def cost(theta, X, y):
'''Return the gradient for given hypothesis function
@Params: X, y, theta'''
m = float(len(X)) # Number of training examples. The float is essential.
cost = (-1/m) * sum ((y * log(sigmoid(X.dot(theta)))) + ((1 - y) * log(1 - sigmoid(X.dot(theta)))))
grad = (1/m) * (X.T).dot((sigmoid(X.dot(theta)) - y))
return cost, grad
def gradients(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y, lam):
theta1_params = nn_params[0: (hidden_layer_size * (input_layer_size + 1))]
theta2_params = nn_params[(hidden_layer_size * (input_layer_size + 1)):]
theta_1 = theta1_params.reshape(hidden_layer_size, input_layer_size + 1)
theta_2 = theta2_params.reshape(num_labels, (hidden_layer_size + 1))
m = X.shape[0]
Z2 = np.c_[np.ones(m), X].dot(theta_1.T)
A2 = sigmoid(Z2)
Z3 = np.c_[np.ones(A2.shape[0]), A2].dot(theta_2.T)
A3 = HX = sigmoid(Z3)
d3 = A3 - y;
d2 = d3.dot(theta_2[:, 1:]) * sigmoidGradient(Z2)
Delta1 = d2.T.dot(np.c_[np.ones(m), X])
Delta2 = d3.T.dot(np.c_[np.ones(A2.shape[0]), A2])
theta_1[:, 0] = 0
theta_2[:, 0] = 0
Theta1Grad = ((1.0/m) * Delta1) + ((lam/m) * theta_1)
Theta2Grad = ((1.0/m) * Delta2) + ((lam/m) * theta_2)
grads = np.append(Theta1Grad.flatten(), Theta2Grad.flatten())
return grads
def costFunction(theta, X, y):
theta = np.matrix(theta)
X = np.matrix(X)
y = np.matrix(y)
first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
return np.sum(first - second) / (len(X))
def costFunction(nn_params, input_layer_size, hidden_layer_size, num_labels, X,
y, lam):
theta1_params = nn_params[0:(hidden_layer_size * (input_layer_size + 1))]
theta2_params = nn_params[(hidden_layer_size * (input_layer_size + 1)):]
theta_1 = theta1_params.reshape(hidden_layer_size, input_layer_size + 1)
theta_2 = theta2_params.reshape(num_labels, (hidden_layer_size + 1))
m = X.shape[0]
Z2 = np.c_[np.ones(m), X].dot(theta_1.T)
A2 = sigmoid(Z2)
Z3 = np.c_[np.ones(A2.shape[0]), A2].dot(theta_2.T)
A3 = HX = sigmoid(Z3)
firstPartOfCost = -((y) * np.log(HX))
secondPartOfCost = ((1.0 - y) * np.log(1.0 - HX))
allThetas = np.append(theta_1.flatten()[1:], theta_2.flatten()[1:])
regularizationTerm = (lam / (2.0 * m)) * np.sum(np.power(allThetas, 2))
J = ((1.0 / m) * np.sum(
np.sum(firstPartOfCost - secondPartOfCost))) + regularizationTerm
return J
def predict(theta1, theta2, x):
# Useful values
m = x.shape[0]
num_labels = theta2.shape[0]
print('shape x {}, theta1 {}, theta2 {}'.format(x.shape, theta1.shape,
theta2.shape))
# You need to return the following variable correctly
p = np.zeros(m)
