(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),
]
##### 16.1 问题
# change tuples to lists
data = list(map(list, data))
# each element is [1, experience, salary]
x = [[1] + row[:2] for row in data]
# each element is paid_account
y = [row[2] for row in data]
print("linear regression:")
rescaled_x = rescale(x)
beta = estimate_beta(rescaled_x, y)
print(beta)
##### 16.2 Logistic函数
# What if we try to model such data as output?
#
# We will try to predict whether or not an individual has a PhD based on other information.
###########################################################################################
# This relationship doesn't show much promise.
plt.scatter(work_hours_per_day,noPhD)
plt.title("noPhD by work_hours_per_day")
plt.xlabel("work_hours_per_day")
plt.ylabel("noPhD")
plt.show()
# The r-squared is about as low as it can be.
random.seed(0)
xtest = work_hours_per_day_list
beta = estimate_beta(xtest, noPhD)
print "\nbeta=", beta, "\nr-squared=", multiple_r_squared(xtest, noPhD, beta), "\n\n"
# The regression line is almost flat.
plt.scatter(work_hours_per_day,noPhD)
plt.title("noPhD by work_hours_per_day")
plt.xlabel("work_hours_per_day")
plt.ylabel("noPhD")
plt.plot([min(work_hours_per_day),max(work_hours_per_day)],[predict([1,min(work_hours_per_day)],beta),predict([1,max(work_hours_per_day)],beta)])
plt.show()
###########################################################################################
# This one is a bit more promising, but there is alot of overlap.
plt.scatter(daily_minutes_good,noPhD)
plt.title("noPhD by daily_minutes_good")
def squared_error_ridge_gradient(x_i, y_i, beta, alpha):
return add_vectors(squared_error_gradient(x_i, y_i, beta),
ridge_penalty_gradient(beta, alpha))
def estimate_beta_ridge(xs, ys, alpha):
beta_initial = [random.random() for _ in range(len(xs[0]))]
return minimize_stochastic(
partial(squared_error_ridge, alpha=alpha),
partial(squared_error_ridge_gradient, alpha=alpha), xs, ys,
beta_initial, 0.0001)
random.seed(0)
trainer_beta = estimate_beta(trainer_party_stats, trainer_badge_counts)
print('trainer_beta = %s' % trainer_beta)
random.seed(0)
trainer_beta_ridge_0 = estimate_beta_ridge(trainer_party_stats,
trainer_badge_counts, 0)
print('trainer_beta_ridge_0 = %s' % trainer_beta_ridge_0)
random.seed(0)
trainer_beta_ridge_point_01 = estimate_beta_ridge(trainer_party_stats,
trainer_badge_counts, 0.01)
print('trainer_beta_ridge_point_01 = %s' % trainer_beta_ridge_point_01)
random.seed(0)
trainer_beta_ridge_point_1 = estimate_beta_ridge(trainer_party_stats,
trainer_badge_counts, 0.1)
def estimate_sample_beta(sample):
x_sample, y_sample = zip(*sample)
return estimate_beta(x_sample, y_sample)
return reduce(vector_add,
[logistic_log_gradient_i(x_i, y_i, beta)
for x_i, y_i in zip(x,y)])
if __name__ == "__main__":
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 = list(map(list, data)) # change tuples to lists
x = [[1] + row[:2] for row in data] # each element is [1, experience, salary]
y = [row[2] for row in data] # each element is paid_account
print("linear regression:")
rescaled_x = rescale(x)
beta = estimate_beta(rescaled_x, y)
print(beta)
print("logistic regression:")
random.seed(0)
x_train, x_test, y_train, y_test = train_test_split(rescaled_x, y, 0.33)
# want to maximize log likelihood on the training data
fn = partial(logistic_log_likelihood, x_train, y_train)
gradient_fn = partial(logistic_log_gradient, x_train, y_train)
# pick a random starting point
beta_0 = [1, 1, 1]
# and maximize using gradient descent
for i, j in enumerate(list_of_dates):
if (i == 34 or i == 217 or i == 399 or i == 582):
multiplyer = multiplyer * -1
season[i - 1] = prev + (multiplyer / 100.0)
prev = season[i - 1]
alpha = ([1] * 731)
random.seed(0)
x_y = zip(alpha, discount_jack, season, count_by_city[0][0])
training = random.sample(x_y, 183) # 25% of the entire data
alpha_train, discount_train, season_train, count_j_train = zip(*training)
x = zip(alpha_train, discount_train, season_train)
y = count_j_train
print len(x)
random.seed(0)
beta1 = estimate_beta(x, y)
print "beta", beta1
print "r-squared", multiple_r_squared(x, y, beta1)
print
#%% 1. Plot
plot_set1 = zip(alpha_train, discount_train, season_train, y)
plot_set1.sort(key=lambda x: x[2])
alpha_train1, discount_train1, season_train1, y1 = zip(*plot_set1)
y_pred1 = []
for i in range(len(count_j_train)):
y_pred1.append(beta1[0] + beta1[1] * discount_train1[i] +
beta1[2] * float(season_train1[i]))
plt.figure(51)
plt.scatter(discount_train1, y1, color='g', label='Data')
plt.scatter(discount_train1, y_pred1, color='r', label='Regression', s=10)
plt.legend()