def test_semi_markov(self):
smm = SemiMarkov(5, min_dwell=3, max_dwell=13, dwell_times=4.3)
n = 28
seq = smm.sample(n)
self.assertEqual(len(seq), n)
def test_pure_markov(self):
smm = SemiMarkov(4)
n = 12
seq = smm.sample(n)
self.assertEqual(len(seq), n)
def test_default_seed_is_zero(self):
smm2 = SemiMarkov(self.n_components, rng=0)
n = 50
seq1 = self.smm.sample(n)
seq2 = smm2.sample(n)
np.testing.assert_equal(seq1, seq2)
def test_int_seed_uses_numpy_default_rng(self):
smm2 = SemiMarkov(self.n_components, rng=np.random.default_rng(0))
n = 43
seq1 = self.smm.sample(n)
seq2 = smm2.sample(n)
np.testing.assert_equal(seq1, seq2)
def setUp(self):
self.n_components = 4
self.min_dwell = [2, 3, 1, 0]
self.max_dwell = [5, 3, np.inf, 4]
self.dwell_times = [2.5, 3.0, 3.5, 2.0]
self.smm = SemiMarkov(
self.n_components,
min_dwell=self.min_dwell,
max_dwell=self.max_dwell,
dwell_times=self.dwell_times,
)
def test_all_transitions_occur_if_dwell_time_larger_than_one(self):
n_components = 3
smm = SemiMarkov(n_components, rng=5, dwell_times=2.0)
n_seq = 5
n = 200
for i in range(n_seq):
seq = smm.sample(n)
pairs = set(zip(seq, seq[1:]))
self.assertEqual(len(pairs), n_components**2)
def test_all_non_dwelling_transitions_occur_by_default(self):
n_components = 3
smm = SemiMarkov(n_components, rng=4)
n_seq = 5
n = 200
for i in range(n_seq):
seq = smm.sample(n)
pairs = set(zip(seq, seq[1:]))
self.assertEqual(len(pairs), n_components * (n_components - 1))
def test_transform_second_retval_is_usage_seq_from_semi_markov_when_ret_usseq(
self):
arma_hsmm = ArmaHSMM(self.armas)
n = 15
_, usage_seq = arma_hsmm.transform(n, return_usage_seq=True)
smm = SemiMarkov(2)
usage_seq_exp = smm.sample(n)
np.testing.assert_allclose(usage_seq, usage_seq_exp)
def test_single_non_zero_initial_prob(self):
n_components = 6
start_prob = np.zeros(n_components)
state_idx = 3
start_prob[state_idx] = 1.0
smm = SemiMarkov(n_components, start_prob=start_prob)
n_seq = 40
n = 4
for i in range(n_seq):
seq = smm.sample(n)
self.assertEqual(seq[0], state_idx, f"at iteration {i}")
def test_all_states_occur_by_default(self):
n_components = 5
smm = SemiMarkov(n_components, rng=2)
n_seq = 50
n = 3
all_ini_states = []
for i in range(n_seq):
seq = smm.sample(n)
all_ini_states.append(seq[0])
self.assertEqual(set(all_ini_states), set(range(n_components)))
def test_additional_init_kwargs_passed_to_semi_markov(self):
kwargs = dict(max_dwell=20, rng=5)
arma_hsmm = ArmaHSMM(self.armas, **kwargs)
n = 15
_, _, usage_seq = arma_hsmm.transform(n,
return_input=True,
return_usage_seq=True)
smm = SemiMarkov(2, **kwargs)
usage_seq_exp = smm.sample(n)
np.testing.assert_allclose(usage_seq, usage_seq_exp)
class TestSemiMarkovDwellTimeConstraintsObeyed(unittest.TestCase):
def setUp(self):
self.n_components = 4
self.min_dwell = [2, 3, 1, 0]
self.max_dwell = [5, 3, np.inf, 4]
self.dwell_times = [2.5, 3.0, 3.5, 2.0]
self.smm = SemiMarkov(
self.n_components,
min_dwell=self.min_dwell,
max_dwell=self.max_dwell,
dwell_times=self.dwell_times,
)
@staticmethod
def to_rle(seq: np.ndarray) -> list:
starts = np.hstack(([0], np.diff(seq).nonzero()[0] + 1, len(seq)))
rle = [(seq[tmp1], tmp2 - tmp1)
for tmp1, tmp2 in zip(starts, starts[1:])]
return rle
def test_dwell_times_reach_minimum_but_do_not_go_below(self):
seq = self.smm.sample(300)
seq_rle = self.to_rle(seq)
for i in range(self.n_components):
# last element of RLE might be truncated due to n_samples
dwell_times = [_[1] for _ in seq_rle[:-1] if _[0] == i]
self.assertGreater(len(dwell_times), 0,
f"State {i} does not occur")
self.assertEqual(np.min(dwell_times), max(1, self.min_dwell[i]),
f"State {i}")
def test_dwell_times_reach_maximum_but_do_not_go_above(self):
seq = self.smm.sample(2000)
seq_rle = self.to_rle(seq)
for i in range(self.n_components):
# last element of RLE might be truncated due to n_samples
dwell_times = [_[1] for _ in seq_rle[:-1] if _[0] == i]
self.assertGreater(len(dwell_times), 0,
f"State {i} does not occur")
if np.isfinite(self.max_dwell[i]):
self.assertEqual(np.max(dwell_times), self.max_dwell[i],
f"State {i}")
else:
self.assertGreater(len(np.unique(dwell_times)), 0,
f"State {i}")
def __init__(self, models: Sequence, **kwargs):
""" Initialize the ARMA HSMM.
