milk_tree_learner

gistfile1.txt

# to come

milk_tree_learner.ipynb

milk_tree_learner.py

# -*- coding: utf-8 -*-
# <nbformat>3.0</nbformat>

# <codecell>

import numpy as np
import milk

# <markdowncell>

# Simulate some labeled data in a two-dimensional feature space.

# <codecell>

features = np.random.randn(100,2) # 2d array of features: 100 examples of 2 features each
labels = np.empty(100)
for i in range(100):
    if features[i,0] < 0:
        if features[i,1] < -1:
            labels[i] = np.random.rand() < .001
        else:
            labels[i] = np.random.rand() < .999
    else:
        if features[i,1] < 1:
            labels[i] = np.random.rand() < .001
        else:
            labels[i] = np.random.rand() < .999

# <markdowncell>

# What is the decision tree for this data?

# <markdowncell>

# Since the data is two-dimensional, we can take a look at it easily.

# <codecell>

plot(features[labels==True,0], features[labels==True,1], 'kx', mec='k', ms=6, mew=3)
plot(features[labels==False,0], features[labels==False,1], 'wo', mec='k', ms=8, mew=1)
grid()

# <markdowncell>

# Fitting the model is easy:

# <codecell>

learner = milk.supervised.tree_learner()
model = learner.train(features, labels)

# <markdowncell>

# Using it is easy, too:

# <codecell>

model.apply([-1,1])

# <markdowncell>

# Visualizing the decision boundary is a bit of a pain...

# <codecell>

x_range = np.linspace(-3,3,100)
y_range = np.linspace(-3,3,100)

val = np.zeros((len(x_range), len(y_range)))

for i, x_i in enumerate(x_range):
    for j, y_j in enumerate(y_range):
        val[i,j] = model.apply([x_i,y_j])

imshow(val[::1,::-1].T, extent=[x_range[0],x_range[-1],y_range[0],y_range[-1]], cmap=cm.Greys)
plot(features[labels==True,0], features[labels==True,1], 'kx', mec='w', ms=7, mew=5)
plot(features[labels==True,0], features[labels==True,1], 'kx', mec='k', ms=5, mew=3)
plot(features[labels==False,0], features[labels==False,1], 'wo', mec='k', ms=8, mew=1)
grid()

# <markdowncell>

# And can we have a picture of the decision tree itself?  It is hidden in the model instance somewhere...

# <codecell>

model.tree

# <codecell>

model.tree.featid, model.tree.featval, model.tree.left, model.tree.right

# <codecell>

def describe_tree(node, prefix=''):
    print prefix + 'if x[%d] < %.2f:' % (node.featid, node.featval)
    if isinstance(node.left, milk.supervised.tree.Node):
        describe_tree(node.left, prefix+'    ')
    else:
        print prefix+'   ', node.left
    print prefix + 'else:'
    if isinstance(node.right, milk.supervised.tree.Node):
        describe_tree(node.right, prefix+'    ')
    else:
        print prefix+'   ', node.right

# <codecell>

describe_tree(model.tree)

# <markdowncell>

# Not as simple as it seemed in the lecture, huh?