# ===================== Your Code Here =====================
# Instructions : Complete the following code to make predictions using
# your learned neural network. You should set p to a
# 1-D array containing labels between 1 to num_labels.
#
x = np.c_[np.ones((m, 1)), x]
a2 = sigmoid(np.dot(x, theta1.T))
a2 = np.c_[np.ones((m, 1)), a2]
a3 = sigmoid(np.dot(a2, theta2.T))
p = np.argmax(a3, axis=1) + 1
return p
def forward_pass(self, inputs):
# We will calculate the output(s), by feeding the inputs forward through the network
# If a forward pass has occured before (i.e., bias term has been appended to y_hidden), then we have to remove the bias from the hidden neurons
if len(self.y_hidden)==(self.n_hidden+1):
self.y_hidden = self.y_hidden[1:]
# set hidden states and output states to zero
self.reset_activations()
# append term to be multiplied with the hidden layer's bias
inputs = np.append(1, inputs)
# activate hidden neurons
for i in range(self.n_hidden):
hidden_neuron = 0.0
for j in range(len(inputs)):
hidden_neuron += + inputs[j] * self.w_hidden[j,i]
self.y_hidden[i] = sigmoid(hidden_neuron)
# append term to be multiplied with the output layer's bias
self.y_hidden = np.append(1.0, self.y_hidden)
# activate output neurons
for i in range(self.n_out):
output_neuron = 0.0
for j in range(len(self.y_hidden)):
output_neuron += self.y_hidden[j] * self.w_out[j,i]
self.y_out[i] = sigmoid(output_neuron)
predictions = self.y_out.copy()
return predictions
def return_cost(theta, X, y, lmd):
J=0
m=y.size
J=(-1/m)*(y.dot(np.log(sigmoid(X.dot(theta))))+\
(1-y).dot(np.log(1-sigmoid(X.dot(theta)))))+\
(lmd/(2*m))*theta[1:].dot(theta[1:])
return J
def gradients(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y,
lam):
theta1_params = nn_params[0:(hidden_layer_size * (input_layer_size + 1))]
theta2_params = nn_params[(hidden_layer_size * (input_layer_size + 1)):]
theta_1 = theta1_params.reshape(hidden_layer_size, input_layer_size + 1)
theta_2 = theta2_params.reshape(num_labels, (hidden_layer_size + 1))
m = X.shape[0]
Z2 = np.c_[np.ones(m), X].dot(theta_1.T)
A2 = sigmoid(Z2)
Z3 = np.c_[np.ones(A2.shape[0]), A2].dot(theta_2.T)
A3 = HX = sigmoid(Z3)
d3 = A3 - y
d2 = d3.dot(theta_2[:, 1:]) * sigmoidGradient(Z2)
Delta1 = d2.T.dot(np.c_[np.ones(m), X])
Delta2 = d3.T.dot(np.c_[np.ones(A2.shape[0]), A2])
theta_1[:, 0] = 0
theta_2[:, 0] = 0
Theta1Grad = ((1.0 / m) * Delta1) + ((lam / m) * theta_1)
Theta2Grad = ((1.0 / m) * Delta2) + ((lam / m) * theta_2)
grads = np.append(Theta1Grad.flatten(), Theta2Grad.flatten())
return grads
def cost_function_reg(theta, X, y, lamda=0):
cost = np.mean(-y * np.log(sigmoid(np.dot(X, theta))) -
(1 - y) * np.log(1 - sigmoid(np.dot(X, theta)))) + lamda / (
2 * X.shape[0]) * sum(theta[1:] * theta[1:])
# 没有theta[0]
return cost
def costFunctionReg(theta, X, y, learningRate):
theta = np.matrix(theta)
X = np.matrix(X)
y = np.matrix(y)
first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
reg = (learningRate /
(2 * len(X))) * np.sum(np.power(theta[:, 1:theta.shape[1]], 2))
