def backward(self):
"""Backward recursion.
Upon completion, the following list of length T is available:
* smth: marginal smoothing probabilities
Note
----
Performs the forward step in case it has not been performed before.
"""
if not self.filt:
self.forward()
self.smth = [self.filt[-1]]
log_trans = np.log(self.hmm.trans_mat)
ctg = np.zeros(
self.hmm.dim) # cost to go (log-lik of y_{t+1:T} given x_t=k)
for filt, next_ft in reversed(list(zip(self.filt[:-1],
self.logft[1:]))):
new_ctg = np.empty(self.hmm.dim)
for k in range(self.hmm.dim):
new_ctg[k] = rs.log_sum_exp(log_trans[k, :] + next_ft + ctg)
ctg = new_ctg
smth = rs.exp_and_normalise(np.log(filt) + ctg)
self.smth.append(smth)
self.smth.reverse()
def filt_step(self, t, yt):
emis = self.hmm.PY(t, None, np.arange(self.hmm.dim)).logpdf(yt)
lp = np.log(self.pred[-1]) + emis
logpyt = rs.log_sum_exp(lp)
f = np.exp(lp - logpyt)
self.logft.append(emis)
self.logpyt.append(lp)
self.filt.append(f)
def update_M(self,
new_weights: rs.Weights,
normalize: bool,
normalize_info: typing.Any = None):
if normalize:
self.pre_normalize_weights.append(self.current_weights)
self.normalize_information.append(normalize_info)
self.current_weights = np.log(new_weights.W)
else:
normalized_new_weights = ut.log(new_weights.W)
normalization_constant_of_current_weights = rs.log_sum_exp(
self.current_weights)
self.current_weights = normalized_new_weights + normalization_constant_of_current_weights
def run(self):
self.setup()
self.points = []
self.log_weights = [np.log(1. - np.exp(-1. / self.N))]
self.step()
self.lZhats = [self.log_weights[0] + self.points[0].llik]
while True:
self.step()
b = self.log_weights[-1] + self.points[-1].llik
self.lZhats.append(log_sum_exp(self.lZhats[-1], b))
if self.stopping_time():
break
next_lw = self.log_weights[-1] - 1. / self.N
self.log_weights.append(next_lw)
if len(self.log_weights) % self.N == 0:
print('iteration %i: log(Z_hat) = %f' %
(len(self.log_weights), self.lZhats[-1]))
def logLT(self) -> float:
return sum([
rs.log_sum_exp(arr)
for arr in self.pre_normalize_weights + [self.current_weights]
])