In [16]:
%matplotlib inline
from __future__ import division
from wwd import *
from linear_regression import *
from ml import *
import matplotlib.pyplot as plt
import seaborn as sns
sns.set_context('poster')
import math
In [2]:
data = [(0.7,48000,1),(1.9,48000,0),(2.5,60000,1),(4.2,63000,0),(6,76000,0),(6.5,69000,0),(7.5,76000,0),(8.1,88000,0),(8.7,83000,1),(10,83000,1),(0.8,43000,0),(1.8,60000,0),(10,79000,1),(6.1,76000,0),(1.4,50000,0),(9.1,92000,0),(5.8,75000,0),(5.2,69000,0),(1,56000,0),(6,67000,0),(4.9,74000,0),(6.4,63000,1),(6.2,82000,0),(3.3,58000,0),(9.3,90000,1),(5.5,57000,1),(9.1,102000,0),(2.4,54000,0),(8.2,65000,1),(5.3,82000,0),(9.8,107000,0),(1.8,64000,0),(0.6,46000,1),(0.8,48000,0),(8.6,84000,1),(0.6,45000,0),(0.5,30000,1),(7.3,89000,0),(2.5,48000,1),(5.6,76000,0),(7.4,77000,0),(2.7,56000,0),(0.7,48000,0),(1.2,42000,0),(0.2,32000,1),(4.7,56000,1),(2.8,44000,1),(7.6,78000,0),(1.1,63000,0),(8,79000,1),(2.7,56000,0),(6,52000,1),(4.6,56000,0),(2.5,51000,0),(5.7,71000,0),(2.9,65000,0),(1.1,33000,1),(3,62000,0),(4,71000,0),(2.4,61000,0),(7.5,75000,0),(9.7,81000,1),(3.2,62000,0),(7.9,88000,0),(4.7,44000,1),(2.5,55000,0),(1.6,41000,0),(6.7,64000,1),(6.9,66000,1),(7.9,78000,1),(8.1,102000,0),(5.3,48000,1),(8.5,66000,1),(0.2,56000,0),(6,69000,0),(7.5,77000,0),(8,86000,0),(4.4,68000,0),(4.9,75000,0),(1.5,60000,0),(2.2,50000,0),(3.4,49000,1),(4.2,70000,0),(7.7,98000,0),(8.2,85000,0),(5.4,88000,0),(0.1,46000,0),(1.5,37000,0),(6.3,86000,0),(3.7,57000,0),(8.4,85000,0),(2,42000,0),(5.8,69000,1),(2.7,64000,0),(3.1,63000,0),(1.9,48000,0),(10,72000,1),(0.2,45000,0),(8.6,95000,0),(1.5,64000,0),(9.8,95000,0),(5.3,65000,0),(7.5,80000,0),(9.9,91000,0),(9.7,50000,1),(2.8,68000,0),(3.6,58000,0),(3.9,74000,0),(4.4,76000,0),(2.5,49000,0),(7.2,81000,0),(5.2,60000,1),(2.4,62000,0),(8.9,94000,0),(2.4,63000,0),(6.8,69000,1),(6.5,77000,0),(7,86000,0),(9.4,94000,0),(7.8,72000,1),(0.2,53000,0),(10,97000,0),(5.5,65000,0),(7.7,71000,1),(8.1,66000,1),(9.8,91000,0),(8,84000,0),(2.7,55000,0),(2.8,62000,0),(9.4,79000,0),(2.5,57000,0),(7.4,70000,1),(2.1,47000,0),(5.3,62000,1),(6.3,79000,0),(6.8,58000,1),(5.7,80000,0),(2.2,61000,0),(4.8,62000,0),(3.7,64000,0),(4.1,85000,0),(2.3,51000,0),(3.5,58000,0),(0.9,43000,0),(0.9,54000,0),(4.5,74000,0),(6.5,55000,1),(4.1,41000,1),(7.1,73000,0),(1.1,66000,0),(9.1,81000,1),(8,69000,1),(7.3,72000,1),(3.3,50000,0),(3.9,58000,0),(2.6,49000,0),(1.6,78000,0),(0.7,56000,0),(2.1,36000,1),(7.5,90000,0),(4.8,59000,1),(8.9,95000,0),(6.2,72000,0),(6.3,63