def test_vbgmm(verbose=0):
# perform the estimation of a gmm
n = 100
dim = 2
x = nr.randn(n, dim)
x[:30] += 2
k = 2
b = VBGMM(k, dim)
b.guess_priors(x)
b.initialize(x)
b.estimate(x, verbose=verbose)
z = b.map_label(x)
# fixme : find a less trivial test
assert z.max() + 1 == b.k
def test_vbgmm_select(kmax=6, verbose=0):
# perform the estimation of a gmm
n = 100
dim = 3
x = nr.randn(n, dim)
x[:30] += 2
show = 0
be = -np.infty
for k in range(1, kmax):
b = VBGMM(k, dim)
b.guess_priors(x)
b.initialize(x)
b.estimate(x)
z = b.map_label(x)
ek = b.evidence(x)
if verbose:
print k, ek
if ek > be:
be = ek
bestk = k
assert bestk < 3
def three_classes_GMM_fit(x, test=None, alpha=0.01, prior_strength=100,
verbose=0, fixed_scale=False, mpaxes=None, bias=0,
theta=0, return_estimator=False):
"""
Fit the data with a 3-classes Gaussian Mixture Model,
i.e. computing some probability that the voxels of a certain map
are in class disactivated, null or active
Parameters
----------
x array of shape (nvox,1): the map to be analysed
test=None array of shape(nbitems,1):
the test values for which the p-value needs to be computed
by default, test=x
alpha = 0.01 the prior weights of the positive and negative classes
prior_strength = 100 the confidence on the prior
(should be compared to size(x))
verbose=0 : verbosity mode
fixed_scale = False, boolean, variance parameterization
if True, the variance is locked to 1
otherwise, it is estimated from the data
mpaxes=None: axes handle used to plot the figure in verbose mode
if None, new axes are created
bias = 0: allows a recaling of the posterior probability
that takes into account the thershold theta. Not rigorous.
theta = 0 the threshold used to correct the posterior p-values
when bias=1; normally, it is such that test>theta
note that if theta = -np.infty, the method has a standard behaviour
return_estimator: boolean, optional
If return_estimator is true, the estimator object is
returned.
Results
-------
bfp : array of shape (nbitems,3):
the posterior probability of each test item belonging to each component
in the GMM (sum to 1 across the 3 classes)
if np.size(test)==0, i.e. nbitem==0, None is returned
estimator : nipy.neurospin.clustering.GMM object
The estimator object, returned only if return_estimator is true.
Note
----
Our convention is that
- class 1 represents the negative class
- class 2 represenst the null class
- class 3 represents the positsive class
"""
nvox = np.size(x)
x = np.reshape(x,(nvox,1))
if test==None:
test = x
if np.size(test)==0:
return None
from nipy.neurospin.clustering.bgmm import VBGMM
from nipy.neurospin.clustering.gmm import grid_descriptor
sx = np.sort(x,0)
nclasses=3
# set the priors from a reasonable model of the data (!)
# prior means
mb0 = np.mean(sx[:alpha*nvox])
mb2 = np.mean(sx[(1-alpha)*nvox:])
prior_means = np.reshape(np.array([mb0,0,mb2]),(nclasses,1))
if fixed_scale:
prior_scale = np.ones((nclasses,1,1)) * 1./(prior_strength)
else:
prior_scale = np.ones((nclasses,1,1)) * 1./(prior_strength*np.var(x))
prior_dof = np.ones(nclasses) * prior_strength
prior_weights = np.array([alpha,1-2*alpha,alpha]) * prior_strength
prior_shrinkage = np.ones(nclasses) * prior_strength
# instantiate the class and set the priors
BayesianGMM = VBGMM(nclasses,1,prior_means,prior_scale,
prior_weights, prior_shrinkage,prior_dof)
BayesianGMM.set_priors(prior_means, prior_weights, prior_scale,
prior_dof, prior_shrinkage)
# estimate the model
BayesianGMM.estimate(x,delta = 1.e-8,verbose=verbose)
# create a sampling grid
if (verbose or bias):
gd = grid_descriptor(1)
gd.getinfo([x.min(),x.max()],100)
gdm = gd.make_grid().squeeze()
lj = BayesianGMM.likelihood(gd.make_grid())
# estimate the prior weights
bfp = BayesianGMM.likelihood(test)
if bias:
lw = np.sum(lj[gdm>theta],0)
weights = BayesianGMM.weights/(BayesianGMM.weights.sum())
bfp = (lw/weights)*BayesianGMM.slikelihood(test)
if verbose>1:
BayesianGMM.show_components(x,gd,lj,mpaxes)
bfp = (bfp.T/bfp.sum(1)).T
if not return_estimator:
return bfp
else:
return bfp, BayesianGMM
def test_evidence(verbose=0,k=1):
"""
Compare the evidence estimated by Chib's method
with the variational evidence (free energy)
fixme : this one really takes time
"""
n=50
dim=2
x = nr.randn(n,dim)
x[:15] += 3
b = VBGMM(k,dim)
b.guess_priors(x)
b.initialize(x)
b.estimate(x)
vbe = b.evidence(x),
if verbose:
print 'vb: ',vbe,
niter = 1000
b = BGMM(k,dim)
b.guess_priors(x)
b.initialize(x)
b.sample(x,100)
w,cent,prec,pz = b.sample(x, niter=niter, mem=1)
bplugin = BGMM(k, dim, cent, prec, w)
bplugin.guess_priors(x)
bfchib = bplugin.bayes_factor(x, pz.astype(np.int), 1)
if verbose:
print ' chib:', bfchib
assert(bfchib>vbe)
def test_evidence(verbose=0, k=1):
# Compare the evidence estimated by Chib's method with the
# variational evidence (free energy) fixme : this one really takes
# time
n = 100
dim = 2
x = nr.randn(n, dim)
x[:30] += 3
show = 0
b = VBGMM(k, dim)
b.guess_priors(x)
b.initialize(x)
b.estimate(x)
vbe = (b.evidence(x),)
if verbose:
print "vb: ", vbe,
niter = 1000
b = BGMM(k, dim)
b.guess_priors(x)
b.initialize(x)
b.sample(x, 100)
w, cent, prec, pz = b.sample(x, niter=niter, mem=1)
bplugin = BGMM(k, dim, cent, prec, w)
bplugin.guess_priors(x)
bfchib = bplugin.Bfactor(x, pz.astype(np.int), 1)
if verbose:
print " chib:", bfchib
assert bfchib > vbe