def fit(self, X, y):
# If polynomial transformation
if self.poly_degree:
X = polynomial_features(X, degree=self.poly_degree)
n_samples, n_features = np.shape(X)
X_X = X.T.dot(X)
# Least squares approximate of beta
beta_hat = np.linalg.pinv(X_X).dot(X.T).dot(y)
# The posterior parameters can be determined analytically since we assume
# conjugate priors for the likelihoods.
# Normal prior / likelihood => Normal posterior
mu_n = np.linalg.pinv(X_X + self.omega0).dot(
X_X.dot(beta_hat) + self.omega0.dot(self.mu0))
omega_n = X_X + self.omega0
# Scaled inverse chi-squared prior / likelihood => Scaled inverse chi-squared posterior
nu_n = self.nu0 + n_samples
sigma_sq_n = (1.0 / nu_n) * (self.nu0 * self.sigma_sq0 + \
(y.T.dot(y) + self.mu0.T.dot(self.omega0).dot(self.mu0) - mu_n.T.dot(
omega_n.dot(mu_n))))
# Simulate parameter values for n_draws
beta_draws = np.empty((self.n_draws, n_features))
for i in range(self.n_draws):
sigma_sq = self._draw_scaled_inv_chi_sq(n=1,
df=nu_n,
scale=sigma_sq_n)
beta = multivariate_normal.rvs(size=1,
mean=mu_n[:, 0],
cov=sigma_sq *
np.linalg.pinv(omega_n))
# Save parameter draws
beta_draws[i, :] = beta
# Select the mean of the simulated variables as the ones used to make predictions
self.w = np.mean(beta_draws, axis=0)
# Lower and upper boundary of the credible interval
l_eti = 50 - self.cred_int / 2
u_eti = 50 + self.cred_int / 2
self.eti = np.array([[np.percentile(beta_draws[:, i], q=l_eti), np.percentile(beta_draws[:, i], q=u_eti)] \
for i in range(n_features)])
def predict(self, X, eti=False):
# If polynomial transformation
if self.poly_degree:
X = polynomial_features(X, degree=self.poly_degree)
y_pred = X.dot(self.w)
# If the lower and upper boundaries for the 95%
# equal tail interval should be returned
if eti:
lower_w = self.eti[:, 0]
upper_w = self.eti[:, 1]
y_lower_pred = X.dot(lower_w)
y_upper_pred = X.dot(upper_w)
return y_pred, y_lower_pred, y_upper_pred
return y_pred
def predict(self, X, eti=False):
# If polynomial transformation
if self.poly_degree:
X = polynomial_features(X, degree=self.poly_degree)
y_pred = X.dot(self.w)
# If the lower and upper boundaries for the 95%
# equal tail interval should be returned
if eti:
lower_w = self.eti[:, 0]
upper_w = self.eti[:, 1]
y_lower_pred = X.dot(lower_w)
y_upper_pred = X.dot(upper_w)
return y_pred, y_lower_pred, y_upper_pred
return y_pred
def fit(self, X, y):
# If polynomial transformation
if self.poly_degree:
X = polynomial_features(X, degree=self.poly_degree)
n_samples, n_features = np.shape(X)
X_X = X.T.dot(X)
# Least squares approximate of beta
beta_hat = np.linalg.pinv(X_X).dot(X.T).dot(y)
# The posterior parameters can be determined analytically since we assume
# conjugate priors for the likelihoods.
# Normal prior / likelihood => Normal posterior
mu_n = np.linalg.pinv(X_X + self.omega0).dot(X_X.dot(beta_hat)+self.omega0.dot(self.mu0))
omega_n = X_X + self.omega0
# Scaled inverse chi-squared prior / likelihood => Scaled inverse chi-squared posterior
nu_n = self.nu0 + n_samples
sigma_sq_n = (1.0/nu_n)*(self.nu0*self.sigma_sq0 + \
(y.T.dot(y) + self.mu0.T.dot(self.omega0).dot(self.mu0) - mu_n.T.dot(omega_n.dot(mu_n))))
# Simulate parameter values for n_draws
beta_draws = np.empty((self.n_draws, n_features))
for i in range(self.n_draws):
sigma_sq = self._draw_scaled_inv_chi_sq(n=1, df=nu_n, scale=sigma_sq_n)
beta = multivariate_normal.rvs(size=1, mean=mu_n[:,0], cov=sigma_sq*np.linalg.pinv(omega_n))
# Save parameter draws
beta_draws[i, :] = beta
# Select the mean of the simulated variables as the ones used to make predictions
self.w = np.mean(beta_draws, axis=0)
# Lower and upper boundary of the credible interval
l_eti = 50 - self.cred_int/2
u_eti = 50 + self.cred_int/2
self.eti = np.array([[np.percentile(beta_draws[:,i], q=l_eti), np.percentile(beta_draws[:,i], q=u_eti)] \
for i in range(n_features)])
def fit(self, X, y):
X_transformed = polynomial_features(X, degree=self.degree)
super(PolynomialRegression, self).fit(X_transformed, y)
def fit(self, X, y):
X_transformed = normalize(polynomial_features(X, degree=self.degree))
super(LassoRegression, self).fit(X_transformed, y)
def fit(self, X, y):
X = normalize(polynomial_features(X, degree=self.degree))
super(ElasticNet, self).fit(X, y)
def predict(self, X):
X = normalize(polynomial_features(X, degree=self.degree))
return super(ElasticNet, self).predict(X)
def fit(self, X, y):
X = normalize(polynomial_features(X, degree=self.degree))
super(PolynomialRidgeRegression, self).fit(X, y)
def predict(self, X):
X = normalize(polynomial_features(X, degree=self.degree))
return super(PolynomialRidgeRegression, self).predict(X)
def fit(self, X, y):
X = polynomial_features(X, degree=self.degree)
super(PolynomialRegression, self).fit(X, y)
def predict(self, X):
X = polynomial_features(X, degree=self.degree)
return super(PolynomialRegression, self).predict(X)
def predict(self, X):
X_transformed = normalize(polynomial_features(X, degree=self.degree))
return super(LassoRegression, self).predict(X_transformed)
def fit(self, X, y):
X = polynomial_features(X, degree=self.degree)
super(PolynomialRegression, self).fit(X, y)
def predict(self, X):
X = normalize(polynomial_features(X, degree=self.degree))
return super(ElasticNet, self).predict(X)
def fit(self, X, y):
X = normalize(polynomial_features(X, degree=self.degree))
super(ElasticNet, self).fit(X, y)
def predict(self, X):
X = normalize(polynomial_features(X, degree=self.degree))
return super(PolynomialRidgeRegression, self).predict(X)
def fit(self, X, y):
X = normalize(polynomial_features(X, degree=self.degree))
super(PolynomialRidgeRegression, self).fit(X, y)
def predict(self, X):
X = polynomial_features(X, degree=self.degree)
return super(PolynomialRegression, self).predict(X)