000,0),(9.1,100000,0),(7.3,61000,1),(5.6,74000,0),(0.5,66000,0),(1.1,59000,0),(5.1,61000,0),(6.2,70000,0),(6.6,56000,1),(6.3,76000,0),(6.5,78000,0),(5.1,59000,0),(9.5,74000,1),(4.5,64000,0),(2,54000,0),(1,52000,0),(4,69000,0),(6.5,76000,0),(3,60000,0),(4.5,63000,0),(7.8,70000,0),(3.9,60000,1),(0.8,51000,0),(4.2,78000,0),(1.1,54000,0),(6.2,60000,0),(2.9,59000,0),(2.1,52000,0),(8.2,87000,0),(4.8,73000,0),(2.2,42000,1),(9.1,98000,0),(6.5,84000,0),(6.9,73000,0),(5.1,72000,0),(9.1,69000,1),(9.8,79000,1),]
data = map(list, data) # change tuples to lists
In [3]:
x = [[1] + row[:2] for row in data]
y = [row[2] for row in data]
In [4]:
rescaled_x = rescale(x)
beta = estimate_beta(rescaled_x, y)
predictions = [predict(x_i, beta) for x_i in rescaled_x]
In [7]:
plt.scatter(predictions, y)
Out[7]:
In [35]:
def logistic(x):
return 1.0 / (1 + math.exp(-x))
def logistic_prime(x):
return logistic(x) * (1 - logistic(x))
def logistic_log_likelihood_i(x_i, y_i, beta):
if y_i == 1:
return math.log(logistic(dot(x_i, beta)))
if y_i == 0:
return math.log(1 - logistic(dot(x_i, beta)))
# assume points are independent
def logistic_log_likelihood(x, y, beta):
return sum(logistic_log_likelihood_i(x_i, y_i, beta)
for x_i, y_i in zip(x, y))
# Gradients
def logistic_log_partial_ij(x_i, y_i, beta, j):
"""i is index of point and j is index of derivative"""
return (y_i - logistic(dot(x_i, beta))) * x_i[j]
def logistic_log_gradient_i(x_i, y_i, beta):
"""gradient of ll for ith point"""
return [logistic_log_partial_ij(x_i, y_i, beta, j)
for j, _ in enumerate(beta)]
def logistic_log_gradient(x, y, beta):
return reduce(vector_add,
[logistic_log_gradient_i(x_i, y_i, beta)
for x_i, y_i in zip(x,y)])
In [37]:
random.seed(0)
x_train, x_test, y_train, y_test = train_test_split(rescaled_x, y, 0.33)
In [38]:
fn = partial(logistic_log_likelihood, x_train, y_train)
gradient_fn = partial(logistic_log_gradient, x_train, y_train)
beta_0 = [random.random() for _ in range(3)]
#beta_hat = maximize_batch(fn, gradient_fn, beta_0)
beta_hat = maximize_stochastic(logistic_log_likelihood_i,
logistic_log_gradient_i,
x_train, y_train, beta_0)
In [39]:
beta_hat
Out[39]:
In [40]:
tp = fp = tn = fn = 0
for x_i, y_i in zip(x_test, y_test):
predict = logistic(dot(beta_hat, x_i))
if y_i == 1 and predict >= 0.5:
tp += 1
elif y_i == 1:
fn += 1
elif predict >= 0.5:
fp += 1
else:
tn += 1
In [41]:
precision(tp, fp, fn, tn)
Out[41]:
In [42]:
recall(tp, fp, fn, tn)
Out[42]:
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