist, eps_dist, mu, sigma2)
source
MondrianForests.generate_uniform_data_normal_errors — Method
generate_uniform_data_normal_errors(d::Int, n::Int)
Generate uniform sample data with normal errors for Mondrian forest estimation.
Draws n independent samples from $Y = \varepsilon$, with $X \sim \mathcal{U}[0, 1]$ and $\varepsilon \sim \mathcal{N}(0, 1)$.
Examples
d = 3
 n = 20
-generate_uniform_data_normal_errors(d, n)
source
MondrianForests.generate_uniform_data_uniform_errors — Method
generate_uniform_data_uniform_errors(d::Int, n::Int)
Generate uniform sample data with uniform errors for Mondrian forest estimation.
Draws n independent samples from $Y = \varepsilon$, with $X \sim \mathcal{U}[0, 1]$ and $\varepsilon \sim \mathcal{U}\big[-\sqrt 3, \sqrt 3\big]$.
Examples
d = 3
+generate_uniform_data_normal_errors(d, n)
source
MondrianForests.generate_uniform_data_uniform_errors — Method
generate_uniform_data_uniform_errors(d::Int, n::Int)
Generate uniform sample data with uniform errors for Mondrian forest estimation.
Draws n independent samples from $Y = \varepsilon$, with $X \sim \mathcal{U}[0, 1]$ and $\varepsilon \sim \mathcal{U}\big[-\sqrt 3, \sqrt 3\big]$.
Examples
d = 3
 n = 20
-generate_uniform_data_uniform_errors(d, n)
source

+generate_uniform_data_uniform_errors(d, n)
source
diff --git a/dev/index.html b/dev/index.html index 91c1846..9bd3646 100644 --- a/dev/index.html +++ b/dev/index.html @@ -51,4 +51,4 @@ println("\ndebiased estimated estimator variance:") display(debiased_forest.Sigma_hat) println("\ndebiased estimated confidence band:") -display(debiased_forest.confidence_band)

Dependencies

Documentation

Documentation for the MondrianForests package is available on the web.

+display(debiased_forest.confidence_band)

Dependencies

Documentation

Documentation for the MondrianForests package is available on the web.

diff --git a/dev/search/index.html b/dev/search/index.html index 6787d26..9d1a400 100644 --- a/dev/search/index.html +++ b/dev/search/index.html @@ -1,2 +1,2 @@ -Search · MondrianForests.jl

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    +Search · MondrianForests.jl

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