def _repeat_param(param, length):
# This function repeats out a parameter so that time-homogeneous models,
# which only have one tuple of lds pair parameters, are represented as
# time-inhomogeneous models (with a list of T lds pair parameter tuples).
if depth(param) == 1:
param = [param] * length
elif len(param) != length:
param = zip(*param)
assert depth(param) == 2 and len(param) == length
return param
def _repeat_param(param, length):
# This function repeats out a parameter so that time-homogeneous models,
# which only have one tuple of lds pair parameters, are represented as
# time-inhomogeneous models (with a list of T lds pair parameter tuples).
if depth(param) == 1:
param = [param]*length
elif len(param) != length:
param = zip(*param)
assert depth(param) == 2 and len(param) == length
return param
def natural_smoother_general(forward_messages, init_params, pair_params,
node_params):
prediction_messages, filter_messages = uninterleave(forward_messages)
inhomog = depth(pair_params) == 2
T = len(prediction_messages)
pair_params, orig_pair_params = _repeat_param(pair_params,
T - 1), pair_params
node_params = list(zip(*_canonical_node_params(node_params)))
def unit(filtered_message):
J, h = filtered_message
mu, Sigma = natural_to_mean(filtered_message)
ExxT = Sigma + np.outer(mu, mu)
return tuple_(J, h, mu), [(mu, ExxT, 0.)]
def bind(result, step):
next_smooth, stats = result
J, h, (mu, ExxT, ExxnT) = step(next_smooth)
return tuple_(J, h, mu), [(mu, ExxT, ExxnT)] + stats
rts = lambda next_pred, filtered, pair_param: lambda next_smooth: \
natural_rts_backward_step(next_smooth, next_pred, filtered, pair_param)
steps = reversed(
list(
map(rts, prediction_messages[1:], filter_messages[:-1],
pair_params)))
_, expected_stats = monad_runner(bind)(unit(filter_messages[-1]), steps)
def make_init_stats(a):
mu, ExxT, _ = a
return (ExxT, mu, 1., 1.)[:len(init_params)]
def make_pair_stats(a, b):
(mu, ExxT, ExnxT), (mu_n, ExnxnT, _) = a, b
return ExxT, ExnxT.T, ExnxnT, 1.
is_diagonal = node_params[0][0].ndim == 1
if is_diagonal:
def make_node_stats(a):
mu, ExxT, _ = a
return np.diag(ExxT), mu, 1.
else:
def make_node_stats(a):
mu, ExxT, _ = a
return ExxT, mu, 1.
E_init_stats = make_init_stats(expected_stats[0])
E_pair_stats = list(
map(make_pair_stats, expected_stats[:-1], expected_stats[1:]))
E_node_stats = list(map(make_node_stats, expected_stats))
if not inhomog:
E_pair_stats = reduce(add, E_pair_stats, zeros_like(orig_pair_params))
E_node_stats = list(map(np.array, list(zip(*E_node_stats))))
return E_init_stats, E_pair_stats, E_node_stats
def natural_smoother_general(forward_messages, init_params, pair_params, node_params):
prediction_messages, filter_messages = uninterleave(forward_messages)
inhomog = depth(pair_params) == 2
T = len(prediction_messages)
pair_params, orig_pair_params = _repeat_param(pair_params, T-1), pair_params
node_params = zip(*_canonical_node_params(node_params))
def unit(filtered_message):
J, h = filtered_message
mu, Sigma = natural_to_mean(filtered_message)
ExxT = Sigma + np.outer(mu, mu)
return make_tuple(J, h, mu), [(mu, ExxT, 0.)]
def bind(result, step):
next_smooth, stats = result
J, h, (mu, ExxT, ExxnT) = step(next_smooth)
return make_tuple(J, h, mu), [(mu, ExxT, ExxnT)] + stats
rts = lambda next_pred, filtered, pair_param: lambda next_smooth: \
natural_rts_backward_step(next_smooth, next_pred, filtered, pair_param)
steps = reversed(map(rts, prediction_messages[1:], filter_messages[:-1], pair_params))
_, expected_stats = monad_runner(bind)(unit(filter_messages[-1]), steps)
def make_init_stats(a):
mu, ExxT, _ = a
return (ExxT, mu, 1., 1.)[:len(init_params)]
def make_pair_stats(a, b):
(mu, ExxT, ExnxT), (mu_n, ExnxnT, _) = a, b
return ExxT, ExnxT.T, ExnxnT, 1.
is_diagonal = node_params[0][0].ndim == 1
if is_diagonal:
def make_node_stats(a):
mu, ExxT, _ = a
return np.diag(ExxT), mu, 1.
else:
def make_node_stats(a):
mu, ExxT, _ = a
return ExxT, mu, 1.
E_init_stats = make_init_stats(expected_stats[0])
E_pair_stats = map(make_pair_stats, expected_stats[:-1], expected_stats[1:])
E_node_stats = map(make_node_stats, expected_stats)
if not inhomog:
E_pair_stats = reduce(add, E_pair_stats, zeros_like(orig_pair_params))
E_node_stats = map(np.array, zip(*E_node_stats))
return E_init_stats, E_pair_stats, E_node_stats