def _fit_rvr_cost(var, K, w, H):
I = w.size
H_inv = np.diag(1 / H)
covariance = K @ H_inv @ K + var * np.eye(I)
f = fitting.gaussian_pdf(w, np.zeros(I), covariance)[0, 0]
f = -np.log(f)
return f
def _fit_blr_cost(var, X, w, var_prior):
I = X.shape[1]
covariance = var_prior * (X.transpose() @ X) + \
np.sqrt(var) ** 2 * np.eye(I)
f = fitting.gaussian_pdf(w, np.zeros(I), covariance)[0, 0]
f = -np.log(f)
return f
def _fit_slr_cost(var, X, w, H):
I = X.shape[1]
H_inv = np.diag(1 / H)
covariance = X.transpose() @ H_inv @ X + var * np.eye(I)
f = fitting.gaussian_pdf(w, np.zeros(I), covariance)[0, 0]
f = -np.log(f)
return f
def _fit_rvc_cost(psi, w, Hd, K):
I = K.shape[0]
L = I * (-np.log(
fitting.gaussian_pdf(psi.reshape(
(1, psi.size)), np.zeros(I), np.diag(1 / Hd))[0, 0]))
predictions = sigmoid(psi @ K)
for i in range(I):
y = predictions[i]
if w[i, 0] == 1:
L -= np.log(y)
else:
L -= np.log(1 - y)
return L
def _fit_klogr_cost(psi, X, w, var_prior, K):
I = X.shape[1]
L = I * (-np.log(
fitting.gaussian_pdf(psi.reshape(
(1, psi.size)), np.zeros(I), var_prior * np.eye(I))[0, 0]))
predictions = sigmoid(psi @ K)
for i in range(I):
y = predictions[i]
if w[i, 0] == 1:
L -= np.log(y)
else:
L -= np.log(1 - y)
return L
def _fit_logr_cost(phi, X, w, var_prior):
I = X.shape[1]
D = X.shape[0] - 1
L = I * (-np.log(
fitting.gaussian_pdf(phi.reshape(
(1, phi.size)), np.zeros(D + 1), var_prior * np.eye(D + 1))[0, 0]))
predictions = sigmoid(phi.reshape((1, D + 1)) @ X)
for i in range(I):
y = predictions[0, i]
if w[i, 0] == 1:
L -= np.log(y)
else:
L -= np.log(1 - y)
return L
elif argv[1] == "fit_by_linear":
granularity = 500
a = -5
b = 5
domain = np.linspace(a, b, granularity)
X, Y = np.meshgrid(domain, domain)
x = X.reshape((X.size, 1))
y = Y.reshape((Y.size, 1))
xy_matrix = np.append(x, y, axis=1)
# Compute the prior 2D normal distribution over phi
mu_1 = np.array([0, 0])
var_prior = 6
covariance_1 = var_prior * np.eye(2)
mvnpdf_1 = fitting.gaussian_pdf(xy_matrix, mu_1, covariance_1).reshape(
granularity, granularity)
plt.figure("Prior and posterior over phi")
plt.subplot(1, 2, 1)
plt.pcolor(X, Y, mvnpdf_1)
# Generate the training and test data
X_train = np.array([[1, 1, 1, 1, 1, 1], [-4, -1, -1, 0, 1, 3.5]])
w = np.array([4.5, 3, 2, 2.5, 2.5, 0]).reshape((6, 1))
X_test = domain.reshape((1, granularity))
X_test = np.append(np.ones((1, granularity)), X_test, axis=0)
# Fit Bayesian linear regression model
mu_test, var_test, var, A_inv = regression.fit_by_linear(
X_train, w, var_prior, X_test)
def _fit_dgpr_cost(var, K, w, var_prior):
I = K.shape[0]
covariance = var_prior * K @ K + var * np.eye(I)
f = fitting.gaussian_pdf(w, np.zeros(I), covariance)[0, 0]
f = -np.log(f)
return f
def _fit_gpr_cost(var, K, w, var_prior):
I = w.size
covariance = var_prior * K + (np.sqrt(var)**2) * np.eye(I)
f = fitting.gaussian_pdf(w, np.zeros(I), covariance)[0, 0]
f = -np.log(f)
return f
argv = sys.argv
if len(argv) != 2:
print("Usage: python test_fitting_pdf.py t_pdf|gamma_pdf|mul_t_pdf")
sys.exit(-1)
if argv[1] == "t_pdf":
plt.figure("T-distribution")
x = np.arange(-5, 5, 0.01)
mu = 0
sig = 1
px1 = fitting.t_pdf(x, mu, sig, 1)
px2 = fitting.t_pdf(x, mu, sig, 2)
px3 = fitting.t_pdf(x, mu, sig, 5)
norm_pdf = fitting.gaussian_pdf(x.reshape((x.size, 1)), np.array([mu]),
np.array([[sig]]))[:, 0]
plt.subplot(121)
line1, = plt.plot(x, px1, 'b')
line2, = plt.plot(x, px2, 'g')
line3, = plt.plot(x, px3, 'y')
norm_line, = plt.plot(x, norm_pdf, 'r')
plt.axis([-5, 5, 0, 0.6])
plt.legend([line1, line2, line3, norm_line], [
't-distribution, nu = 1', 't-distribution, nu = 2',
't-distribution, nu = 5', 'normal distribution'
])
plt.subplot(122)
line1, = plt.semilogy(x, px1, 'b')
line2, = plt.semilogy(x, px2, 'g')
X1 = np.random.multivariate_normal(mu1, sig1, round(I * p_lambda1))
X2 = np.random.multivariate_normal(mu2, sig2, round(I * p_lambda2))
X = np.append(X1, X2, axis=0)
I = X.shape[0]
p_lambda, mu, sig = fitting.em_mog(X, K, 0.01)
XX, YY = np.meshgrid(np.arange(-10, 10, 0.1), np.arange(-10, 10, 0.1))
x = XX.reshape((XX.size, 1))
y = YY.reshape((XX.size, 1))
xy_matrix = np.append(x, y, axis=1)
mog = np.zeros((XX.size, 1))
for k in range(K):
mog[:, 0] += p_lambda[k] * \
fitting.gaussian_pdf(xy_matrix, mu[k], sig[k])[:, 0]
mog = mog.reshape((XX.shape[0], XX.shape[1]))
plt.figure("EM MoG")
plt.subplot(211)
plt.scatter(X[:, 0], X[:, 1], marker=".")
plt.axis([-6, 6, -1, 9])
plt.contour(XX, YY, mog)
XX, YY = np.meshgrid(np.arange(-10, 10, 0.05), np.arange(-10, 10, 0.05))
x = XX.reshape((XX.size, 1))
y = YY.reshape((XX.size, 1))
xy_matrix = np.append(x, y, axis=1)
mog = p_lambda1 * fitting.gaussian_pdf(xy_matrix, mu1, sig1)[:, 0] + \
p_lambda2 * fitting.gaussian_pdf(xy_matrix, mu2, sig2)[:, 0]
mog = mog.reshape((XX.shape[0], XX.shape[1]))