def test_loose_bound(self):
leaf = Tree()
stump = Tree(leaf, leaf)
tree = Tree(stump, leaf)
pfub = PartitioningFunctionUpperBound(tree, 10, loose=True)
pfub(100, 2)
pfub(100, 3)
def test_vcdim_upper_bound():
leaf = Tree()
stump = Tree(leaf, leaf)
tree = Tree(stump, leaf)
assert vcdim_upper_bound(leaf, 10) == 1
assert vcdim_upper_bound(stump, 10) == 6
assert vcdim_upper_bound(tree, 10) == 16
def test_compute_upper_bound_stump(self):
stump = Tree(Tree(), Tree())
pfub = PartitioningFunctionUpperBound(stump, 10)
assert pfub(4,1) == 1
assert pfub(50,1) == 1
assert pfub(1,2) == 0
assert pfub(6,2) == 2**5-1
assert pfub(7,2) < 2**6-1
def test_compute_upper_bound_other_trees(self):
leaf = Tree()
stump = Tree(leaf, leaf)
tree = Tree(stump, leaf)
pfub = PartitioningFunctionUpperBound(tree, 10)
m = 16
assert pfub(m,2) == 2**(m-1)-1
m = 17
assert pfub(m,2) < 2**(m-1)-1
def test_compute_bound_with_precomputed_tables(self):
leaf = Tree()
stump = Tree(leaf, leaf)
tree = Tree(stump, leaf)
pfub = PartitioningFunctionUpperBound(tree, 10)
pfub(16, 2)
other_tree = Tree(tree, tree)
pfub = PartitioningFunctionUpperBound(other_tree, 10, pfub.pfub_table)
assert pfub.pfub_table[tree][2, 16, 10] == 2**(16-1)-1
pfub(17, 2)
def test__eq__(self, trees):
leaf = Tree()
assert leaf == Tree()
tree2 = Tree(Tree(leaf, leaf), leaf)
tree2_mirror = Tree(leaf, Tree(leaf, leaf))
assert tree2 == tree2_mirror
assert trees[1] == trees[2].left_subtree
def trees():
trees = [Tree()]
trees.append(Tree(deepcopy(trees[0]), deepcopy(trees[0])))
trees.append(Tree(deepcopy(trees[1]), deepcopy(trees[0])))
trees.append(Tree(deepcopy(trees[1]), deepcopy(trees[1])))
trees.append(Tree(deepcopy(trees[2]), deepcopy(trees[0])))
trees.append(Tree(deepcopy(trees[2]), deepcopy(trees[1])))
trees.append(Tree(deepcopy(trees[3]), deepcopy(trees[0])))
trees.append(Tree(deepcopy(trees[2]), deepcopy(trees[2])))
trees.append(Tree(deepcopy(trees[3]), deepcopy(trees[1])))
trees.append(Tree(deepcopy(trees[3]), deepcopy(trees[2])))
trees.append(Tree(deepcopy(trees[3]), deepcopy(trees[3])))
return trees
def test_split_leaf(self, trees):
tree = Tree()
tree.split_leaf()
assert tree == trees[1]
def test_replace_leaf_by_leaf(self, trees):
tree = Tree(Tree(), Tree())
tree.left_subtree.replace_subtree(Tree())
assert tree == trees[1]
def test_replace_stump_by_leaf(self, trees):
tree = Tree(Tree(), Tree())
tree.replace_subtree(Tree())
assert tree.is_leaf()
def test_replace_leaf_by_stump(self, trees):
tree = Tree(Tree(), Tree())
tree.left_subtree.replace_subtree(deepcopy(tree))
assert tree == trees[2]
assert [t.height for t in tree] == [2, 1, 0, 0, 0]
assert [t.depth for t in tree] == [0, 1, 2, 2, 1]
"""
In this script, we compute the VCdim upper bound for the first 11 non-equivalent binary trees.
"""
from partitioning_machines import Tree, vcdim_upper_bound
leaf = Tree() # tree 1
stump = Tree(leaf, leaf) # tree 2
tree3 = Tree(stump, leaf)
tree4 = Tree(stump, stump)
tree5 = Tree(tree3, leaf)
tree6 = Tree(tree4, leaf)
tree7 = Tree(tree3, stump)
tree8 = Tree(tree3, tree3)
tree9 = Tree(tree4, stump)
tree10 = Tree(tree4, tree3)
tree11 = Tree(tree4, tree4)
trees = [
leaf,
stump,
tree3,
tree4,
tree5,
tree6,
tree7,
tree8,
tree9,
tree10,
tree11
]
def test_growth_function_upper_bound():
assert growth_function_upper_bound(Tree(Tree(), Tree()), n_features=10, n_classes=3)(1) == 3
assert growth_function_upper_bound(Tree(Tree(), Tree()), n_features=10, n_classes=3)(2) == 3 + 6
def test_compute_upper_bound_leaf(self):
leaf = Tree()
pfub = PartitioningFunctionUpperBound(leaf, 10)
assert pfub(4,1) == 1
assert pfub(4,2) == 0