/usr/lib/python2.7/dist-packages/pymc/NormalApproximation.py is in python-pymc 2.2+ds-1.1.
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__author__ = 'Anand Patil, anand.prabhakar.patil@gmail.com'
__all__ = ['NormApproxMu', 'NormApproxC', 'MAP', 'NormApprox']
from .Node import ZeroProbability
from .Model import Model, Sampler
from numpy import zeros, inner, asmatrix, ndarray
from numpy import reshape, shape, arange, ravel, log, Inf
from numpy.random import normal
from .utils import msqrt, check_type, round_array, logp_of_set
from copy import copy
from pymc import six
from pymc.six import print_
xrange = six.moves.xrange
try:
from scipy.optimize import fmin_ncg, fmin, fmin_powell, fmin_cg, fmin_bfgs, fmin_ncg, fmin_l_bfgs_b
from scipy.misc import derivative
scipy_imported = True
except ImportError:
scipy_imported = False
class NormApproxMu(object):
"""
Returns the mean vector of some variables.
Usage: If p1 and p2 are array-valued stochastic variables and N is a
NormApprox or MAP object,
N.mu(p1,p2)
will give the approximate posterior mean of the ravelled, concatenated
values of p1 and p2.
"""
def __init__(self, owner):
self.owner = owner
def __getitem__(self, *stochastics):
if not self.owner.fitted:
raise ValueError('NormApprox object must be fitted before mu can be accessed.')
tot_len = 0
try:
for p in stochastics[0]:
pass
stochastic_tuple = stochastics[0]
except:
stochastic_tuple = stochastics
for p in stochastic_tuple:
tot_len += self.owner.stochastic_len[p]
mu = zeros(tot_len, dtype=float)
start_index = 0
for p in stochastic_tuple:
mu[start_index:(start_index + self.owner.stochastic_len[p])] = self.owner._mu[self.owner._slices[p]]
start_index += self.owner.stochastic_len[p]
return mu
class NormApproxC(object):
"""
Returns the covariance matrix of some variables.
Usage: If p1 and p2 are array-valued stochastic variables and N is a
NormApprox or MAP object,
N.C(p1,p2)
will give the approximate covariance matrix of the ravelled, concatenated
values of p1 and p2
"""
def __init__(self, owner):
self.owner = owner
def __getitem__(self, *stochastics):
if not self.owner.fitted:
raise ValueError('NormApprox object must be fitted before C can be accessed.')
tot_len = 0
try:
for p in stochastics[0]:
pass
stochastic_tuple = stochastics[0]
except:
stochastic_tuple = stochastics
for p in stochastic_tuple:
tot_len += self.owner.stochastic_len[p]
C = asmatrix(zeros((tot_len, tot_len)), dtype=float)
start_index1 = 0
for p1 in stochastic_tuple:
start_index2 = 0
for p2 in stochastic_tuple:
C[start_index1:(start_index1 + self.owner.stochastic_len[p1]), \
start_index2:(start_index2 + self.owner.stochastic_len[p2])] = \
self.owner._C[self.owner._slices[p1],self.owner._slices[p2]]
start_index2 += self.owner.stochastic_len[p2]
start_index1 += self.owner.stochastic_len[p1]
return C
class MAP(Model):
"""
N = MAP(input, eps=.001, diff_order = 5)
Sets all parameters to maximum a posteriori values.
Useful methods:
revert_to_max: Sets all stochastic variables to mean value under normal approximation
fit: Finds the normal approximation.
Useful attributes (after fit() is called):
logp: Returns the log-probability of the model
logp_at_max: Returns the maximum log-probability of the model
len: The number of free stochastic variables in the model ('k' in AIC and BIC)
data_len: The number of datapoints used ('n' in BIC)
AIC: Akaike's Information Criterion for the model
BIC: Bayesian Information Criterion for the model
:Arguments:
input: As for Model
eps: 'h' for computing numerical derivatives. May be a dictionary keyed by stochastic variable
as well as a scalar.
diff_order: The order of the approximation used to compute derivatives.
:SeeAlso: Model, EM, Sampler, scipy.optimize
"""
def __init__(self, input=None, eps=.001, diff_order = 5, verbose=-1):
if not scipy_imported:
raise ImportError('Scipy must be installed to use NormApprox and MAP.')
Model.__init__(self, input, verbose=verbose)
# Allocate memory for internal traces and get stochastic slices
self._slices = {}
self.len = 0
self.stochastic_len = {}
self.fitted = False
self.stochastic_list = list(self.stochastics)
self.N_stochastics = len(self.stochastic_list)
self.stochastic_indices = []
self.stochastic_types = []
self.stochastic_type_dict = {}
for i in xrange(len(self.stochastic_list)):
stochastic = self.stochastic_list[i]
# Check types of all stochastics.
type_now = check_type(stochastic)[0]
self.stochastic_type_dict[stochastic] = type_now
if not type_now is float:
print_("Warning: Stochastic " + stochastic.__name__ + "'s value is neither numerical nor array with " + \
"floating-point dtype. Recommend fitting method fmin (default).")