return np.sum(first - second) / len(X) + reg
def predict(theta1, theta2, x):
m = x.shape[0]
x = np.c_[np.ones(m), x]
h1 = sigmoid(np.dot(x, theta1.T))
h1 = np.c_[np.ones(h1.shape[0]), h1]
h2 = sigmoid(np.dot(h1, theta2.T))
p = np.argmax(h2, axis=1) + 1
return p
def value(self, x):
layer1 = sigmoid(np.dot(x, self.weights1))
output = sigmoid(np.dot(layer1, self.weights2))
if output[0][0] > 0.5:
print("White")
else:
print("Black")
def feedForward(theta, X):
t1, t2 = deserialize(theta)
m = X.shape[0]
a1 = X
z2 = a1 @ t1.T
a2 = np.insert(sigmoid(z2), 0, np.ones(m), axis=1)
z3 = a2 @ t2.T
h = sigmoid(z3)
return a1, z2, a2, z3, h
def sigmoid_gradient(z):
g = np.zeros(z.shape)
# ===================== Your Code Here =====================
# Instructions : Compute the gradient of the sigmoid function evaluated at
# each value of z (z can be a matrix, vector or scalar)
#
g = sigmoid(z) * (1 - sigmoid(z))
# ===========================================================
return g
def costFunction(theta, X, y):
m = len(y)
grad = np.zeros(np.shape(theta))
J = 0
thetat = theta.transpose()
for i in range(0,m):
J = J + 1.0/ m * ( -y[i] * np.log(sigmoid(thetat*X[i, :].transpose())) - (1 - y[i]) * np.log(1-sigmoid(thetat*X[i, :].transpose())))
for j in range(0, len(theta)):
for i in range(0, m):
grad[j] = grad[j] + 1.0 / m * (sigmoid(thetat*X[i,:].transpose())-y[i])* X[i,j]
return [J, grad]
def predict(theta1, theta2, x):
m = x.shape[0]
num_label = theta2.shape[0]
x = np.c_[np.ones(m), x] # 5000*401
p = np.zeros(m)
z2 = x.dot(theta1.T) # 5000*401
a2 = sigmoid(z2) # 5000*25
a2 = np.c_[np.ones(m), a2] #5000*26
z3 = a2.dot(theta2.T) # 5000*10
a3 = sigmoid(z3)
p = np.argmax(a3, axis=1)
p += 1
return p
def predict(theta1, theta2, X):
# Useful values
m = X.shape[0]
a1 = np.c_[np.ones(m), X] # 输入层
z2 = a1.dot(theta1.T)
a2 = np.insert(sigmoid(z2), 0, np.ones(m),
axis=1) # a2 = sigmoid(z2) # 隐藏层
z3 = a2.dot(theta2.T)
a3 = sigmoid(z3) # 输出层
p = np.argmax(a3, axis=1) + 1
return p
def regularized_cost(theta, X, y, l):
"""
don't penalize theta_0
args:
X: feature matrix, (m, n+1) # 插入了x0=1
y: target vector, (m, )
l: lambda constant for regularization
"""
thetaReg = theta[1:]
first = (-y*np.log(sigmoid(X@theta))) + (y-1)*np.log(1-sigmoid(X@theta))
reg = (thetaReg@thetaReg)*l / (2*len(X))
cost = np.mean(first) + reg
return cost
def cost(theta, X, y):
m = len(y)
grad = np.zeros(np.shape(theta))
J = 0.0
thetat = theta.transpose()
for i in range(0,m):
if y[i]==1:
J = J + 1.0/ m * ( -y[i] * np.log(sigmoid(thetat*X[i, :].transpose())))
else:
J = J + 1.0/ m * (-(1 - y[i]) * np.log(1-sigmoid(thetat*X[i, :].transpose())))
#J = J + 1.0/ m * ( -y[i] * np.log(sigmoid(thetat*X[i, :].transpose())) - (1 - y[i]) * np.log(1-sigmoid(thetat*X[i, :].transpose())))
print J
return J
def costFunctionReg(theta, X, y, RegParam):
'''
J = COSTFUNCTIONREG(theta, X, y, RegParam) computes the cost of using
theta as the parameter for regularized logistic regression and the
gradient of the cost w.r.t. to the parameters.
