def test_DiscreteMarkovChain_point():
test_Gammas = at.as_tensor_variable(np.array([[[1.0, 0.0], [0.0, 1.0]]]))
with pm.Model():
# XXX: `draw_values` won't use the `Deterministic`s values in the `point` map!
# Also, `Constant` is only for integer types (?!), so we can't use that.
test_gamma_0 = pm.Dirichlet("gamma_0", np.r_[1.0, 1000.0], shape=2)
test_point = {"gamma_0": np.r_[1.0, 0.0]}
assert np.all(
DiscreteMarkovChain.dist(test_Gammas, test_gamma_0,
shape=10).random(point=test_point) == 0)
assert np.all(
DiscreteMarkovChain.dist(test_Gammas, 1.0 -
test_gamma_0, shape=10).random(
point=test_point) == 1)
def test_DiscreteMarkovChain_logp(Gammas, gamma_0, obs, exp_res):
aesara.config.compute_test_value = "warn"
test_dist = DiscreteMarkovChain.dist(Gammas, gamma_0, shape=obs.shape[-1])
test_logp_tt = test_dist.logp(obs)
test_logp_val = test_logp_tt.eval()
if exp_res is None:
def logp_single_chain(Gammas, gamma_0, obs):
state_transitions = np.stack([obs[:-1], obs[1:]]).T
p_S_0_to_1 = gamma_0.dot(Gammas[0])
p_S_obs = np.empty_like(obs, dtype=np.float64)
p_S_obs[0] = p_S_0_to_1[obs[0]]
for t, (S_tm1, S_t) in enumerate(state_transitions):
p_S_obs[t + 1] = Gammas[t, S_tm1, S_t]
return np.log(p_S_obs)
logp_fn = np.vectorize(logp_single_chain,
signature="(n,m,m),(m),(n)->(n)")
Gammas = np.broadcast_to(Gammas, (obs.shape[0], ) + Gammas.shape[-2:])
exp_res = logp_fn(Gammas, gamma_0, obs)
exp_res = exp_res.sum(-1)
assert np.allclose(test_logp_val, exp_res)
def test_DiscreteMarkovChain_random():
# A single transition matrix and initial probabilities vector for each
# element in the state sequence
test_Gamma = np.array([[[1.0, 0.0], [0.0, 1.0]]])
test_gamma_0 = np.r_[0.0, 1.0]
test_sample = DiscreteMarkovChain.dist(test_Gamma, test_gamma_0,
shape=10).random()
assert np.all(test_sample == 1)
test_sample = DiscreteMarkovChain.dist(test_Gamma,
1.0 - test_gamma_0,
shape=10).random()
assert np.all(test_sample == 0)
test_sample = DiscreteMarkovChain.dist(test_Gamma, test_gamma_0,
shape=10).random(size=12)
assert test_sample.shape == (
12,
10,
)
test_sample = DiscreteMarkovChain.dist(test_Gamma, test_gamma_0,
shape=10).random(size=2)
assert np.array_equal(test_sample,
np.stack([np.ones(10), np.ones(10)], 0).astype(int))
# Now, the same set-up, but--this time--generate two state sequences
# samples
test_Gamma = np.array([[[0.8, 0.2], [0.2, 0.8]]])
test_gamma_0 = np.r_[0.2, 0.8]
test_sample = DiscreteMarkovChain.dist(test_Gamma, test_gamma_0,
shape=10).random(size=2)
# TODO: Fix the seed, and make sure there's at least one 0 and 1?
assert test_sample.shape == (2, 10)