# Inspect shapes of all stochastics and create stochastic slices.
if isinstance(stochastic.value, ndarray):
self.stochastic_len[stochastic] = len(ravel(stochastic.value))
else:
self.stochastic_len[stochastic] = 1
self._slices[stochastic] = slice(self.len, self.len + self.stochastic_len[stochastic])
self.len += self.stochastic_len[stochastic]
# Record indices that correspond to each stochastic.
for j in range(len(ravel(stochastic.value))):
self.stochastic_indices.append((stochastic, j))
self.stochastic_types.append(type_now)
self.data_len = 0
for datum in self.observed_stochastics:
self.data_len += len(ravel(datum.value))
# Unpack step
self.eps = zeros(self.len,dtype=float)
if isinstance(eps,dict):
for stochastic in self.stochastics:
self.eps[self._slices[stochastic]] = eps[stochastic]
else:
self.eps[:] = eps
self.diff_order = diff_order
self._len_range = arange(self.len)
# Initialize gradient and Hessian matrix.
self.grad = zeros(self.len, dtype=float)
self.hess = asmatrix(zeros((self.len, self.len), dtype=float))
self._mu = None
# Initialize NormApproxMu object.
self.mu = NormApproxMu(self)
def func_for_diff(val, index):
"""
The function that gets passed to the derivatives.
"""
self[index] = val
return self.i_logp(index)
self.func_for_diff = func_for_diff
def fit(self, method = 'fmin', iterlim=1000, tol=.0001, verbose=0):
"""
N.fit(method='fmin', iterlim=1000, tol=.001):
Causes the normal approximation object to fit itself.
method: May be one of the following, from the scipy.optimize package:
-fmin_l_bfgs_b
-fmin_ncg
-fmin_cg
-fmin_powell
-fmin
"""
self.tol = tol
self.method = method
self.verbose = verbose
p = zeros(self.len,dtype=float)
for stochastic in self.stochastics:
p[self._slices[stochastic]] = ravel(stochastic.value)
if not self.method == 'newton':
if not scipy_imported:
raise ImportError('Scipy is required to use EM and NormApprox')
if self.verbose > 0:
def callback(p):
try:
print_('Current log-probability : %f' % self.logp)
except ZeroProbability:
print_('Current log-probability : %f' % -Inf)
else:
def callback(p):
pass
if self.method == 'fmin_ncg':
p=fmin_ncg( f = self.func,
x0 = p,
fprime = self.gradfunc,
fhess = self.hessfunc,
epsilon=self.eps,
maxiter=iterlim,
callback=callback,
avextol=tol,
disp=verbose)
elif self.method == 'fmin':
p=fmin( func = self.func,
x0=p,
callback=callback,
maxiter=iterlim,
ftol=tol,
disp=verbose)
elif self.method == 'fmin_powell':
p=fmin_powell( func = self.func,
x0=p,
callback=callback,
maxiter=iterlim,
ftol=tol,
disp=verbose)
elif self.method == 'fmin_cg':
p=fmin_cg( f = self.func, x0 = p,
fprime = self.gradfunc,
epsilon=self.eps,
callback=callback,
maxiter=iterlim,
gtol=tol,
disp=verbose)
elif self.method == 'fmin_l_bfgs_b':
p=fmin_l_bfgs_b(func = self.func,
x0 = p,
fprime = self.gradfunc,
epsilon = self.eps,
# callback=callback,
pgtol=tol,
iprint=verbose-1)[0]
else:
raise ValueError('Method unknown.')
self._set_stochastics(p)
self._mu = p
try:
self.logp_at_max = self.logp
except:
raise RuntimeError('Posterior probability optimization converged to value with zero probability.')
lnL = sum([x.logp for x in self.observed_stochastics]) # log-likelihood of observed stochastics
self.AIC = 2. * (self.len - lnL) # 2k - 2 ln(L)
try:
self.BIC = self.len * log(self.data_len) - 2. * lnL # k ln(n) - 2 ln(L)
except FloatingPointError:
self.BIC = -Inf
self.fitted = True
def func(self, p):
"""
The function that gets passed to the optimizers.
"""
self._set_stochastics(p)
try:
return -1. * self.logp
except ZeroProbability:
return Inf
def gradfunc(self, p):
"""
The gradient-computing function that gets passed to the optimizers,
if needed.
