def proceed(self, y=None, mu=None, s2=None, inffunc=None, der=None, nargout=1):
sn2 = np.exp(2. * self.hyp[0])
if inffunc == None: # prediction mode
if y == None:
y = np.zeros_like(mu)
s2zero = True
if (not s2==None) and np.linalg.norm(s2) > 0:
s2zero = False
if s2zero: # log probability
lp = -(y-mu)**2 /sn2/2 - np.log(2.*np.pi*sn2)/2.
s2 = 0.
else:
inf_func = inf.infEP() # prediction
lp = self.proceed(y, mu, s2, inf_func)
if nargout>1:
ymu = mu # first y moment
if nargout>2:
ys2 = s2 + sn2 # second y moment
varargout = [lp,ymu,ys2]
else:
varargout = [lp,ymu]
else:
varargout = lp
else:
if isinstance(inffunc, inf.infEP):
if der == None: # no derivative mode
lZ = -(y-mu)**2/(sn2+s2)/2. - np.log(2*np.pi*(sn2+s2))/2. # log part function
if nargout>1:
dlZ = (y-mu)/(sn2+s2) # 1st derivative w.r.t. mean
if nargout>2:
d2lZ = -1/(sn2+s2) # 2nd derivative w.r.t. mean
varargout = [lZ,dlZ,d2lZ]
else:
varargout = [lZ,dlZ]
else:
varargout = lZ
else: # derivative mode
dlZhyp = ((y-mu)**2/(sn2+s2)-1) / (1+s2/sn2) # deriv. w.r.t. hyp.lik
varargout = dlZhyp
'''
elif isinstance(inffunc, infLaplace):
if der == None: # no derivative mode
if not y:
y=0
ymmu = y-mu
lp = -ymmu**2/(2*sn2) - np.log(2*np.pi*sn2)/2.
if nargout>1:
dlp = ymmu/sn2 # dlp, derivative of log likelihood
if nargout>2: # d2lp, 2nd derivative of log likelihood
d2lp = -np.ones_like(ymmu)/sn2
if nargout>3: # d3lp, 3rd derivative of log likelihood
d3lp = np.zeros_like(ymmu)
varargout = [lp,dlp,d2lp,d3lp]
else:
varargout = [lp,dlp,d2lp]
else:
varargout = [lp,dlp]
else:
varargout = lp
else: # derivative mode
lp_dhyp = (y-mu)**2/sn2 - 1 # derivative of log likelihood w.r.t. hypers
dlp_dhyp = 2*(mu-y)/sn2 # first derivative,
d2lp_dhyp = 2*np.ones_like(mu)/sn2 # and also of the second mu derivative
varargout = [lp_dhyp,dlp_dhyp,d2lp_dhyp]
elif isinstance(inffunc, infVB):
if der == None:
# variational lower site bound
# t(s) = exp(-(y-s)^2/2sn2)/sqrt(2*pi*sn2)
# the bound has the form: b*s - s.^2/(2*ga) - h(ga)/2 with b=y/ga
ga = s2
n = len(ga)
b = y/ga
y = y*np.ones((n,1))
db = -y/ga**2
d2b = 2*y/ga**3
h = np.zeros((n,1))
dh = h
d2h = h # allocate memory for return args
id = (ga <= sn2 + 1e-8) # OK below noise variance
h[id] = y[id]**2/ga[id] + np.log(2*np.pi*sn2)
h[np.logical_not(id)] = np.inf
dh[id] = -y[id]**2/ga[id]**2
d2h[id] = 2*y[id]**2/ga[id]**3
id = ga < 0
h[id] = np.inf
dh[id] = 0
d2h[id] = 0 # neg. var. treatment
varargout = [h,b,dh,db,d2h,d2b]
else:
ga = s2
n = len(ga)
dhhyp = np.zeros((n,1))
dhhyp[ga<=sn2] = 2
dhhyp[ga<0] = 0 # negative variances get a special treatment
varargout = dhhyp # deriv. w.r.t. hyp.lik
else:
raise Exception('Incorrect inference in lik.Gauss\n')
'''
return varargout
def proceed(self, y=None, mu=None, s2=None, inffunc=None, der=None, nargout=1):
if not y == None:
y = np.sign(y)
y[y==0] = 1
else:
y = 1; # allow only +/- 1 values
if inffunc == None: # prediction mode if inf is not present
y = y*np.ones_like(mu) # make y a vector
s2zero = True;
if not s2 == None:
if np.linalg.norm(s2)>0:
s2zero = False # s2==0?
if s2zero: # log probability evaluation
[p,lp] = self.cumGauss(y,mu,2)
else: # prediction
lp = self.proceed(y, mu, s2, inf.infEP())
p = np.exp(lp)
if nargout>1:
ymu = 2*p-1 # first y moment
if nargout>2:
ys2 = 4*p*(1-p) # second y moment
varargout = [lp,ymu,ys2]
else:
varargout = [lp,ymu]
else:
varargout = lp
else: # inference mode
if isinstance(inffunc, inf.infLaplace):
if der == None: # no derivative mode
f = mu; yf = y*f # product latents and labels
[p,lp] = self.cumGauss(y,f,2)
if nargout>1: # derivative of log likelihood
n_p = self.gauOverCumGauss(yf,p)
dlp = y*n_p # derivative of log likelihood
if nargout>2: # 2nd derivative of log likelihood
d2lp = -n_p**2 - yf*n_p
if nargout>3: # 3rd derivative of log likelihood
d3lp = 2*y*n_p**3 + 3*f*n_p**2 + y*(f**2-1)*n_p
varargout = [lp,dlp,d2lp,d3lp]
else:
varargout = [lp,dlp,d2lp]
else:
varargout = [lp,dlp]
else:
varargout = lp
else: # derivative mode
varargout = nargout*[] # derivative w.r.t. hypers
elif isinstance(inffunc, inf.infEP):
if der == None: # no derivative mode
z = mu/np.sqrt(1+s2)
[junk,lZ] = self.cumGauss(y,z,2) # log part function
if not y == None:
z = z*y
if nargout>1:
if y == None: y = 1
n_p = self.gauOverCumGauss(z,np.exp(lZ))
dlZ = y*n_p/np.sqrt(1.+s2) # 1st derivative wrt mean
if nargout>2:
d2lZ = -n_p*(z+n_p)/(1.+s2) # 2nd derivative wrt mean
varargout = [lZ,dlZ,d2lZ]
else:
varargout = [lZ,dlZ]
else:
varargout = lZ
else: # derivative mode
varargout = [] # deriv. wrt hyp.lik
'''
if inffunc == 'inf.infVB':
if der == None: # no derivative mode
# naive variational lower bound based on asymptotical properties of lik
# normcdf(t) -> -(t*A_hat^2-2dt+c)/2 for t->-np.inf (tight lower bound)
d = 0.158482605320942;
c = -1.785873318175113;
ga = s2; n = len(ga); b = d*y*np.ones((n,1)); db = np.zeros((n,1)); d2b = db
h = -2.*c*np.ones((n,1)); h[ga>1] = np.inf; dh = np.zeros((n,1)); d2h = dh
varargout = [h,b,dh,db,d2h,d2b]
else: # derivative mode
varargout = [] # deriv. wrt hyp.lik
'''
return varargout
