def pdf_comp(self, x, cid, log=False):
"""Computes the pdf of the model at given points, at given component.
:Parameters:
x : ndarray
points where to estimate the pdf. One row for one
multi-dimensional sample (eg to estimate the pdf at 100
different points in 10 dimension, data's shape should be (100,
20)).
cid: int
the component index.
log : bool
If true, returns the log pdf instead of the pdf.
:Returns:
y : ndarray
the pdf at points x."""
if self.mode == 'diag':
va = self.va[cid]
elif self.mode == 'full':
va = self.va[cid * self.d:(cid + 1) * self.d]
else:
raise GmParamError("""var mode %s not supported""" % self.mode)
if log:
return D.gauss_den(x, self.mu[cid], va, log = True) \
+ N.log(self.w[cid])
else:
return D.multiple_gauss_den(x, self.mu[cid], va) * self.w[cid]
def pdf_comp(self, x, cid, log=False):
"""Computes the pdf of the model at given points, at given component.
:Parameters:
x : ndarray
points where to estimate the pdf. One row for one
multi-dimensional sample (eg to estimate the pdf at 100
different points in 10 dimension, data's shape should be (100,
20)).
cid: int
the component index.
log : bool
If true, returns the log pdf instead of the pdf.
:Returns:
y : ndarray
the pdf at points x."""
if self.mode == "diag":
va = self.va[cid]
elif self.mode == "full":
va = self.va[cid * self.d : (cid + 1) * self.d]
else:
raise GmParamError("""var mode %s not supported""" % self.mode)
if log:
return D.gauss_den(x, self.mu[cid], va, log=True) + N.log(self.w[cid])
else:
return D.multiple_gauss_den(x, self.mu[cid], va) * self.w[cid]
def pdf(self, x, log=False):
"""Computes the pdf of the model at given points.
:Parameters:
x : ndarray
points where to estimate the pdf. One row for one
multi-dimensional sample (eg to estimate the pdf at 100
different points in 10 dimension, data's shape should be (100,
20)).
log : bool
If true, returns the log pdf instead of the pdf.
:Returns:
y : ndarray
the pdf at points x."""
if log:
return D.logsumexp(D.multiple_gauss_den(x, self.mu, self.va, log=True) + N.log(self.w))
else:
return N.sum(D.multiple_gauss_den(x, self.mu, self.va) * self.w, 1)
def likelihood(self, data):
""" Returns the current log likelihood of the model given
the data """
assert (self.isinit)
# compute the gaussian pdf
tgd = densities.multiple_gauss_den(data, self.gm.mu, self.gm.va)
# multiply by the weight
tgd *= self.gm.w
return N.sum(N.log(N.sum(tgd, axis=1)), axis=0)
def likelihood(self, data):
""" Returns the current log likelihood of the model given
the data """
assert(self.isinit)
# compute the gaussian pdf
tgd = densities.multiple_gauss_den(data, self.gm.mu, self.gm.va)
# multiply by the weight
tgd *= self.gm.w
return N.sum(N.log(N.sum(tgd, axis = 1)), axis = 0)
def pdf(self, x, log=False):
"""Computes the pdf of the model at given points.
:Parameters:
x : ndarray
points where to estimate the pdf. One row for one
multi-dimensional sample (eg to estimate the pdf at 100
different points in 10 dimension, data's shape should be (100,
20)).
log : bool
If true, returns the log pdf instead of the pdf.
:Returns:
y : ndarray
the pdf at points x."""
if log:
return D.logsumexp(
D.multiple_gauss_den(x, self.mu, self.va, log=True) +
N.log(self.w))
else:
return N.sum(D.multiple_gauss_den(x, self.mu, self.va) * self.w, 1)
def compute_responsabilities(self, data):
"""Compute responsabilities.
Return normalized and non-normalized respondabilities for the model.
Note
----
Computes the latent variable distribution (a posteriori probability)
knowing the explicit data for the Gaussian model (w, mu, var): gamma(t,
i) = P[state = i | observation = data(t); w, mu, va]
This is basically the E step of EM for finite mixtures."""
# compute the gaussian pdf
tgd = densities.multiple_gauss_den(data, self.gm.mu, self.gm.va)
# multiply by the weight
tgd *= self.gm.w
# Normalize to get a pdf
gd = tgd / N.sum(tgd, axis=1)[:, N.newaxis]
return gd, tgd
def compute_responsabilities(self, data):
"""Compute responsabilities.
Return normalized and non-normalized respondabilities for the model.
Note
----
Computes the latent variable distribution (a posteriori probability)
knowing the explicit data for the Gaussian model (w, mu, var): gamma(t,
i) = P[state = i | observation = data(t); w, mu, va]
This is basically the E step of EM for finite mixtures."""
# compute the gaussian pdf
tgd = densities.multiple_gauss_den(data, self.gm.mu, self.gm.va)
# multiply by the weight
tgd *= self.gm.w
# Normalize to get a pdf
gd = tgd / N.sum(tgd, axis=1)[:, N.newaxis]
return gd, tgd
def compute_log_responsabilities(self, data):
"""Compute log responsabilities.
Return normalized and non-normalized responsabilities for the model (in
the log domain)
Note
----
Computes the latent variable distribution (a posteriori probability)
knowing the explicit data for the Gaussian model (w, mu, var): gamma(t,
i) = P[state = i | observation = data(t); w, mu, va]
This is basically the E step of EM for finite mixtures."""
# compute the gaussian pdf
tgd = densities.multiple_gauss_den(data, self.gm.mu,
self.gm.va, log = True)
# multiply by the weight
tgd += N.log(self.gm.w)
# Normalize to get a (log) pdf
gd = tgd - densities.logsumexp(tgd)[:, N.newaxis]
return gd, tgd
def compute_log_responsabilities(self, data):
"""Compute log responsabilities.