'''
(m, n) = X.shape
theta = theta.reshape((n, 1))
h = sigmoid(np.dot(X, theta))
# Regularize Cost function:
# NB. Regularization term starts at theta1
J = 1/m * (-np.dot(np.transpose(np.vstack(y)), np.log(h))
- np.dot(np.transpose(np.vstack(1-y)), np.log(1-h))) \
+ (RegParam/(2*m)) * np.sum(np.power(theta[1:n], 2))
# NB. Regularization term starts at theta1
# compute regularization term for all
grad = np.dot(np.transpose(X), (h-np.vstack(y)))/m \
+ np.dot((RegParam/m), theta)
# adjust for the fist term, theta0
grad[0] = np.dot(np.transpose(np.vstack(X.iloc[:, 0])),
(h - np.vstack(y))) / m
return J, grad.flatten()
def backprop(self, x, y):
"""Return a tuple ``(nabla_b, nabla_w)`` representing the
gradient for the cost function C_x. ``nabla_b`` and
``nabla_w`` are layer-by-layer lists of numpy arrays, similar
to ``self.biases`` and ``self.weights``."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# feedforward
activation = x
activations = [x] # list to store all the activations, layer by layer
zs = [] # list to store all the z vectors, layer by layer
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# backward pass
delta = self.cost_derivative(activations[-1], y) * \
sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
# Note that the variable l in the loop below is used a little
# differently to the notation in Chapter 2 of the book. Here,
# l = 1 means the last layer of neurons, l = 2 is the
# second-last layer, and so on. It's a renumbering of the
# scheme in the book, used here to take advantage of the fact
# that Python can use negative indices in lists.
for l in xrange(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return (nabla_b, nabla_w)
def gradient_reg(theta, X, y, lamda=0):
temp = np.zeros(X.shape[1])
temp[1:] = lamda / X.shape[0] * theta[1:] # 不惩罚第一项 theta[0]
grad = (1 / X.shape[0]) * np.dot(X.T, sigmoid(np.dot(X, theta)) - y) + temp
return grad
def lr_cost_function(theta, X, y, lmd):
m = y.size
# You need to return the following values correctly
cost = 0
grad = np.zeros(theta.shape)
# ===================== Your Code Here =====================
# Instructions : Compute the cost of a particular choice of theta
# You should set cost and grad correctly.
#
hypothesis = sigmoid(np.dot(X, theta))
reg_theta = theta[1:]
cost = np.sum(-y * np.log(hypothesis) - np.subtract(1, y) * np.log(np.subtract(1, hypothesis))) / m \
+ (lmd / (2 * m)) * np.sum(reg_theta * reg_theta)
error = np.subtract(hypothesis, y)
grad = np.dot(X.T, error) / m
grad[1:] = grad[1:] + reg_theta * (lmd / m)
# =========================================================
return cost, grad
def cost_function_reg(theta, X, y, lmd):
m = y.size
# You need to return the following values correctly
cost = 0
grad = np.zeros(theta.shape)
# ===================== Your Code Here =====================
# Instructions : Compute the cost of a particular choice of theta
# You should set cost and grad correctly.
#
h = sigmoid(np.dot(X, theta))
# no penalty for theta0
cost = 1. / m * np.sum(-y * np.log(h) - (1 - y) * np.log(1 - h))
cost = cost + lmd / (2. * m) * np.dot(theta,
theta) - lmd / (2. * m) * theta[0]**2
loss = h - y
grad = 1. / m * np.dot(np.transpose(X), loss) + lmd / (1. * m) * theta
grad[0] -= lmd / (1. * m) * theta[0]
# ===========================================================
return cost, grad
def cost_function_reg(theta, X, y, lmd):
m = y.size
# You need to return the following values correctly
cost = 0
grad = np.zeros(theta.shape)
# ===================== Your Code Here =====================
# Instructions : Compute the cost of a particular choice of theta
# You should set cost and grad correctly.
#
hypothesis = sigmoid(np.dot(X, theta))
reg_theta = theta[1:]
cost = np.sum(-y * np.log(hypothesis) - (1 - y) * np.log(1 - hypothesis)) / m \
+ (lmd / (2 * m)) * np.sum(reg_theta * reg_theta)
normal_grad = (np.dot(X.T, hypothesis - y) / m).flatten()
grad[0] = normal_grad[0]
grad[1:] = normal_grad[1:] + reg_theta * (lmd / m)
# ===========================================================
return cost, grad
def predict_one_vs_all(all_theta, X):
m = X.shape[0]
num_labels = all_theta.shape[0]
# You need to return the following variable correctly;
p = np.zeros(m)
# Add ones to the X data matrix
X = np.c_[np.ones(m), X]
