def likelihood_under_the_prior(self, x):
""" Computes the likelihood of x under the prior
Parameters
----------
x, array of shape (self.n_samples,self.dim)
returns
-------
w, the likelihood of x under the prior model (unweighted)
"""
if self.prior_dens is not None:
return self.prior_dens * np.ones(x.shape[0])
a = self._prior_dof
tau = self._prior_shrinkage
tau /= (1 + tau)
m = self._prior_means
b = self._prior_scale
ib = np.linalg.inv(b[0])
ldb = np.log(detsh(b[0]))
scalar_w = np.log(tau / np.pi) * self.dim
scalar_w += 2 * gammaln((a + 1) / 2)
scalar_w -= 2 * gammaln((a - self.dim) / 2)
scalar_w -= ldb * a
w = scalar_w * np.ones(x.shape[0])
for i in range(x.shape[0]):
w[i] -= (a + 1) * np.log(detsh(ib + tau * (m - x[i:i + 1]) *
(m - x[i:i + 1]).T))
w /= 2
return np.exp(w)
def likelihood_under_the_prior(self, x):
""" Computes the likelihood of x under the prior
Parameters
----------
x, array of shape (self.n_samples,self.dim)
returns
-------
w, the likelihood of x under the prior model (unweighted)
"""
if self.prior_dens is not None:
return self.prior_dens * np.ones(x.shape[0])
a = self._prior_dof
tau = self._prior_shrinkage
tau /= (1 + tau)
m = self._prior_means
b = self._prior_scale
ib = np.linalg.inv(b[0])
ldb = np.log(detsh(b[0]))
scalar_w = np.log(tau / np.pi) * self.dim
scalar_w += 2 * gammaln((a + 1) / 2)
scalar_w -= 2 * gammaln((a - self.dim) / 2)
scalar_w -= ldb * a
w = scalar_w * np.ones(x.shape[0])
for i in range(x.shape[0]):
w[i] -= (a + 1) * np.log(
detsh(ib + tau * (m - x[i:i + 1]) * (m - x[i:i + 1]).T))
w /= 2
return np.exp(w)
def set_priors(self, x):
""" Set the priors in order of having them weakly uninformative
this is from Fraley and raftery;
Journal of Classification 24:155-181 (2007)
Parameters
----------
x, array of shape (n_samples,self.dim)
the data used in the estimation process
"""
# a few parameters
small = 0.01
elshape = (1, self.dim, self.dim)
mx = np.reshape(x.mean(0), (1, self.dim))
dx = x - mx
vx = np.maximum(1.e-15, np.dot(dx.T, dx) / x.shape[0])
px = np.reshape(np.diag(1.0 / np.diag(vx)), elshape)
# set the priors
self._prior_means = mx
self.prior_means = mx
self.prior_weights = self.alpha
self._prior_scale = px
self.prior_scale = px
self._prior_dof = self.dim + 2
self.prior_dof = [self._prior_dof]
self._prior_shrinkage = small
self.prior_shrinkage = [self._prior_shrinkage]
# cache some pre-computations
self._dets_ = detsh(px[0])
self._dets = [self._dets_]
self._inv_prior_scale_ = np.reshape(np.linalg.inv(px[0]), elshape)
self.prior_dens = None
def set_priors(self, x):
""" Set the priors in order of having them weakly uninformative
this is from Fraley and raftery;
Journal of Classification 24:155-181 (2007)
Parameters
----------
x, array of shape (n_samples,self.dim)
the data used in the estimation process
"""
# a few parameters
small = 0.01
elshape = (1, self.dim, self.dim)
mx = np.reshape(x.mean(0), (1, self.dim))
dx = x - mx
vx = np.maximum(1.e-15, np.dot(dx.T, dx) / x.shape[0])
px = np.reshape(np.diag(1.0 / np.diag(vx)), elshape)
# set the priors
self._prior_means = mx
self.prior_means = mx
self.prior_weights = self.alpha
self._prior_scale = px
self.prior_scale = px
self._prior_dof = self.dim + 2
self.prior_dof = [self._prior_dof]
self._prior_shrinkage = small
self.prior_shrinkage = [self._prior_shrinkage]
# cache some pre-computations
self._dets_ = detsh(px[0])
self._dets = [self._dets_]
self._inv_prior_scale_ = np.reshape(np.linalg.inv(px[0]), elshape)
self.prior_dens = None