def training(inffunc, meanfunc, covfunc, likfunc, x, y, optimizer):
'''
train optimal hyperparameters
adjust to all mean/cov/lik functions
no return value
if you want to check hyp after training, it's now become property of each function
(e.g.) print myCov.hyp
print myMean.hyp
'''
if not meanfunc:
meanfunc = mean.meanZero()
if not covfunc:
raise Exception('Covariance function cannot be empty')
if not likfunc:
likfunc = lik.likGauss([0.1])
if not inffunc:
inffunc = inf.infExact()
# if covFTIC then infFITC, leave this part aside now
# optimize here
out = optimizer.findMin(inffunc, meanfunc, covfunc, likfunc, x, y)
optimalHyp = out[0]
optimalNlZ = out[1]
# apply optimal hyp to all mean/cov/lik functions here
optimizer.apply_in_objects(optimalHyp, meanfunc, covfunc, likfunc)
return optimalNlZ
def analyze(inffunc, meanfunc, covfunc, likfunc, x, y, der=False):
'''
Middle Step, or maybe useful for experts to analyze sth.
return [nlZ, post] if der = False
or [nlZ, dnlZ, post] if der = True
'''
if not meanfunc:
meanfunc = mean.meanZero()
if not covfunc:
raise Exception('Covariance function cannot be empty')
if not likfunc:
likfunc = lik.likGauss([0.1])
if not inffunc:
inffunc = inf.infExact()
# if covFTIC then infFITC
# call inference method
if isinstance(likfunc, lik.likErf): #or isinstance(likfunc, likelihood.likLogistic)
uy = unique(y)
ind = ( uy != 1 )
if any( uy[ind] != -1):
raise Exception('You attempt classification using labels different from {+1,-1}')
print 'unique is not defined'
if not der:
vargout = inffunc.proceed(meanfunc, covfunc, likfunc, x, y, 2)
post = vargout[0]
nlZ = vargout[1]
return [nlZ[0], post] # report -log marg lik, and post
else:
vargout = inffunc.proceed(meanfunc, covfunc, likfunc, x, y, 3)
post = vargout[0]
nlZ = vargout[1]
dnlZ = vargout[2]
return [nlZ[0], dnlZ, post] # report -log marg lik, derivatives and post
def prediction(inffunc, meanfunc, covfunc, likfunc, x, y, xs, ys=None):
'''
prediction according to given inputs
return [ymu, ys2, fmu, fs2, lp, post]
If given ys, lp will be calculated.
Otherwise, lp is None
'''
if not meanfunc:
meanfunc = mean.meanZero()
if not covfunc:
raise Exception('Covariance function cannot be empty')
if not likfunc:
likfunc = lik.likGauss([0.1])
if not inffunc:
inffunc = inf.infExact()
# if covFTIC then infFITC
post = analyze(inffunc, meanfunc, covfunc, likfunc, x, y, der=False)[1]
alpha = post.alpha
L = post.L
sW = post.sW
#if issparse(alpha) # handle things for sparse representations
# nz = alpha != 0 # determine nonzero indices
# if issparse(L), L = full(L(nz,nz)); end # convert L and sW if necessary
# if issparse(sW), sW = full(sW(nz)); end
#else:
nz = range(len(alpha[:,0])) # non-sparse representation
if L == []: # in case L is not provided, we compute it
K = covfunc.proceed(x[nz,:])
L = np.linalg.cholesky( (np.eye(nz) + np.dot(sW,sW.T)*K).T )
Ltril = np.all( np.tril(L,-1) == 0 ) # is L an upper triangular matrix?
ns = xs.shape[0] # number of data points
nperbatch = 1000 # number of data points per mini batch
nact = 0 # number of already processed test data points
ymu = np.zeros((ns,1))
ys2 = np.zeros((ns,1))
fmu = np.zeros((ns,1))
fs2 = np.zeros((ns,1))
lp = np.zeros((ns,1))
while nact<ns-1: # process minibatches of test cases to save memory
id = range(nact,min(nact+nperbatch,ns)) # data points to process
kss = covfunc.proceed(xs[id,:], 'diag') # self-variances
Ks = covfunc.proceed(x[nz,:], xs[id,:]) # cross-covariances
ms = meanfunc.proceed(xs[id,:])
N = (alpha.shape)[1] # number of alphas (usually 1; more in case of sampling)
Fmu = np.tile(ms,(1,N)) + np.dot(Ks.T,alpha[nz]) # conditional mean fs|f
fmu[id] = np.reshape(Fmu.sum(axis=1)/N,(len(id),1)) # predictive means
if Ltril: # L is triangular => use Cholesky parameters (alpha,sW,L)
V = np.linalg.solve(L.T,np.tile(sW,(1,len(id)))*Ks)
fs2[id] = kss - np.array([(V*V).sum(axis=0)]).T # predictive variances
else: # L is not triangular => use alternative parametrization
fs2[id] = kss + np.array([(Ks*np.dot(L,Ks)).sum(axis=0)]).T # predictive variances
fs2[id] = np.maximum(fs2[id],0) # remove numerical noise i.e. negative variances
Fs2 = np.tile(fs2[id],(1,N)) # we have multiple values in case of sampling
if ys == None:
[Lp, Ymu, Ys2] = likfunc.proceed(None,Fmu[:],Fs2[:],None,None,3)
else:
[Lp, Ymu, Ys2] = likfunc.proceed(np.tile(ys[id],(1,N)), Fmu[:], Fs2[:],None,None,3)
lp[id] = np.reshape( np.reshape(Lp,(np.prod(Lp.shape),N)).sum(axis=1)/N , (len(id),1) ) # log probability; sample averaging
ymu[id] = np.reshape( np.reshape(Ymu,(np.prod(Ymu.shape),N)).sum(axis=1)/N ,(len(id),1) ) # predictive mean ys|y and ...
ys2[id] = np.reshape( np.reshape(Ys2,(np.prod(Ys2.shape),N)).sum(axis=1)/N , (len(id),1) ) # .. variance
nact = id[-1] # set counter to index of last processed data point
if ys == None:
return [ymu, ys2, fmu, fs2, None, post]
else:
return [ymu, ys2, fmu, fs2, lp, post]