def time_laplace_em_end2end(ncalls=5):
print("Benchmarking 1 iter of laplace-em fitting on Vanilla LDS.")
params_list = [SINGLE_DATA_PARAMS, MULT_DATA_PARAMS]
for (N, D, T, num_datas) in params_list:
lds_true = ssm.LDS(N, D, dynamics="gaussian", emissions="gaussian")
datas = [lds_true.sample(T)[1] for _ in range(num_datas)]
lds_new = ssm.LDS(N, D, dynamics="gaussian", emissions="gaussian")
print("N, D, T, num_datas: = ", N, D, T, num_datas)
total = timeit.timeit(
lambda: lds_new.fit(datas, initialize=False, num_iters=1),
number=ncalls)
print("Avg time per call: %f" % (total / ncalls))
def time_lds_sample(ncalls=20):
print("Testing continuous sample performance:")
params_list = [SINGLE_DATA_PARAMS, MULT_DATA_PARAMS]
for (N, D, T, num_datas) in params_list:
lds_true = ssm.LDS(N, D, dynamics="gaussian", emissions="gaussian")
datas = [lds_true.sample(T)[1] for _ in range(num_datas)]
# Calling fit will return a variational posterior object.
# This is simpler than creating one ourselves.
_, posterior = lds_true.fit(datas,
initialize=False,
num_iters=1,
method="laplace_em")
# Now we test the speed of sampling from this object.
print("N, D, T, num_datas: = ", N, D, T, num_datas)
total = timeit.timeit(lambda: posterior.sample_continuous_states(),
number=ncalls)
print("Avg time per call: %f" % (total / ncalls))
# Specify whether or not to save figures save_figures = False # In[2]: # Set the parameters of the HMM T = 200 # number of time bins K = 5 # number of discrete states D = 2 # number of latent dimensions N = 10 # number of observed dimensions # In[3]: # Make an LDS with the somewhat interesting dynamics parameters true_lds = ssm.LDS(N, D, emissions="gaussian") A0 = .99 * random_rotation(D, theta=np.pi / 20) # S = (1 + 3 * npr.rand(D)) S = np.arange(1, D + 1) R = np.linalg.svd(npr.randn(D, D))[0] * S A = R.dot(A0).dot(np.linalg.inv(R)) b = npr.randn(D) true_lds.dynamics.As[0] = A true_lds.dynamics.bs[0] = b _, x, y = true_lds.sample(T) # In[4]: # Plot the dynamics vector field xmins = x.min(axis=0) xmaxs = x.max(axis=0)
from ssm.util import random_rotation, find_permutation
# In[2]:
# Set the parameters of the LDS
T = 50 # number of time bins per batch
B = 20 # number of batches
D = 2 # number of latent dimensions
N = 10 # number of observed dimensions
# In[3]:
# Make an SLDS with the true parameters
true_lds = ssm.LDS(N,
D,
emissions="poisson_nn",
emission_kwargs=dict(link="softplus",
hidden_layer_sizes=(50, 50)))
true_lds.dynamics.As[0] = .95 * random_rotation(D, theta=(1) * np.pi / 20)
# Sample a bunch of short trajectories
# (they all converge so we only learn from the initial condition)
zs, xs, ys = list(zip(*[true_lds.sample(T) for _ in range(B)]))
# In[4]:
for x in xs:
plt.plot(x[:, 0], x[:, 1])
plt.xlabel("$x_1$")
plt.ylabel("$x_2$")
plt.title("Simulated latent trajectories")