def get_v(self, X):
C = dot((1 / (self.K)), dot(X, transpose(X)))
V, _ = qr(C)
eigV = eigvals(C)
eigV = np.sort(eigV)[::-1]
ind = np.where(eigV > 0)[0]
r = len(ind)
return V, r
def find_roots(p,scaling=10):
"""Find roots of a polynomial with coefficients `p` by
computing eigenvalues of the associated companion matrix.
Overflow can be avoided during the eigenvalue calculation
by preconditioning the companion matrix with a similarity
transformation defined by scaling factor `scaling` > 1.
This transformation will render the eigenvectors in a new
basis, but the eigenvalues will remain unchanged.
Empirically, `scaling=10` appears to enable successful
root-finding on polynomials up to degree 192."""
scaling=numpy.float64(scaling)
M=companion_matrix(p); N=len(M)
D=numpy.matrix(numpy.diag(scaling**numpy.arange(N)))
Dinv=numpy.matrix(numpy.diag((1/scaling)**numpy.arange(N)))
Mstar=Dinv*M*D # Similarity transform will leave the eigenvalues unchanged
return linalg.eigvals(Mstar)
def mapMStep(self, dist, posterior, data, mix_pi=None, dist_ind=None):
""" This funciton is based on an empirical bayesian estimation of a linear gaussian with a gaussian prior over B.
See bishop page 169 for details.
"""
assert isinstance(dist, LinearGaussianDistribution)
if isinstance(data, DataSet):
dt = data.internalData
elif hasattr(data, "__iter__"):
dt = data
else:
raise TypeError, "Unknown/Invalid input to MStep."
# First column of data set of the matrix
y = dt[:, 0]
# Matrix column of 1's concatenated with rest of columns of data set of the matrix
#x = np.concatenate((np.array([np.ones(len(dt))]).T, dt[:,1:]), axis=1)
x = dt[:, 1:]
yaux = np.array(np.multiply(y, np.matrix(posterior).T))
mean = np.mean(yaux)
#eigen values of X^t.X/sigma^2
xaux = np.array(np.multiply(x, np.matrix(posterior).T))
XXs = np.dot(xaux.T, x) / np.power(dist.sigma[0], 2)
if (self.fixed == 0):
lambdas = la.eigvals(XXs)
# estimate gamma
self.gamma = np.sum(np.divide(lambdas, lambdas + self.alpha[dist_ind]))
# Beta estimation
beta_numerator = np.dot(xaux.T, y) / np.power(dist.sigma[0], 2)
beta_denominator = self.alpha[dist_ind] * np.identity(len(x[0])) + XXs
try:
betashort = np.dot(np.linalg.inv(beta_denominator), beta_numerator)
dist.beta = np.concatenate(([mean], betashort), axis=1)
except la.LinAlgError:
raise EmptyComponent, "Empty Component: Singular Matrix"
# Sigma estimation
dist.predicted = mean + np.dot(x, betashort)
y_x_betat = np.subtract(y, dist.predicted)
dist.predicted = np.multiply(dist.predicted, posterior)
sigma_numerator = np.dot(np.multiply(y_x_betat, posterior), y_x_betat)
if (self.fixed == 0):
sigma_denominator = posterior.sum() - self.gamma
else:
sigma_denominator = posterior.sum() - 1
try:
dist.sigma[0] = np.sqrt(sigma_numerator / sigma_denominator)
except FloatingPointError:
dist.sigma[0] = 0.0001
# alpha
if (self.fixed == 0):
self.alpha[dist_ind] = self.gamma / np.dot(dist.beta, dist.beta.T)
dist.currentPosterior = posterior
def is_pos_def(x):
return np.all(eigvals(x) > 0)
def mapMStep(self, dist, posterior, data, mix_pi=None, dist_ind=None):
""" This funciton is based on an empirical bayesian estimation of a linear gaussian with a gaussian prior over B.
See bishop page 169 for details.
"""
assert isinstance(dist, LinearGaussianDistribution)
if isinstance(data, DataSet):
dt = data.internalData
elif hasattr(data, "__iter__"):
dt = data
else:
raise TypeError, "Unknown/Invalid input to MStep."
# First column of data set of the matrix
y = dt[:, 0]
# Matrix column of 1's concatenated with rest of columns of data set of the matrix
#x = np.concatenate((np.array([np.ones(len(dt))]).T, dt[:,1:]), axis=1)
x = dt[:, 1:]
yaux = np.array(np.multiply(y, np.matrix(posterior).T))
mean = np.mean(yaux)
#eigen values of X^t.X/sigma^2
xaux = np.array(np.multiply(x, np.matrix(posterior).T))
XXs = np.dot(xaux.T, x) / np.power(dist.sigma[0], 2)
if (self.fixed == 0):
lambdas = la.eigvals(XXs)
# estimate gamma
self.gamma = np.sum(
np.divide(lambdas, lambdas + self.alpha[dist_ind]))
# Beta estimation
beta_numerator = np.dot(xaux.T, y) / np.power(dist.sigma[0], 2)
beta_denominator = self.alpha[dist_ind] * np.identity(len(x[0])) + XXs
try:
betashort = np.dot(np.linalg.inv(beta_denominator), beta_numerator)
dist.beta = np.concatenate(([mean], betashort), axis=1)
except la.LinAlgError:
raise EmptyComponent, "Empty Component: Singular Matrix"
# Sigma estimation
dist.predicted = mean + np.dot(x, betashort)
y_x_betat = np.subtract(y, dist.predicted)
dist.predicted = np.multiply(dist.predicted, posterior)
sigma_numerator = np.dot(np.multiply(y_x_betat, posterior), y_x_betat)
if (self.fixed == 0):
sigma_denominator = posterior.sum() - self.gamma
else:
sigma_denominator = posterior.sum() - 1
try:
dist.sigma[0] = np.sqrt(sigma_numerator / sigma_denominator)
except FloatingPointError:
dist.sigma[0] = 0.0001
# alpha
if (self.fixed == 0):
self.alpha[dist_ind] = self.gamma / np.dot(dist.beta, dist.beta.T)
dist.currentPosterior = posterior