# ===================== Your Code Here =====================
# Instructions : Complete the following code to make predictions using
# your learned logistic regression parameters (one vs all).
# You should set p to a vector of predictions (from 1 to
# num_labels)
#
# Hint : This code can be done all vectorized using the max function
# In particular, the max function can also return the index of the
# max element, for more information see 'np.argmax' function.
#
y = sigmoid(np.matmul(X, all_theta.T))
p = np.argmax(y, axis=1)
p[p == 0] = 10
return p
def costReg(lam, theta, X, y): m = len(y) grad = np.zeros(np.shape(theta)) J = 0.0 thetat = theta.transpose() for i in range(0,m): if y[i]==1: J = J + 1.0/ m * ( -y[i] * np.log(sigmoid(thetat*X[i, :].transpose()))) else: J = J + 1.0/ m * (-(1 - y[i]) * np.log(1-sigmoid(thetat*X[i, :].transpose()))) #J = J + 1.0/ m * ( -y[i] * np.log(sigmoid(thetat*X[i, :].transpose())) - (1 - y[i]) * np.log(1-sigmoid(thetat*X[i, :].transpose()))) for j in range(1, len(theta)): J = J + lam/ (2*m) *theta[j]**2 print J return J
def cross_entropy_loss(theta, X, y):
m, n = X.shape
y = y.reshape((m, 1))
theta = theta.reshape((n, 1))
h = sigmoid(np.dot(X, theta))
J = np.sum(-y * np.log(h) - (1 - y) * np.log(1 - h)) / m
return J
def cross_entropy_loss_reg(theta, X, y, reg_lambda):
m, n = X.shape
y = y.reshape((m, 1))
theta = theta.reshape((n, 1))
h = sigmoid(np.dot(X, theta))
J = (2 * np.sum(-y * np.log(h) - (1 - y) * np.log(1 - h)) + reg_lambda * np.sum(theta ** 2)) / (2 * m)
return J
def CostFunction(theta, X, y):
m = len(y)
J = 0
grad = np.zeros(np.shape(theta))
g = sigmoid(np.dot(X, theta))
J = np.mean(((-y) * (np.log(g))) - ((1 - y) * (np.log(1 - g))))
grad = np.mean((g.reshape(m, 1) - y.reshape(m, 1)) * X, axis=0)
return J, grad
def feedForward(self, activation):
#return output of network
#iterate over all layers and feed activation forward
activation = np.array(activation)
for b, w in zip(self.biases, self.weights):
activation = sigmoid(np.matmul(w, activation) + b[0])
return activation
def plot_sigmoid():
x = np.linspace(1, 2000) / 100.0 - 10
y = sigmoid(x)
fig, ax1 = plt.subplots()
ax1.plot(x, y)
# set label of horizontal axis
ax1.set_xlabel('x')
# set label of vertical axis
ax1.set_ylabel('sigmoid(x)')
def grad(theta, X, y):
m = len(y)
grad = np.zeros(np.shape(theta))
thetat = theta.transpose()
for j in range(0, len(theta)):
for i in range(0, m):
grad[j] = grad[j] + 1.0 / m * (sigmoid(thetat*X[i,:].transpose())-y[i])* X[i,j]
return grad
def costFunction(theta, X, y, lamda): m = shape(X)[0] hypo = sigmoid(X.dot(theta)) term1 = log(hypo).T.dot(-y) term2 = log(1.0 - hypo).T.dot(1-y) left = (term1 - term2)/m right = theta.T.dot(theta)*lamda/(2*m) return left + right
def cross_entropy_gradient(theta, X, y):
m, n = X.shape
