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
def natural_smooth_backward(forward_messages, natparam):
prediction_messages, filter_messages = uninterleave(forward_messages)
init_params, pair_params, node_params = _unpack_repeated(natparam)
pair_params = map(itemgetter(0, 1, 2), pair_params)
unit = lambda (J, h): [(J, h)]
bind = lambda result, step: [step(result[0])] + result
rts = lambda next_prediction, filtered, pair_param: lambda next_smoothed: \
natural_rts_backward_step(next_smoothed, next_prediction, filtered, pair_param)
steps = map(rts, prediction_messages[1:], filter_messages, pair_params)
return map(itemgetter(2), monad_runner(bind)(unit(filter_messages[-1]), steps))
def natural_sample_backward_general(forward_messages, pair_params, num_samples=None):
filtered_messages = forward_messages[1::2]
pair_params = _repeat_param(pair_params, len(filtered_messages) - 1)
pair_params = map(itemgetter(0, 1), pair_params)
unit = lambda sample: [sample]
bind = lambda result, step: [step(result[0])] + result
sample = lambda (J11, J12), (J_filt, h_filt): lambda next_sample: \
natural_sample(*natural_condition_on(J_filt, h_filt, next_sample, J11, J12))
steps = reversed(map(sample, pair_params, filtered_messages[:-1]))
last_sample = natural_sample(*filtered_messages[-1], num_samples=num_samples)
samples = monad_runner(bind)(unit(last_sample), steps)
return np.concatenate([sample[None,...] for sample in samples])
def natural_sample_backward(forward_messages, natparam):
_, filter_messages = uninterleave(forward_messages)
_, pair_params, _ = _unpack_repeated(natparam, len(filter_messages))
pair_params = map(itemgetter(0, 1), pair_params)
unit = lambda sample: [sample]
bind = lambda result, step: [step(result[0])] + result
sample = lambda (J11, J12), (J_filt, h_filt): lambda next_sample: \
natural_sample(*natural_condition_on(J_filt, h_filt, next_sample, J11, J12))
steps = reversed(map(sample, pair_params, filter_messages[:-1]))
last_sample = natural_sample(*filter_messages[-1])
samples = monad_runner(bind)(unit(last_sample), steps)
return np.array(samples)
def natural_sample_backward_general(forward_messages,
pair_params,
num_samples=None):
filtered_messages = forward_messages[1::2]
pair_params = _repeat_param(pair_params, len(filtered_messages) - 1)
pair_params = map(itemgetter(0, 1), pair_params)
unit = lambda sample: [sample]
bind = lambda result, step: [step(result[0])] + result
sample = lambda (J11, J12), (J_filt, h_filt): lambda next_sample: \
natural_sample(*natural_condition_on(J_filt, h_filt, next_sample, J11, J12))
steps = reversed(map(sample, pair_params, filtered_messages[:-1]))
last_sample = natural_sample(*filtered_messages[-1],
num_samples=num_samples)
samples = monad_runner(bind)(unit(last_sample), steps)
return np.concatenate([sample[None, ...] for sample in samples])
def natural_filter_forward_general(init_params, pair_params, node_params):
init_params = _canonical_init_params(init_params)
node_params = zip(*_canonical_node_params(node_params))
pair_params = _repeat_param(pair_params, len(node_params) - 1)
def unit(J, h, logZ):
return [(J, h)], logZ
def bind(result, step):
messages, lognorm = result
new_message, term = step(messages[-1])
return messages + [new_message], lognorm + term
condition = lambda node_param: lambda (J, h): natural_condition_on_general(J, h, *node_param)
predict = lambda pair_param: lambda (J, h): natural_predict(J, h, *pair_param)
steps = interleave(map(condition, node_params), map(predict, pair_params))
messages, lognorm = monad_runner(bind)(unit(*init_params), steps)
lognorm += natural_lognorm(*messages[-1])
return messages, lognorm
def natural_filter_forward(natparam, data):
T, p = data.shape
init_params, pair_params, node_params = _unpack_repeated(natparam, T)
def unit(J, h):
return [(J, h)], 0.
def bind(result, step):
messages, lognorm = result
new_message, term = step(messages[-1])
return messages + [new_message], lognorm + term
condition = lambda node_param, y: lambda (J, h): natural_condition_on(J, h, y, *node_param)
predict = lambda pair_param: lambda (J, h): natural_predict(J, h, *pair_param)
steps = interleave(map(condition, node_params, data), map(predict, pair_params))
J_init, h_init, logZ_init = init_params
messages, lognorm = monad_runner(bind)(unit(J_init, h_init), steps)
lognorm += natural_lognorm(*messages[-1]) + logZ_init
return messages, lognorm - T*p/2*np.log(2*np.pi)
def sample_backward(filtered_mus, filtered_sigmas, A, sigma_states):
def filtered_sampler(mu_filt, sigma_filt):
def sample_cond(next_state):
(mu_cond, sigma_cond), _ = condition_on(
mu_filt, sigma_filt, A, next_state, sigma_states)
return sample(mu_cond, sigma_cond)
return sample_cond
def unit(sample):
return [sample]
def bind(result, step):
samples = result
sample = step(samples[0])
return [sample] + samples
last_sample = sample(filtered_mus[-1], filtered_sigmas[-1])
steps = reversed(map(filtered_sampler, filtered_mus[:-1], filtered_sigmas[:-1]))
samples = monad_runner(bind)(unit(last_sample), steps)
return np.array(samples)
def filter_forward(data, mu_init, sigma_init, A, sigma_states, C, sigma_obs):
def observe(y):
def update_belief(mu, sigma):
mu_pred, sigma_pred = predict(mu, sigma, A, sigma_states)
(mu_filt, sigma_filt), ll = condition_on(mu_pred, sigma_pred, C, y, sigma_obs)
return (mu_filt, sigma_filt), ll
return update_belief
def unit(mu, sigma):
return ([mu], [sigma]), 0.
def bind(result, step):
(mus, sigmas), lognorm = result
(mu, sigma), term = step(mus[-1], sigmas[-1])
return (mus + [mu], sigmas + [sigma]), lognorm + term
(mu_filt, sigma_filt), ll = condition_on(mu_init, sigma_init, C, data[0], sigma_obs)
(filtered_mus, filtered_sigmas), loglike = \
monad_runner(bind)(unit(mu_filt, sigma_filt), map(observe, data[1:]))
return (filtered_mus, filtered_sigmas), loglike + ll
def natural_filter_forward_general(init_params, pair_params, node_params):
init_params = _canonical_init_params(init_params)
node_params = zip(*_canonical_node_params(node_params))
pair_params = _repeat_param(pair_params, len(node_params) - 1)
def unit(J, h, logZ):
return [(J, h)], logZ
def bind(result, step):
messages, lognorm = result
new_message, term = step(messages[-1])
return messages + [new_message], lognorm + term
condition = lambda node_param: lambda (J, h): natural_condition_on_general(
J, h, *node_param)
predict = lambda pair_param: lambda (J, h): natural_predict(
J, h, *pair_param)
steps = interleave(map(condition, node_params), map(predict, pair_params))
messages, lognorm = monad_runner(bind)(unit(*init_params), steps)
lognorm += natural_lognorm(*messages[-1])
return messages, lognorm