def graph(self):
"""
Graph the model and data
:return None
"""
graph_function_and_data(lambda x: func(*self.theta, x),
x_data=self.x,
y_data=self.y)
def fit(self,
x,
y,
init_theta=None,
lr=0.001,
steps=1000,
graph=False,
dx=0.0001):
"""
Fit the model
:param x: X data
:param y: Y data
:param init_theta: Initial Theta values; can be set to none for all 0s
:param lr: Learning Rate
:param steps: Number of steps do go through
:param graph: Set true to graph function and data
:param to_print: Print loss and step number every this number
:param batch_size: Size of batches
:return: None
"""
self._check_length(x, y)
self.x = list(x)
self.y = list(x)
func = self.func
if init_theta is None:
init_theta = [0 for _ in range(self.k)]
try:
_ = self.func(*init_theta, 0)
except TypeError:
raise Error("Initial Theta does not match with function")
def _loss(*args):
loss = 0
for i in range(len(x)):
loss += (func(*args, x[i]) - y[i])**2
loss = loss * (1 / len(x))
return loss
optim = GradientDescentOptimizer(_loss, num_theta=self.k)
theta = optim.optimize(learning_rate=lr,
steps=steps,
init_theta=init_theta)
if graph:
graph_function_and_data(lambda x: func(*theta, x),
x_data=x,
y_data=y)
return theta
# Data
x1 = [0.00, 4.48, 8.96, 13.44, 17.92, 22.41, 26.89, 31.37, 35.85, 40.33, 44.81]
y1 = [0.00, 2.89, 5.14, 6.74, 7.71, 8.03, 7.71, 6.74, 5.14, 2.89, 0.00]
# Defining Cost Function to optimize
def cost_function(a, b, c):
j = 1 / 11
sigma = 0
for i in range(11):
sigma = sigma + (y1[i] - func(a, b, c, x1[i]))**2
j = j * sigma
return j
# Function to fit the points
def func(a, b, c, x):
return a * (x**2) + b * x + c
# Define the function
# This can be compressed to:
start_time = time.time()
theta = gradient_descent.optimize(cost_function, 7e-7, 50000, [0, 0, 0],
0.0001, 3)
print("--- %s seconds ---" % (time.time() - start_time))
# Graph the function by using the theta learnt
graph_function_and_data(lambda x: func(*theta, x), x_data=x1, y_data=y1)