y = np.matrix((allData[:, -1])).T
n, d = X.shape
# Add a row of ones for the bias term
X = np.c_[np.ones((n, 1)), X]
# initialize the model
init_theta = np.matrix(
np.ones((d + 1, 1))
) * 10 # note that we really should be initializing this to be near zero, but starting it near [10,10] works better to visualize gradient descent for this particular problem
n_iter = 1500
alpha = 0.01
# Instantiate objects
lr_model = LinearRegression(init_theta=init_theta,
alpha=alpha,
n_iter=n_iter)
plotData1D(X[:, 1], y)
lr_model.fit(X, y)
plotRegLine1D(lr_model, X, y)
# Visualize the objective function convex shape
theta1_vals = np.linspace(-10, 10, 100)
theta2_vals = np.linspace(-10, 10, 100)
visualizeObjective(lr_model, theta1_vals, theta2_vals, X, y)
# Compute the closed form solution in one line of code
theta_closed_form = 0 # TODO: replace "0" with closed form solution
print "theta_closed_form: ", theta_closed_form
file = open(filePath,'r')
allData = np.loadtxt(file, delimiter=',')
X = np.matrix(allData[:,:-1])
y = np.matrix((allData[:,-1])).T
n,d = X.shape
# Standardize
mean = X.mean(axis=0)
std = X.std(axis=0)
X = (X - mean) / std
# Add a row of ones for the bias term
X = np.c_[np.ones((n,1)), X]
# initialize the model
init_theta = np.matrix(np.random.randn((d+1))).T
n_iter = 2000
alpha = 0.01
# Instantiate objects
lr_model = LinearRegression(init_theta = init_theta, alpha = alpha, n_iter = n_iter)
lr_model.fit(X,y)
# Compute the closed form solution in one line of code
thetaClosedForm = linalg.inv((X.T*X))*X.T*y # TODO: replace "0" with closed form solution
print "thetaClosedForm: ", thetaClosedForm
for i in range(my):
img[:,i] = img[:,i]/np.max(img[:,i])
xs = []
ys = []
for x in counts:
for y in counts[x]:
xs.append(x)
ys.append(y)
xs = np.array(xs)
ys = np.array(ys)
xs = xs.reshape((len(xs), 1))
ys = ys.reshape((len(ys), 1))
print ys.shape, xs.shape
x = LinearRegression()
y = x.fit(xs,ys)#,weight)
fig = pplot.figure()
ax = fig.add_subplot(111)
ax.imshow(img, interpolation='nearest',cmap=Reds,vmin=0,vmax=1,origin='lower')
ax.set_title("Distribution of degree per avalanche size")
ax.set_xlabel("Avalanche size s")
ax.set_ylabel("Degree of first defaulting node")
pplot.show()