# Two transition matrices--for two distinct state sequences--and one vector
# of initial probs.
test_Gamma = np.stack([
np.array([[[1.0, 0.0], [0.0, 1.0]]]),
np.array([[[1.0, 0.0], [0.0, 1.0]]])
])
test_gamma_0 = np.r_[0.0, 1.0]
test_dist = DiscreteMarkovChain.dist(test_Gamma,
test_gamma_0,
shape=(2, 10))
test_sample = test_dist.random()
assert np.array_equal(test_sample,
np.stack([np.ones(10), np.ones(10)], 0).astype(int))
assert test_sample.shape == (2, 10)
# Now, the same set-up, but--this time--generate three state sequence
# samples
test_sample = test_dist.random(size=3)
assert np.array_equal(
test_sample,
np.tile(
np.stack([np.ones(10), np.ones(10)], 0).astype(int), (3, 1, 1)),
)
assert test_sample.shape == (3, 2, 10)
# Two transition matrices and initial probs. for two distinct state
# sequences
test_Gamma = np.stack([
np.array([[[1.0, 0.0], [0.0, 1.0]]]),
np.array([[[1.0, 0.0], [0.0, 1.0]]])
])
test_gamma_0 = np.stack([np.r_[0.0, 1.0], np.r_[1.0, 0.0]])
test_dist = DiscreteMarkovChain.dist(test_Gamma,
test_gamma_0,
shape=(2, 10))
test_sample = test_dist.random()
assert np.array_equal(test_sample,
np.stack([np.ones(10), np.zeros(10)], 0).astype(int))
assert test_sample.shape == (2, 10)
# Now, the same set-up, but--this time--generate three state sequence
# samples
test_sample = test_dist.random(size=3)
assert np.array_equal(
test_sample,
np.tile(
np.stack([np.ones(10), np.zeros(10)], 0).astype(int), (3, 1, 1)),
)
assert test_sample.shape == (3, 2, 10)
# "Time"-varying transition matrices with a single vector of initial
# probabilities
test_Gamma = np.stack(
[
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[1.0, 0.0], [0.0, 1.0]]),
],
axis=0,
)
test_gamma_0 = np.r_[1, 0]
test_dist = DiscreteMarkovChain.dist(test_Gamma, test_gamma_0, shape=3)
test_sample = test_dist.random()
assert np.array_equal(test_sample, np.r_[1, 0, 0])
# Now, the same set-up, but--this time--generate three state sequence
# samples
test_sample = test_dist.random(size=3)
assert np.array_equal(test_sample,
np.tile(np.r_[1, 0, 0].astype(int), (3, 1)))
# "Time"-varying transition matrices with two initial
# probabilities vectors
test_Gamma = np.stack(
[
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[1.0, 0.0], [0.0, 1.0]]),
],
axis=0,
)
test_gamma_0 = np.array([[1, 0], [0, 1]])
test_dist = DiscreteMarkovChain.dist(test_Gamma,
test_gamma_0,
shape=(2, 3))
test_sample = test_dist.random()
assert np.array_equal(test_sample, np.array([[1, 0, 0], [0, 1, 1]]))
# Now, the same set-up, but--this time--generate three state sequence
# samples
test_sample = test_dist.random(size=3)
assert np.array_equal(
test_sample,
np.tile(np.array([[1, 0, 0], [0, 1, 1]]).astype(int), (3, 1, 1)))
# Two "Time"-varying transition matrices with two initial
# probabilities vectors
test_Gamma = np.stack(
[
[
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[1.0, 0.0], [0.0, 1.0]]),
],
[
np.array([[1.0, 0.0], [0.0, 1.0]]),
np.array([[1.0, 0.0], [0.0, 1.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
],
],
axis=0,
)
test_gamma_0 = np.array([[1, 0], [0, 1]])
test_dist = DiscreteMarkovChain.dist(test_Gamma,
test_gamma_0,
shape=(2, 3))
test_sample = test_dist.random()
assert np.array_equal(test_sample, np.array([[1, 0, 0], [1, 1, 0]]))
# Now, the same set-up, but--this time--generate three state sequence
# samples
test_sample = test_dist.random(size=3)
assert np.array_equal(
test_sample,
np.tile(np.array([[1, 0, 0], [1, 1, 0]]).astype(int), (3, 1, 1)))