y = y.reshape((m, 1))
theta = theta.reshape((n, 1))
h = sigmoid(np.dot(X, theta))
grad = np.dot(np.transpose(X), h - y) / m
grad = np.ndarray.flatten(grad)
return grad
def cross_entropy_gradient_reg(theta, X, y, reg_lambda):
m, n = X.shape
y = y.reshape((m, 1))
theta = theta.reshape((n, 1))
h = sigmoid(np.dot(X, theta))
grad = (np.dot(np.transpose(X), h - y))
grad[1:] = grad[1:] + (reg_lambda / m) * theta[1:]
grad = np.ndarray.flatten(grad)
return grad
def gradReg(lam, theta, X, y): m = len(y) grad = np.zeros(np.shape(theta)) thetat = theta.transpose() for j in range(0, len(theta)): if (j!=0): grad[j] = grad[j] + lam/(2*m)*theta[j]**2 for i in range(0, m): grad[j] = grad[j] + 1.0 / m * (sigmoid(thetat*X[i,:].transpose())-y[i])* X[i,j] return grad
def costFunction(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y, lam):
theta1_params = nn_params[0: (hidden_layer_size * (input_layer_size + 1))]
theta2_params = nn_params[(hidden_layer_size * (input_layer_size + 1)):]
theta_1 = theta1_params.reshape(hidden_layer_size, input_layer_size + 1)
theta_2 = theta2_params.reshape(num_labels, (hidden_layer_size + 1))
m = X.shape[0]
Z2 = np.c_[np.ones(m), X].dot(theta_1.T)
A2 = sigmoid(Z2)
Z3 = np.c_[np.ones(A2.shape[0]), A2].dot(theta_2.T)
A3 = HX = sigmoid(Z3)
firstPartOfCost = -( (y) * np.log(HX) )
secondPartOfCost = ((1.0 - y) * np.log(1.0-HX))
allThetas = np.append(theta_1.flatten()[1:], theta_2.flatten()[1:])
regularizationTerm = (lam/(2.0 * m)) * np.sum( np.power(allThetas, 2))
J = ((1.0/m) * np.sum(np.sum(firstPartOfCost - secondPartOfCost)) ) + regularizationTerm
return J
def costFunctionReg(theta, X, y, _lambda):
'''costFunctionReg() - Regularized Logistic Regression Cost'''
m = len(X)
z = np.dot(X, theta.T)
h = sigmoid(z)
# cost
pos = np.dot(-y, np.log(h))
neg = np.dot(1 - y, np.log(1 - h))
cost = (pos - neg)
# regularization term
reg_para = (_lambda / (2. * m)) * sum([th ** 2 for th in theta[1:]])
# cost with regularization
costReg = (1. / m) * (cost + reg_para)
return costReg
def gradient(theta, X, y):
m = float(len(y))
print 'shape sigmoid(X.dot(theta)): ', shape(sigmoid(X.dot(theta)))
grad = (1/m) * (X.T).dot((sigmoid(X.dot(theta)) - y))
return grad
def sigSq(X):
return np.square(sigmoid(X))
def costFunction(theta, X, y): m = shape(X)[0] hypo = sigmoid(X.dot(theta)) term1 = log(hypo).T.dot(-y) term2 = log(1.0 - hypo).T.dot(1-y) return ((term1 - term2)/m).flatten()
def ex2():
#%% Load Data
#% The first two columns contains the exam scores and the third column
#% contains the label.
data = np.loadtxt('data/ex2data1.txt', delimiter=',')
x = data[:, :2]
y = data[:, 2]
#%% ==================== Part 1: Plotting ====================
#% We start the exercise by first plotting the data to understand the
#% the problem we are working with.