Parameters
----------
models
Sequence of models to use. This sets the number of states in the
semi-Markov model.
All other keyword arguments are passed to the semi-Markov model
constructor.
"""
self.models = models
self.smm = SemiMarkov(len(models), **kwargs)
self.n_features = 1
self.n_components = 1
def test_several_non_zero_initial_prob(self):
n_components = 6
start_prob = np.zeros(n_components)
state_idxs = [1, 3, 5]
start_prob[state_idxs] = 1.0 / len(state_idxs)
smm = SemiMarkov(n_components, start_prob=start_prob, rng=1)
n_seq = 40
n = 4
all_ini_states = []
for i in range(n_seq):
seq = smm.sample(n)
self.assertIn(seq[0], state_idxs, f"at iteration {i}")
all_ini_states.append(seq[0])
self.assertEqual(set(all_ini_states), set(state_idxs))
def test_absorbing_state(self):
n_components = 3
abs_idx = 2
dwell_times = np.ones(n_components)
dwell_times[abs_idx] = np.inf
smm = SemiMarkov(n_components, dwell_times=dwell_times)
n_seq = 10
n = 16
for i in range(n_seq):
seq = smm.sample(n)
where_abs = (seq == abs_idx).nonzero()[0]
# make sure we reach absorbing state
self.assertGreater(len(where_abs), 0)
# and stay there once we've reached it
np.testing.assert_equal(seq[where_abs[0]:], abs_idx)
def __getitem__(self, idx: int) -> SwitchingSnippetSignal:
""" Generate a signal.
Parameters
----------
idx
The index of the signal to generate.
Returns a `SwitchingSnippetSignal` instance. Note that the signal is generated
anew every time it is accessed, making this a potentially time-consuming
operation.
"""
if idx < 0:
idx = self.n_signals + idx
if idx < 0 or idx >= self.n_signals:
raise IndexError("index out of range")
seed = self.signal_seeds[idx]
rng = np.random.default_rng(seed)
# create an ArmaHSMM instance
semi_markov = SemiMarkov(len(self.snippets),
rng=rng,
**self.semi_markov_kws)
usage_seq = semi_markov.sample(self.n_samples)
# generate the signal
y = np.zeros(self.n_samples)
usage_rle = rle_encode(usage_seq)
idx = 0
for elem, n in usage_rle:
crt_snippet = self.snippets[elem]
crt_start = rng.integers(0, len(crt_snippet) - n + 1)
y[idx:idx + n] = crt_snippet[crt_start:crt_start + n]
idx += n
# normalize, if asked to
if self.normalize:
scale = 1.0 / np.std(y)
y *= scale
else:
scale = 1.0
return SwitchingSnippetSignal(y=y, usage_seq=usage_seq, scale=scale)
def test_deterministic_cyclic_transitions(self):
n_components = 4
cycle = [2, 3, 1, 0]
trans_mat = np.zeros((n_components, n_components))
allowed_pairs = set()
for i in range(len(cycle)):
s1 = cycle[i]
s2 = cycle[(i + 1) % len(cycle)]
trans_mat[s1, s2] = 1.0
allowed_pairs.add((s1, s2))
smm = SemiMarkov(n_components, trans_mat=trans_mat)
n_seq = 6
n = 40
for i in range(n_seq):
seq = smm.sample(n)
pairs = set(zip(seq, seq[1:]))
for s1, s2 in pairs:
self.assertIn((s1, s2), allowed_pairs, f"iteration {i}")
class TestSemiMarkovStateContentOfOutputIsRight(unittest.TestCase):
def setUp(self):
self.n_components = 4
self.smm = SemiMarkov(self.n_components, rng=1)
def test_all_states_are_between_zero_and_n_components(self):
n = 100
seq = self.smm.sample(n)
self.assertGreaterEqual(np.min(seq), 0)
self.assertLess(np.max(seq), self.n_components)
def test_lowest_state_in_long_sequence_is_zero(self):
n = 200
seq = self.smm.sample(n)
