def log_marginal_likelihood(self,data):
n = getdatasize(data)
mu_0, kappa_0, sigmasq_0, nu_0 = self.mu_0, self.kappa_0, self.sigmasq_0, self.nu_0
mu_n, kappa_n, sigmasq_n, nu_n = self._posterior_hypparams(*self._get_statistics(data))
return special.gammaln(nu_n/2) - special.gammaln(nu_0/2) \
+ 0.5*(np.log(kappa_0) - np.log(kappa_n) \
+ nu_0 * (np.log(nu_0) + np.log(sigmasq_0)) \
- nu_n * (np.log(nu_n) + np.log(sigmasq_n)) \
- n*np.log(np.pi))
def max_likelihood(self,data,weights=None):
if weights is not None:
raise NotImplementedError
assert isinstance(data,list) or isinstance(data,np.ndarray)
if isinstance(data,list):
data = np.concatenate(data)
if getdatasize(data) > 0:
self.add_data(data)
self.EM_fit()
self.labels_list = []
def max_likelihood(self, data, weights=None):
if weights is not None:
raise NotImplementedError
assert isinstance(data, list) or isinstance(data, np.ndarray)
if isinstance(data, list):
data = np.concatenate(data)
if getdatasize(data) > 0:
self.add_data(data)
self.EM_fit()
self.labels_list = []
def _get_statistics(self,data):
assert isinstance(data,np.ndarray) or \
(isinstance(data,list) and all(isinstance(d,np.ndarray) for d in data))
n = getdatasize(data)
if n > 0:
if isinstance(data,np.ndarray):
xbar = data.mean()
else:
xbar = sum(d.sum() for d in data)/n
else:
xbar = None
return n, xbar
def _get_statistics(data,D):
n = getdatasize(data)
if n > 0:
if isinstance(data,np.ndarray):
xbar = np.reshape(data,(-1,D)).mean(0)
centered = data - xbar
sumsq = np.dot(centered.T,centered)
else:
xbar = sum(np.reshape(d,(-1,D)).sum(0) for d in data) / n
sumsq = sum(np.dot((np.reshape(d,(-1,D))-xbar).T,(np.reshape(d,(-1,D))-xbar))
for d in data)
else:
xbar, sumsq = None, None
return n, xbar, sumsq
def resample(self,data=[],niter=20):
if getdatasize(data) == 0:
self.p = np.random.beta(self.alpha_0,self.beta_0)
self.r = np.random.gamma(self.k_0,self.theta_0)
else:
data = flattendata(data)
N = len(data)
for itr in range(niter):
### resample r
msum = 0.
for n in data:
msum += (np.random.rand(n) < self.r/(np.arange(n)+self.r)).sum()
self.r = np.random.gamma(self.k_0 + msum, 1/(1/self.theta_0 - N*np.log(1-self.p)))
### resample p
self.p = np.random.beta(self.alpha_0 + data.sum(), self.beta_0 + N*self.r)
def resample(self,data,niter=25,temp=None):
# doesn't keep a reference to the data like a model would
assert isinstance(data,list) or isinstance(data,np.ndarray)
if getdatasize(data) > 0:
if not isinstance(data,np.ndarray):
data = np.concatenate(data)
self.add_data(data)
for itr in range(niter):
self.resample_model(temp=temp)
self.labels_list.pop()
else:
self.resample_model(temp=temp)
def resample(self, data):
# doesn't keep a reference to the data like a model would
assert isinstance(data, list) or isinstance(data, np.ndarray)
if getdatasize(data) > 0:
if not isinstance(data, np.ndarray):
data = np.concatenate(data)
self.add_data(data, initialize_from_prior=False)
for itr in range(self.niter):
self.resample_model()
self.labels_list.pop()
else:
self.resample_model()
def resample(self,data):
# doesn't keep a reference to the data like a model would
assert isinstance(data,list) or isinstance(data,np.ndarray)
if getdatasize(data) > 0:
if not isinstance(data,np.ndarray):
data = np.concatenate(data)
self.add_data(data,initialize_from_prior=False)
for itr in range(self.niter):
self.resample_model()
self.labels_list.pop()
else:
self.resample_model()
def _resample_logseriesaug(self,data=[],niter=20):