print(
'Plotting data with o indicating (y = 1) examples and x indicating (y = 0) examples.\n')
plotData(x, y)
plt.xlabel('Exam 1 Score')
plt.ylabel('Exam 2 Score')
plt.legend(['Admitted', 'Not admitted'], bbox_to_anchor=(1.5, 1))
plt.show()
#%% ============ Part 2: Compute Cost and Gradient ============
#% In this part of the exercise, you will implement the cost and gradient
#% for logistic regression. You neeed to complete the code in costFunction()
#% Setup the data matrix appropriately, and add ones for the intercept term
[m, n] = x.shape
#% Add intercept term to x and X_test
ones = np.ones(m)
X = np.array([ones, x[:, 0], x[:, 1]]).T
#% Initialize fitting parameters
initial_theta = np.zeros(n + 1)
#% Compute and display initial cost and gradient
cost = costFunction(initial_theta, X, y)
print('Cost at initial theta (zeros):\n{}'.format(cost))
# ============= Part 3: Optimizing using fmin() or minimize()
print('Gradient at initial theta (zeros):\n{}'.format(initial_theta))
# % In this exercise, you will use a built-in function (scipy.optimize.fmin) to find the
# % optimal parameters theta.
f = lambda t: costFunction(t, X, y) # % Set options for fmin()
fmin_opt = {'full_output': True, 'maxiter': 400, 'retall': True}
# % Run fmin to obtain the optimal theta
theta, cost, iters, calls, warnflag, allvecs = fmin(
f, initial_theta, **fmin_opt)
print('Cost at theta found by fmin(): {}'.format(cost))
print('theta: {}'.format(theta))
# % Set options for minimize()
# mini_opt = {'maxiter': 400, 'disp': True}
# % Run minimize to obtain the optimal theta
# results = minimize(f, initial_theta, method='Nelder-Mead', options=mini_opt)
# cost = results['fun']
# theta = results['x']
# print('Cost at theta found by minimize(): {}'.format(cost))
# print('theta: {}'.format(theta))
cost_change = [costFunction(allvecs[i], X, y) for i in range(156)]
plt.plot(cost_change)
plt.grid()
plt.title('cost function $y$ per iteration $x$')
plt.show() # % Print theta to screen
print('Cost at theta found by fmin:\n{}\n'.format(cost))
print('theta: \n')
print('{}\n'.format(theta))
# % Plot Boundary
plotDecisionBoundary(theta, X, y)
# % Show plot
plt.show()
# %% ============== Part 4: Predict and Accuracies ==============
# % After learning the parameters, you'll like to use it to predict the outcomes
# % on unseen data. In this part, you will use the logistic regression model
# % to predict the probability that a student with score 45 on exam 1 and
# % score 85 on exam 2 will be admitted.
# %
# % Furthermore, you will compute the training and test set accuracies of
# % our model.
# %
# % Your task is to complete the code in predict.m
# % Predict probability for a student with score 45 on exam 1
# % and score 85 on exam 2
scores = np.array([1, 45, 85])
prob = sigmoid(np.dot(scores, theta))
print(
'For a student with scores 45 and 85, we predict an admission probability of:\n{}\n\n'.format(prob))
# % Compute accuracy on our training set
p = predict(theta, X)
print('Train Accuracy: {}\n'.format(np.mean(np.double(p == y)) * 100))
def sigSqgrad(X):
return 2*(sigmoid(X))*sigmoidGrad(X)
def sigmoidGradient(z):
return sigmoid(z) * (1 - sigmoid(z))
def predict(theta, X):
p = sigmoid(X.dot(theta)) >= 0.5
return p
x1_abs = []
x1_ord = []
for i in range(0,len(label)):
if label[i]==1:
x1_abs.append(list_abs[i])
x1_ord.append(list_ord[i])
else:
x0_abs.append(list_abs[i])
x0_ord.append(list_ord[i])
sets = [[x0_abs,x0_ord,'o'],[x1_abs,x1_ord,'+']]
MultiScatter(sets)
zz = np.mat([[1,2,3],[4,5,6]])
zz = np.mat(1)
zz = np.mat([-723.2])
gg = sigmoid(zz)
print gg
[m, n] = np.shape(X)
initial_theta = np.zeros((n, 1))
result_jg = costFunction(initial_theta, X ,y)
print result_jg
#xx = map(lambda t: 0.206+t/25.0,range(-25,25, 1))
#yy = map(lambda t: 0.201+t/25.0,range(-25,25, 1))
#zz = [0.0]*len(xx)
#for i in range(0,len(xx)):
#Plot(xx,zz)