self.assertEqual(np.min(seq), 0)
def test_highest_state_in_long_sequence_is_n_components_minus_one(self):
n = 200
seq = self.smm.sample(n)
self.assertEqual(np.max(seq), self.n_components - 1)
class TestSemiMarkovWithPseudorandom(unittest.TestCase):
def setUp(self):
self.n_components = 4
self.smm = SemiMarkov(self.n_components)
def test_repeated_runs_yield_different_results(self):
n = 100
seq1 = self.smm.sample(n)
seq2 = self.smm.sample(n)
self.assertGreater(np.max(np.abs(seq1 - seq2)), 0)
def test_default_seed_is_zero(self):
smm2 = SemiMarkov(self.n_components, rng=0)
n = 50
seq1 = self.smm.sample(n)
seq2 = smm2.sample(n)
np.testing.assert_equal(seq1, seq2)
def test_output_is_int(self):
n = 23
seq = self.smm.sample(n)
dtype = np.asarray(seq).dtype
self.assertTrue(np.issubdtype(dtype, np.integer))
def test_int_seed_uses_numpy_default_rng(self):
smm2 = SemiMarkov(self.n_components, rng=np.random.default_rng(0))
n = 43
seq1 = self.smm.sample(n)
seq2 = smm2.sample(n)
np.testing.assert_equal(seq1, seq2)
def setUp(self):
self.n_components = 3
self.start_prob = np.asarray([0.2, 0.5, 0.3])
self.trans_mat = np.asarray([[0.0, 0.3, 0.7], [0.1, 0.0, 0.9],
[0.5, 0.5, 0.0]])
self.dwell_times = np.asarray([2.5, 4.5, 3.0])
self.min_dwell = np.asarray([2, 3, 1])
self.max_dwell = np.asarray([np.inf, 10, 8])
self.rng = np.random.default_rng(4)
self.smm = SemiMarkov(
self.n_components,
start_prob=self.start_prob,
trans_mat=self.trans_mat,
dwell_times=self.dwell_times,
min_dwell=self.min_dwell,
max_dwell=self.max_dwell,
rng=self.rng,
)
def test_default_dwell_times_are_equal_to_one(self):
ns = 3
rng = np.random.default_rng(3)
trans_mat = rng.uniform(size=(ns, ns))
smm1 = SemiMarkov(ns, trans_mat=trans_mat)
n = 10
seq1 = smm1.sample(n)
smm2 = SemiMarkov(ns, trans_mat=trans_mat, dwell_times=1)
seq2 = smm2.sample(n)
np.testing.assert_equal(seq1, seq2)
def test_diagonal_trans_mat_elements_are_ignored(self):
ns = 5
rng = np.random.default_rng(1)
trans_mat1 = rng.uniform(size=(ns, ns))
trans_mat2 = np.copy(trans_mat1)
trans_mat1 += np.diag(rng.uniform(low=-1, high=1, size=ns))
smm1 = SemiMarkov(ns, trans_mat=trans_mat1)
n = 32
seq1 = smm1.sample(n)
smm2 = SemiMarkov(ns, trans_mat=trans_mat2)
seq2 = smm2.sample(n)
np.testing.assert_equal(seq1, seq2)
def test_dwell_times_affect_generated_sequence(self):
ns = 3
rng = np.random.default_rng(4)
trans_mat = rng.uniform(size=(ns, ns))
dwell_times1 = rng.uniform(low=0, high=10, size=ns)
smm1 = SemiMarkov(ns, trans_mat=trans_mat, dwell_times=dwell_times1)
n = 100
seq1 = smm1.sample(n)
dwell_times2 = rng.uniform(low=0, high=10, size=ns)
smm2 = SemiMarkov(ns, trans_mat=trans_mat, dwell_times=dwell_times2)
seq2 = smm2.sample(n)
self.assertGreater(np.max(np.abs(seq1 - seq2)), 0)
def test_offdiagonal_trans_mat_elements_are_normalized(self):
ns = 4
rng = np.random.default_rng(2)
trans_mat1 = rng.uniform(size=(ns, ns))
trans_mat1 -= np.diag(np.diag(trans_mat1))
trans_mat2 = 3.2 * trans_mat1
smm1 = SemiMarkov(ns, trans_mat=trans_mat1)
n = 27
seq1 = smm1.sample(n)
smm2 = SemiMarkov(ns, trans_mat=trans_mat2)
seq2 = smm2.sample(n)
np.testing.assert_equal(seq1, seq2)
class ArmaHSMM(object):
""" A hidden semi-Markov model with ARMA emissions.
