def partition_function(self, batch_size, prec):
"""The exact value of Z calculated with precision prec.
Only feasible for small number of hidden units."""
with decimal.localcontext() as ctx:
if prec != 0:
ctx.prec = prec
batches = ml.common.util.pack_in_batches(all_states(self.n_hid),
batch_size)
if prec != 0:
s = decimal.Decimal(0)
else:
allfhes = np.array([])
seen_samples = 0L
total_samples = 2L**self.n_hid
for hid in batches:
print >>stderr, "%i / %i \r" % (seen_samples, total_samples),
fhes = self.free_hidden_energy(hid)
if prec != 0:
for fhe in gp.as_numpy_array(fhes):
p = decimal.Decimal(-fhe).exp()
s += p
else:
allfhes = np.concatenate((allfhes,
-gp.as_numpy_array(fhes)))
seen_samples += hid.shape[0]
if prec != 0:
return s
else:
return logsum(allfhes)
def log_partition_function(self, betas, ais_runs, sampling_gibbs_steps=1,
mean_precision=0):
"Computes the partition function of the RBM"
start_time = time()
assert betas[0] == 0 and betas[-1] == 1
irbm = ml.rbm.RestrictedBoltzmannMachine(0,
self.rbm.n_vis,
self.rbm.n_hid,
0)
iw = gp.zeros(ais_runs)
for i, beta in enumerate(betas):
#print >>stderr, "%d / %d \r" % (i, len(betas)),
if ml.common.show_progress and i % 1000 == 0:
print "%d / %d" % (i, len(betas))
beta = float(beta)
# calculate log p_(i-1)(v)
if beta != 0:
lp_prev_vis = -irbm.free_energy(vis)
# build intermediate RBM
irbm.weights = beta * self.rbm.weights
irbm.bias_hid = beta * self.rbm.bias_hid
irbm.bias_vis = ((1.0-beta) * self.base_bias_vis +
beta * self.rbm.bias_vis)
# calculate log p_i(v_i)
if beta != 0:
lp_vis = -irbm.free_energy(vis)
# update importance weight
if beta != 0:
iw += lp_vis - lp_prev_vis
# sample v_(i+1)
if beta == 0:
vis = self.base_sample_vis(ais_runs)
else:
vis, _ = irbm.gibbs_sample(vis, sampling_gibbs_steps)
# calculate mean and standard deviation
if mean_precision == 0:
npiw = gp.as_numpy_array(iw)
w = npiw + self.base_log_partition_function()
wmean = logsum(w) - np.log(w.shape[0])
wsqmean = logsum(2 * w) - np.log(w.shape[0])
wstd = logminus(wsqmean, wmean) / 2.0
wmeanstd = wstd - 0.5 * math.log(w.shape[0])
wmean_plus_3_std = logplus(wmean, wmeanstd + math.log(3.0))
wmean_minus_3_std = logminus(wmean, wmeanstd + math.log(3.0),
raise_when_negative=False)
else:
with decimal.localcontext() as ctx:
ctx.prec = mean_precision
blpf = self.base_log_partition_function()
ewsum = decimal.Decimal(0)
ewsqsum = decimal.Decimal(0)
for w in gp.as_numpy_array(iw):
ew = decimal.Decimal(w + blpf).exp()
ewsum += ew
ewsqsum += ew ** 2
ewmean = ewsum / iw.shape[0]
ewsqmean = ewsqsum / iw.shape[0]
ewstd = (ewsqmean - ewmean**2).sqrt()
ewstdmean = ewstd / math.sqrt(iw.shape[0])
wmean = float(ewmean.ln())
wmean_plus_3_std = float((ewmean + 3*ewstdmean).ln())
if ewmean - 3*ewstd > 0:
wmean_minus_3_std = float((ewmean - 3*ewstdmean).ln())
else:
wmean_minus_3_std = float('-inf')
end_time = time()
print "AIS took %d s" % (end_time - start_time)
return wmean, wmean_minus_3_std, wmean_plus_3_std
