def plot_linear():
X, Y = utils.load_reg_data()
w = linear_normal(X, Y)
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(X=X, Y=Y, Z=(X + Y) * w / (X + Y))
plt.xlabel('x_data')
plt.ylabel('y_data')
# return plot
return plt
def plot_linear():
# return plot
X, Y = utils.load_reg_data()
w = linear_normal(X, Y)
x_min, x_max = X.min(), X.max()
x = np.linspace(x_min, x_max, num=10000)
x = np.insert(x, 0, 1, 1)
fig = plt.figure()
plt.plot(x[:1], x @ w)
plt.scatter(X, Y, c='r')
return fig
def plot_poly():
# return plot
X, Y = utils.load_reg_data()
w = poly_normal(X, Y)
plt.plot(X, Y, X, (w[2] * X**2 + w[1] * X + w[0]))
plt.title('Polynomial Regression')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
def plot_linear():
'''
Returns:
Figure: the figure plotted with matplotlib
'''
X, Y = utils.load_reg_data()
plt.scatter(X, Y, s=None, color='black')
y = linear_normal(X, Y)
Z = X
n_by_d = Z.shape
Z_new = torch.ones(n_by_d[0], 1)
Z = torch.cat((Z_new, Z), 1)
plt.plot(X, torch.matmul(Z, y), 'g')
myplot = plt.gcf()
myplot.savefig('3c.png')
def nn_iris():
X, y = utils.load_reg_data()
n = X.shape[0]
X_test = X[:int(n * 0.3), :]
y_test = y[:int(n * 0.3)]
# model
X_train = X[int(n * 0.3) + 1:, :]
y_train = y[int(n * 0.3) + 1:]
y_hat = nn(X_train, y_train, X_test)
print(y_hat)
print(y_test)
error = np.count_nonzero(np.abs(y_hat - y_test)) / y_test.shape[0]
return error
def plot_linear():
X, y = utils.load_reg_data()
w_numpy = linear_normal(X, y)
X = np.hstack((X, np.ones((X.shape[0], 1), dtype=X.dtype)))
X = torch.tensor(X, requires_grad=True).type(torch.FloatTensor)
y = torch.tensor(y, requires_grad=True).type(torch.FloatTensor)
# return plot
X_numpy = X.detach().numpy()[:, 0]
y_numpy = y.detach().numpy()
# utils.contour_plot(min(X_numpy), max(X_numpy), min(y_numpy), max(y_numpy), M, ngrid = 33)
plt.figure()
plt.plot(X_numpy, y_numpy)
plt.plot(X_numpy, X_numpy * w_numpy[1] + w_numpy[0])
plt.title('Linear Normal Regression')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
def plot_poly():
'''
Returns:
Figure: the figure plotted with matplotlib
'''
X, Y = utils.load_reg_data()
plt.scatter(X, Y, s=None, color='black')
y = poly_normal(X, Y)
Z = X
n_by_d = Z.shape
Z_new = torch.ones(n_by_d[0], 1)
Z = torch.cat((Z, Z * Z), 1)
for j in range(0, n_by_d[1] - 1):
for k in range(j + 1, n_by_d[1]):
j_col = torch.FloatTensor([[Z[i][j]] for i in range(0, n_by_d[0])])
k_col = torch.FloatTensor([[Z[i][k]] for i in range(0, n_by_d[0])])
Z = torch.cat((Z, j_col * k_col), 1)
Z = torch.cat((Z_new, Z), 1)
plt.plot(X, torch.matmul(Z, y), 'g')
myplot = plt.gcf()
myplot.savefig('polynomial_regression_fit.png')
plt.show()
def plot_poly():
# return plot
X, Y = utils.load_reg_data()
length = X.shape[1]
X_p = X.copy()
for i in range(length):
for j in range(i, length):
X_p = np.insert(X_p, X_p.shape[1], X_p[:,i]*X_p[:,j], 1)
w = linear_normal(X_p, Y)
x_min, x_max = X.min(), X.max()
x = np.linspace(x_min, x_max, num=10000).reshape((-1,1))
print(x.shape)
for i in range(1):
for j in range(i, 1):
x = np.insert(x, 1, x[:,i]*x[:,j], 1)
x = np.insert(x, 0, 1, 1)
fig = plt.figure()
print(x.shape)
plt.plot(x[:,1], x @ w)
plt.scatter(X, Y, c='r')
return fig
while (counter < num_iter):
cprev = c
# update0 = lrate * partial_cost_theta0(w0,w1,X,Y)
update1 = lrate * partial_cost_thetal(w0, w1, X, Y)
w1 -= update1
theta1s.append(w1)
c = cost(w0, w1, X, Y)
costs.append(c)
counter += 1
return w1, costs, theta1s
# w0 -= update0
# theta0s.append(w0)
X, Y = utils.load_reg_data()
w1, costs, theta1s = linear_gd(X, Y, 0.1, 1000)
print(w1)
plt.scatter(costs, theta1s)
plt.show()
def cost(theta0, theta1, x, y):
#Initialize cost
J = 0
# The number of observations
m = len(x)
# Loop through each obervation
for i in range(m):
# Compute the hypothesis
h = theta1 * x[i] + theta0