def train(self, X, y, intercept=False **kwarg): if intercept == False: self.X = prepend_ones_col(X) self.y = y self.find_theta()
def normalEquationRegression(X, y):
'''Assuming rows correspond to samples'''
X_new = prepend_ones_col(X)
temp = np.dot(X_new.T, X_new)
temp = np.linalg.inv(temp)
temp = np.dot(temp, X_new.T)
theta = np.dot(temp, y)
return theta
def normalEquationRidgeRegression(X, y, lmbd=0.1):
'''Assuming rows correspond to samples'''
X_new = prepend_ones_col(X)
_, dim = X_new.shape
temp = np.dot(X_new.T, X_new) + np.eye(dim) * (lmbd**2)
temp = np.linalg.inv(temp)
temp = np.dot(temp, X_new.T)
theta = np.dot(temp, y)
return theta
def gradientDescentAutogradLasso(X, y, alpha=0.01, lmbd=0.1, it=300):
X_new = prepend_ones_col(X)
X_new = anp.array(X_new)
y = anp.array(y)
th = anp.random.rand(X_new.shape[1])
for i in range(it):
dw = lasso_grad(th, X_new, y, lmbd)
th = th - alpha * (dw)
return th
def gradientDescentAutogradRegression(X, y, alpha=0.001, it=1000):
X_new = prepend_ones_col(X)
X_new = anp.array(X_new)
n, m = X_new.shape
th = anp.array([0.] * m)
for i in range(it):
dw = rms_grad(th, X_new, y)
th = th - alpha * (dw)
return th
def gradientDescentPytorchRegression(X, y, alpha=0.001, it=1000):
X_new = torch.from_numpy(prepend_ones_col(X))
y = torch.from_numpy(y[:, None])
n, m = X_new.shape
th = Variable(torch.rand(m, 1), requires_grad=True)
for i in range(it):
error = cost(th, X_new, y)
error.backward()
th = Variable(th - alpha * th.grad, requires_grad=True)
nump = th.detach().numpy()
return nump.squeeze()
def gradientDescentRegression(X, y, alpha=0.001, it=1000):
X_new = prepend_ones_col(X)
n, m = X_new.shape
th = np.array([0.] * m)
for i in range(it):
yhat = np.matmul(X_new, th[:, None])
e = y[:, None] - yhat
weighted_e = X_new * e
sumz = weighted_e.sum(axis=0)
th = th + (2 * alpha * (sumz))
return th
def sgdRegression(X, y, alpha=0.001, it=100):
X_new = prepend_ones_col(X)
n, m = X_new.shape
th = np.zeros(m)
ths = []
for i in range(it):
for j in range(n):
yhat = (X_new[j, :] * th).sum()
e = y[j] - yhat
weighted_e = X_new[j, :] * e
th = th + (2 * alpha * (weighted_e))
ths.append(np.copy(th))
return th, ths
def coodrdinateDescentRegression(X, y, it=100):
X_new = prepend_ones_col(X)
n, m = X_new.shape
th = np.array([0.] * m)
ths = []
for iteration in range(it): # for a num of iterations
for i in range(m): # for num of thetas
# calculate y_hat without th_i*X_i
y_hat_red = np.dot(np.delete(X_new, i, axis=1),
np.delete(th, i, axis=0))
temp = np.dot(X_new[:, i].T, (y - y_hat_red))
th[i] = temp / np.matmul(X_new[:, i].T, X_new[:, i])
ths.append(np.copy(th))
return th, ths
def coodrdinateDescentLasso(X, y, lmbd=0.2, it=100):
X_new = prepend_ones_col(X)
n, m = X_new.shape
th = np.array([0.] * m)
for iteration in range(it): # for a num of iterations
for i in range(m): # for num of thetas
# calculate y_hat without th_i*X_i
y_hat_red = np.dot(np.delete(X_new, i, axis=1),
np.delete(th, i, axis=0))
p_i = np.dot(X_new[:, i].T, (y - y_hat_red))
z_i = np.matmul(X_new[:, i].T, X_new[:, i])
const = (lmbd) / 2
if p_i < -const:
th[i] = (p_i + const) / z_i
elif p_i >= -const and p_i <= const:
th[i] = 0
else: # p_i > const
th[i] = (p_i - const) / z_i
return th