# an alternative algorithm, kind of opaque and no advantages...
if getdatasize(data) == 0:
self.p = np.random.beta(self.alpha_0,self.beta_0)
self.r = np.random.gamma(self.k_0,self.theta_0)
else:
data = flattendata(data)
N = data.shape[0]
logF = self.logF
L_i = np.zeros(N)
data_nz = data[data > 0]
for itr in range(niter):
logR = np.arange(1,logF.shape[1]+1)*np.log(self.r) + logF
L_i[data > 0] = sample_discrete_from_log(logR[data_nz-1,:data_nz.max()],axis=1)+1
self.r = np.random.gamma(self.k_0 + L_i.sum(), 1/(1/self.theta_0 - np.log(1-self.p)*N))
self.p = np.random.beta(self.alpha_0 + data.sum(), self.beta_0 + N*self.r)
def resample(self, data, niter=25, temp=None):
# doesn't keep a reference to the data like a model would
assert isinstance(data, list) or isinstance(data, np.ndarray)
if getdatasize(data) > 0:
if not isinstance(data, np.ndarray):
data = np.concatenate(data)
self.add_data(data)
for itr in range(niter):
self.resample_model(temp=temp)
self.labels_list.pop()
else:
self.resample_model(temp=temp)
def _get_statistics(self,data):
assert isinstance(data,np.ndarray) or \
(isinstance(data,list) and all(isinstance(d,np.ndarray) for d in data))
D = self.D
n = getdatasize(data)
if n > 0:
if isinstance(data,np.ndarray):
data = np.reshape(data,(-1,D))
xbar = data.mean(0)
sumsq = ((data-xbar)**2).sum()
else:
xbar = sum(np.reshape(d,(-1,D)).sum(0) for d in data) / n
sumsq = sum(((np.reshape(data,(-1,D)) - xbar)**2).sum() for d in data)
else:
xbar, sumsq = None, None
return n, xbar, sumsq
def resample(self,data=[],niter=None):
n = getdatasize(data)
niter = self.niter if niter is None else niter
if n > 0:
data = flattendata(data)
datasum = data.sum()
nu_n = self.nu_0 + n
for itr in range(niter):
# resample mean
tausq_n = 1/(1/self.tausq_0 + n/self.sigmasq)
mu_n = tausq_n*(self.mu_0/self.tausq_0 + datasum/self.sigmasq)
self.mu = np.sqrt(tausq_n)*np.random.normal() + mu_n
# resample variance
sigmasq_n = (self.nu_0*self.sigmasq_0 + ((data-self.mu)**2).sum())/(nu_n)
self.sigmasq = sigmasq_n*nu_n/np.random.chisquare(nu_n)
else:
self.mu = np.sqrt(self.tausq_0) * np.random.normal() + self.mu_0
self.sigmasq = self.sigmasq_0*self.nu_0/np.random.chisquare(self.nu_0)
if self.mubin is not None and self.sigmasqbin is not None:
self.mubin[...] = self.mu
self.sigmasqbin[...] = self.sigmasq
def _get_statistics(self,data):
assert isinstance(data,np.ndarray) or \
(isinstance(data,list) and all((isinstance(d,np.ndarray))
for d in data)) or \
(isinstance(data,int) or isinstance(data,float))
n = getdatasize(data)
if n > 0:
if isinstance(data,np.ndarray):
ybar = data.mean()
sumsqc = ((data-ybar)**2).sum()
elif isinstance(data,list):
ybar = sum(d.sum() for d in data)/n
sumsqc = sum(np.sum((d-ybar)**2) for d in data)
else:
ybar = data
sumsqc = 0
else:
ybar = None
sumsqc = None
return n, ybar, sumsqc
def log_marginal_likelihood(self,data):
n, D = getdatasize(data), self.D
return self._log_partition_function(*self._posterior_hypparams(*self._get_statistics(data,self.D))) \
- self._log_partition_function(self.mu_0,self.sigma_0,self.kappa_0,self.nu_0) \
- n*D/2 * np.log(2*np.pi)
def meanfieldupdate(self,data,weights):
assert getdatasize(data) > 0
# update
self._mu_mf, self._sigma_mf, self._kappa_mf, self._nu_mf = \
self._posterior_hypparams(*self._get_weighted_statistics(data,weights,self.D))
self.mu, self.sigma = self._mu_mf, self._sigma_mf/(self._nu_mf - self.D - 1) # for plotting