def minimize_stochastic(target_fn, gradient_fn, x, y, theta_0, alpha_0=0.01):
data = zip(x, y)
theta = theta_0 # initial guess
alpha = alpha_0 # initial step size
min_theta, min_value = None, float("inf") # the minimum so far
iterations_with_no_improvement = 0
# if we ever got 100 iterations with no improvement, stop
while iterations_with_no_improvement < 100:
value = sum(target_fn(x_i, y_i, theta) for x_i, y_i in data)
if value < min_value:
# if we have found a new minimum, remember it and go back to the
# original step size
min_theta, min_value = theta, value
iterations_with_no_improvement = 0
alpha = alpha_0
else:
# otherwise we are not improving, so try shrinking the step size
iterations_with_no_improvement = iterations_with_no_improvement + 1
alpha = alpha * 0.9
# and take a gradient step for each of the data points
for x_i, y_i in in_random_order(data):
gradient_i = gradient_fn(x_i, y_i, theta)
theta = vector_subtract(theta, scalar_multiply(alpha, gradient_i))
return min_theta
def minimize_stochastic(target_fn, gradient_fn, x, y, theta_0, alpha_0=0.01):
data = zip(x, y)
theta = theta_0 # initial guess
alpha = alpha_0 # initial step size
min_theta, min_value = None, float("inf") # the minimum so far
iterations_with_no_improvement = 0
# if we ever got 100 iterations with no improvement, stop
while iterations_with_no_improvement < 100:
value = sum(target_fn(x_i, y_i, theta) for x_i, y_i in data)
if value < min_value:
# if we have found a new minimum, remember it and go back to the
# original step size
min_theta, min_value = theta, value
iterations_with_no_improvement = 0
alpha = alpha_0
else:
# otherwise we are not improving, so try shrinking the step size
iterations_with_no_improvement = iterations_with_no_improvement + 1
alpha = alpha * 0.9
# and take a gradient step for each of the data points
for x_i, y_i in in_random_order(data):
gradient_i = gradient_fn(x_i, y_i, theta)
theta = vector_subtract(theta, scalar_multiply(alpha, gradient_i))
return min_theta
def remove_projection_from_vector(v, w):
"""If we want to find further components beyond the first, we first remove the
projections from the data using this function"""
"""projects v onto w and subtracts the result from v"""
return vector_subtract(v, project(v, w))