Quick Example#

(See the [full Jupyter notebook](examples/Quick_Example.ipynb).)

from nomopy.fhmm import FHMM

Generate some simulated data:

N = 1    # Number of time series
T = 200  # Number of samples per time series
d = 2    # Number of hidden fluctuators
k = 2    # Number of states for each fluctuator
o = 1    # Observable dimension

W, A, C, pi = FHMM.generate_random_model_params(T, d, k, o, seed=36)
C = np.array([[0.001]])  # Set low noise level

X, states = FHMM(T=T, d=d, o=o, k=k, W_fixed=W, A_fixed=A, C_fixed=C, pi_fixed=pi)\
            .generate(N, T, return_states=True)
# X has shape (N, T, o)
plt.plot(X[0, :, 0])
_images/example_X.png

Example timeseries#

Fitting a FHMM using the exact method:

fhmm = FHMM(T=T, d=d, o=o, k=k, em_max_iter=100, method='exact', verbose=False)
fhmm.fit(X)
fhmm.plot_fit()
_images/example_fit.png

Example fit#

Calculate the most likely (Viterbi) hidden state trajectories:

viterbi = fhmm.viterbi(0)  # Sample 0

fig, axs = plt.subplots(2, 1, figsize=(20, 8))
axs[0].plot(viterbi[:, 0, 0])  # shape=(T, d, k)
axs[1].plot(states[0, :, 0, 0], c='r')  # shape=(N, T, d, k)
axs[0].set_ylabel('Viterbi', fontsize=15)
axs[1].set_ylabel('Actual', fontsize=15)
Hidden state trajectory inferred by Viterbi algorithm

Inferred hidden state trajectory for fluctuator 1 as inferred by the Viterbi algorithm (above) and the true trajectory (below)#

fig, axs = plt.subplots(2, 1, figsize=(20, 8))
axs[0].plot(viterbi[:, 1, 0])
axs[1].plot(states[0, :, 1, 0], c='r')
axs[0].set_ylabel('Viterbi', fontsize=15)
_images/example_viterbi_1.png

Inferred hidden state trajectory for fluctuator 2 as inferred by the Viterbi algorithm (above) and the true trajectory (below)#

Hidden state trajectory

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