"""
self._set_stochastics(p)
for i in xrange(self.len):
self.grad[i] = self.diff(i)
return -1 * self.grad
def _set_stochastics(self, p):
for stochastic in self.stochastics:
if self.stochastic_type_dict[stochastic] is int:
stochastic.value = round_array(reshape(ravel(p)[self._slices[stochastic]],shape(stochastic.value)))
else:
stochastic.value = reshape(ravel(p)[self._slices[stochastic]],shape(stochastic.value))
def __setitem__(self, index, value):
p, i = self.stochastic_indices[index]
val = ravel(p.value).copy()
val[i] = value
p.value = reshape(val, shape(p.value))
def __getitem__(self, index):
p, i = self.stochastic_indices[index]
val = ravel(p.value)
return val[i]
def i_logp(self, index):
"""
Evaluates the log-probability of the Markov blanket of
a stochastic owning a particular index.
"""
all_relevant_stochastics = set()
p,i = self.stochastic_indices[index]
try:
return p.logp + logp_of_set(p.extended_children)
except ZeroProbability:
return -Inf
def diff(self, i, order=1):
"""
N.diff(i, order=1)
Derivative wrt index i to given order.
"""
old_val = copy(self[i])
d = derivative(func=self.func_for_diff, x0=old_val, dx=self.eps[i], n=order, args=[i], order=self.diff_order)
self[i] = old_val
return d
def diff2(self, i, j):
"""
N.diff2(i,j)
Mixed second derivative. Differentiates wrt both indices.
"""
old_val = copy(self[j])
if not self.stochastic_indices[i][0] in self.stochastic_indices[j][0].moral_neighbors:
return 0.
def diff_for_diff(val):
self[j] = val
return self.diff(i)
d = derivative(func=diff_for_diff, x0=old_val, dx=self.eps[j], n=1, order=self.diff_order)
self[j] = old_val
return d
def grad_and_hess(self):
"""
Computes self's gradient and Hessian. Used if the
optimization method for a NormApprox doesn't
use gradients and hessians, for instance fmin.
"""
for i in xrange(self.len):
di = self.diff(i)
self.grad[i] = di
self.hess[i,i] = self.diff(i,2)
if i < self.len - 1:
for j in xrange(i+1, self.len):
dij = self.diff2(i,j)
self.hess[i,j] = dij
self.hess[j,i] = dij
def hessfunc(self, p):
"""
The Hessian function that will be passed to the optimizer,
if needed.
"""
self._set_stochastics(p)
for i in xrange(self.len):
di = self.diff(i)
self.hess[i,i] = self.diff(i,2)
if i < self.len - 1:
for j in xrange(i+1, self.len):
dij = self.diff2(i,j)
self.hess[i,j] = dij
self.hess[j,i] = dij
return -1. * self.hess
def revert_to_max(self):
"""
N.revert_to_max()
Sets all N's stochastics to their MAP values.
"""
self._set_stochastics(self.mu[self.stochastics])
class NormApprox(MAP, Sampler):
"""
N = NormApprox(input, db='ram', eps=.001, diff_order = 5, **kwds)
Normal approximation to the posterior of a model.
Useful methods:
draw: Draws values for all stochastic variables using normal approximation
revert_to_max: Sets all stochastic variables to mean value under normal approximation
fit: Finds the normal approximation.
Useful attributes (after fit() is called):
mu[p1, p2, ...]: Returns the posterior mean vector of stochastic variables p1, p2, ...
C[p1, p2, ...]: Returns the posterior covariance of stochastic variables p1, p2, ...
logp: Returns the log-probability of the model
logp_at_max: Returns the maximum log-probability of the model
len: The number of free stochastic variables in the model ('k' in AIC and BIC)
data_len: The number of datapoints used ('n' in BIC)
AIC: Akaike's Information Criterion for the model
BIC: Bayesian Information Criterion for the model
:Arguments:
input: As for Model
db: A database backend
eps: 'h' for computing numerical derivatives. May be a dictionary keyed by stochastic variable
as well as a scalar.
diff_order: The order of the approximation used to compute derivatives.
:SeeAlso: Model, EM, Sampler, scipy.optimize
"""
def __init__(self, input=None, db='ram', eps=.001, diff_order = 5, **kwds):
if not scipy_imported:
raise ImportError('Scipy must be installed to use NormApprox and MAP.')
MAP.__init__(self, input, eps, diff_order)
Sampler.__init__(self, input, db, reinit_model=False, **kwds)
self.C = NormApproxC(self)
def fit(self, *args, **kwargs):
MAP.fit(self, *args, **kwargs)
self.fitted = False
self.grad_and_hess()
self._C = -1. * self.hess.I
self._sig = msqrt(self._C).T
self.fitted = True
def draw(self):
"""
N.draw()
Sets all N's stochastics to random values drawn from
the normal approximation to the posterior.
"""
devs = normal(size=self._sig.shape[1])
p = inner(self._sig,devs) + self._mu
self._set_stochastics(p)
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