This class can be used to generate samples from a non-stationary stochastic
process that stochastically switches between several ARMA processes based on
a hidden semi-Markov model.
Attributes
==========
n_features : int
Number of input dimensions. This is always equal to 1.
n_components : int
Number of output dimensions.This is always equal to 1.
models
Sequence of models to use.
smm
Semi-Markov model used to generate ARMA states.
"""
def __init__(self, models: Sequence, **kwargs):
""" Initialize the ARMA HSMM.
Parameters
----------
models
Sequence of models to use. This sets the number of states in the
semi-Markov model.
All other keyword arguments are passed to the semi-Markov model
constructor.
"""
self.models = models
self.smm = SemiMarkov(len(models), **kwargs)
self.n_features = 1
self.n_components = 1
def transform(
self,
n_samples: Optional[int] = None,
X: Union[None, Sequence, Callable] = None,
initial_conditions: Optional[Tuple[Sequence, Sequence]] = None,
return_input: bool = False,
return_usage_seq: bool = False,
) -> Union[
np.ndarray,
Tuple[np.ndarray, np.ndarray],
Tuple[np.ndarray, np.ndarray, np.ndarray],
]:
""" Process input samples.
The function uses exactly `n_samples` input samples.
If no input source is explicitly provided, the default source for each
of the ARMAs is used. An exception is raised if a process needs to be
used that does not have a default source.
Parameters
----------
n_samples
Number of samples to generate. If not provided, `U` must be provided
and it must be a sequence.
X
Input samples or input generator. See `Arma.transform`.
initial_conditions
A tuple, `(initial_y, initial_x)`, of recent samples of the output
and input sequences used to seed the simulation. If these are not
provided, they are assumed equal to zero.
return_input
If true, returns both output and input. If false (the default), returns only
the output.
return_usage_seq
If true, returns the `usage_seq` in addition to output (and potentially
input).
Returns either a single array (`Y`) if `return_input` and `return_usage_seq` are
both false; or a tuple `(Y, X)` or `(Y, usage_sea)` if only `return_input` or
only `return_usage_seq` is true, respectively; or a tuple `(Y, X, usage_seq)` if
both are true. Here `Y` is an array of generated `y`; `X` contains the input `x`
samples; and `usage_seq` is an integer array indicating which model was used at
each time step. If the `X` parameter was used and was a sequence, the output `X`
simply mirrors the input `X`.
"""
# check inputs
if n_samples is None:
if X is None or not hasattr(X, "__len__"):
raise ValueError("Need either n_samples or sequence U.")
n_samples = len(X)
# generate usage sequence, then use sample_switching_models
usage_seq = self.smm.sample(n_samples)
y, x = sample_switching_models(
self.models,
usage_seq,
X=X,
initial_conditions=initial_conditions,
return_input=True,
)
res = (y,)
if return_input:
res = res + (x,)
if return_usage_seq:
res = res + (usage_seq,)
if len(res) == 1:
return res[0]
else:
return res
def __repr__(self) -> str:
r = f"ArmaHSMM(models={repr(self.models)}, smm={repr(self.smm)})"
return r
def __str__(self) -> str:
s = f"ArmaHSMM(models={str(self.models)}, smm={str(self.smm)})"
return s
def setUp(self):
self.n_components = 4
self.smm = SemiMarkov(self.n_components)
def test_no_error(self):
smm = SemiMarkov(5, rng=np.random.RandomState(1))
n = 13
seq = smm.sample(n)
self.assertEqual(len(seq), n)
def test_raises_value_error_if_dwell_times_not_below_dwell_max(self):
with self.assertRaises(ValueError):
SemiMarkov(2, dwell_times=[100, 10], max_dwell=20)
def test_raises_value_error_if_dwell_times_not_above_dwell_min(self):
with self.assertRaises(ValueError):
SemiMarkov(2, dwell_times=[100, 10], min_dwell=20)