def test_DiscreteMarkovChain_logp():
theano.config.compute_test_value = "warn"
# A single transition matrix and initial probabilities vector for each
# element in the state sequence
test_Gammas = np.array([[[0.0, 1.0], [1.0, 0.0]]])
test_gamma_0 = np.r_[1.0, 0.0]
test_obs = np.r_[1, 0, 1, 0]
test_dist = DiscreteMarkovChain.dist(test_Gammas,
test_gamma_0,
shape=test_obs.shape[-1])
test_logp_tt = test_dist.logp(test_obs)
assert test_logp_tt.eval() == 0
# "Time"-varying transition matrices with a single vector of initial
# probabilities
test_Gammas = np.stack(
[
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
],
axis=0,
)
test_gamma_0 = np.r_[1.0, 0.0]
test_obs = np.r_[1, 0, 1, 0]
test_dist = DiscreteMarkovChain.dist(test_Gammas,
test_gamma_0,
shape=test_obs.shape[-1])
test_logp_tt = test_dist.logp(test_obs)
assert test_logp_tt.eval() == 0
# Static transition matrix and two state sequences
test_Gammas = np.array([[[0.0, 1.0], [1.0, 0.0]]])
test_obs = np.array([[1, 0, 1, 0], [0, 1, 0, 1]])
test_gamma_0 = np.r_[0.5, 0.5]
test_dist = DiscreteMarkovChain.dist(test_Gammas,
test_gamma_0,
shape=test_obs.shape[-1])
test_logp_tt = test_dist.logp(test_obs)
test_logp = test_logp_tt.eval()
assert test_logp[0] == test_logp[1]
# Time-varying transition matrices and two state sequences
test_Gammas = np.stack(
[
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
],
axis=0,
)
test_obs = np.array([[1, 0, 1, 0], [0, 1, 0, 1]])
test_gamma_0 = np.r_[0.5, 0.5]
test_dist = DiscreteMarkovChain.dist(test_Gammas,
test_gamma_0,
shape=test_obs.shape[-1])
test_logp_tt = test_dist.logp(test_obs)
test_logp = test_logp_tt.eval()
assert test_logp[0] == test_logp[1]
# Two sets of time-varying transition matrices and two state sequences
test_Gammas = np.stack(
[
[
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
np.array([[0.0, 1.0], [1.0, 0.0]]),
],
[
np.array([[1.0, 0.0], [0.0, 1.0]]),
np.array([[1.0, 0.0], [0.0, 1.0]]),
np.array([[1.0, 0.0], [0.0, 1.0]]),
np.array([[1.0, 0.0], [0.0, 1.0]]),
],
],
axis=0,
)
test_obs = np.array([[1, 0, 1, 0], [0, 0, 0, 0]])
test_gamma_0 = np.r_[0.5, 0.5]
test_dist = DiscreteMarkovChain.dist(test_Gammas,
test_gamma_0,
shape=test_obs.shape[-1])
test_logp_tt = test_dist.logp(test_obs)
test_logp = test_logp_tt.eval()
assert test_logp[0] == test_logp[1]
# Two sets of time-varying transition matrices--via `gamma_0`
# broadcasting--and two state sequences
test_gamma_0 = np.array([[0.5, 0.5], [0.5, 0.5]])
test_dist = DiscreteMarkovChain.dist(test_Gammas,
test_gamma_0,
shape=test_obs.shape[-1])
test_logp_tt = test_dist.logp(test_obs)
test_logp = test_logp_tt.eval()
assert test_logp[0] == test_logp[1]
# "Time"-varying transition matrices with a single vector of initial
# probabilities, but--this time--with better test values
test_Gammas = np.stack(
[
np.array([[0.1, 0.9], [0.5, 0.5]]),
np.array([[0.2, 0.8], [0.6, 0.4]]),
np.array([[0.3, 0.7], [0.7, 0.3]]),
np.array([[0.4, 0.6], [0.8, 0.2]]),
],
axis=0,
)
test_gamma_0 = np.r_[0.3, 0.7]
test_obs = np.r_[1, 0, 1, 0]
test_dist = DiscreteMarkovChain.dist(test_Gammas,
test_gamma_0,
shape=test_obs.shape[-1])
test_logp_tt = test_dist.logp(test_obs)
logp_res = test_logp_tt.eval()
logp_exp = np.concatenate(
[
test_gamma_0.dot(test_Gammas[0])[None, ...],
test_Gammas[(np.ogrid[1:4], test_obs[:-1])],
],
axis=-2,
)
logp_exp = logp_exp[(np.ogrid[:4], test_obs)]
logp_exp = np.log(logp_exp).sum()
assert np.allclose(logp_res, logp_exp)