Return normalized and non-normalized responsabilities for the model (in
the log domain)
Note
----
Computes the latent variable distribution (a posteriori probability)
knowing the explicit data for the Gaussian model (w, mu, var): gamma(t,
i) = P[state = i | observation = data(t); w, mu, va]
This is basically the E step of EM for finite mixtures."""
# compute the gaussian pdf
tgd = densities.multiple_gauss_den(data,
self.gm.mu,
self.gm.va,
log=True)
# multiply by the weight
tgd += N.log(self.gm.w)
# Normalize to get a (log) pdf
gd = tgd - densities.logsumexp(tgd)[:, N.newaxis]
return gd, tgd
def plot1d(self, level=misc.DEF_LEVEL, fill=False, gpdf=False):
"""Plots the pdf of each component of the 1d mixture.
:Parameters:
level : int
level of confidence (to use with fill argument)
fill : bool
if True, the area of the pdf corresponding to the given
confidence intervales is filled.
gpdf : bool
if True, the global pdf is plot.
:Returns:
h : dict
Returns a dictionary h of plot handles so that their properties
can be modified (eg color, label, etc...):
- h['pdf'] is a list of lines, one line per component pdf
- h['gpdf'] is the line for the global pdf
- h['conf'] is a list of filling area
"""
if not self.__is1d:
raise ValueError("This function does not make sense for " "mixtures which are not unidimensional")
from scipy.stats import norm
pval = N.sqrt(self.va[:, 0]) * norm(0, 1).ppf((1 + level) / 2)
# Compute reasonable min/max for the normal pdf: [-mc * std, mc * std]
# gives the range we are taking in account for each gaussian
mc = 3
std = N.sqrt(self.va[:, 0])
mi = N.amin(self.mu[:, 0] - mc * std)
ma = N.amax(self.mu[:, 0] + mc * std)
np = 500
x = N.linspace(mi, ma, np)
# Prepare the dic of plot handles to return
ks = ["pdf", "conf", "gpdf"]
hp = dict((i, []) for i in ks)
# Compute the densities
y = D.multiple_gauss_den(x[:, N.newaxis], self.mu, self.va, log=True) + N.log(self.w)
yt = self.pdf(x[:, N.newaxis])
try:
import pylab as P
for c in range(self.k):
h = P.plot(x, N.exp(y[:, c]), "r", label="_nolegend_")
hp["pdf"].extend(h)
if fill:
# Compute x coordinates of filled area
id1 = -pval[c] + self.mu[c]
id2 = pval[c] + self.mu[c]
xc = x[:, N.where(x > id1)[0]]
xc = xc[:, N.where(xc < id2)[0]]
# Compute the graph for filling
yf = self.pdf_comp(xc, c)
xc = N.concatenate(([xc[0]], xc, [xc[-1]]))
yf = N.concatenate(([0], yf, [0]))
h = P.fill(xc, yf, facecolor="b", alpha=0.1, label="_nolegend_")
hp["conf"].extend(h)
if gpdf:
h = P.plot(x, yt, "r:", label="_nolegend_")
hp["gpdf"] = h
return hp
except ImportError:
raise GmParamError("matplotlib not found, cannot plot...")
def plot1d(self, level=misc.DEF_LEVEL, fill=False, gpdf=False):
"""Plots the pdf of each component of the 1d mixture.
:Parameters:
level : int
level of confidence (to use with fill argument)
fill : bool
if True, the area of the pdf corresponding to the given
confidence intervales is filled.
gpdf : bool
if True, the global pdf is plot.
:Returns:
h : dict
Returns a dictionary h of plot handles so that their properties
can be modified (eg color, label, etc...):
- h['pdf'] is a list of lines, one line per component pdf
- h['gpdf'] is the line for the global pdf
- h['conf'] is a list of filling area
"""
if not self.__is1d:
raise ValueError("This function does not make sense for "\
"mixtures which are not unidimensional")
from scipy.stats import norm
pval = N.sqrt(self.va[:, 0]) * norm(0, 1).ppf((1 + level) / 2)
# Compute reasonable min/max for the normal pdf: [-mc * std, mc * std]
# gives the range we are taking in account for each gaussian
mc = 3
std = N.sqrt(self.va[:, 0])
mi = N.amin(self.mu[:, 0] - mc * std)
ma = N.amax(self.mu[:, 0] + mc * std)
np = 500
x = N.linspace(mi, ma, np)
# Prepare the dic of plot handles to return
ks = ['pdf', 'conf', 'gpdf']
hp = dict((i, []) for i in ks)
# Compute the densities
y = D.multiple_gauss_den(x[:, N.newaxis], self.mu, self.va, \
log = True) \
+ N.log(self.w)
yt = self.pdf(x[:, N.newaxis])
try:
import pylab as P
for c in range(self.k):
h = P.plot(x, N.exp(y[:, c]), 'r', label='_nolegend_')
hp['pdf'].extend(h)
if fill:
# Compute x coordinates of filled area
id1 = -pval[c] + self.mu[c]
id2 = pval[c] + self.mu[c]
xc = x[:, N.where(x > id1)[0]]
xc = xc[:, N.where(xc < id2)[0]]
# Compute the graph for filling
yf = self.pdf_comp(xc, c)
xc = N.concatenate(([xc[0]], xc, [xc[-1]]))
yf = N.concatenate(([0], yf, [0]))
h = P.fill(xc,
yf,
facecolor='b',
alpha=0.1,
label='_nolegend_')
hp['conf'].extend(h)
if gpdf:
h = P.plot(x, yt, 'r:', label='_nolegend_')
hp['gpdf'] = h
return hp
except ImportError:
raise GmParamError("matplotlib not found, cannot plot...")