Getting Started

Let’s implement an HMM with the following state transition graph using HidTen:

IR -> E0 -> E1 -> E2
^------^-----------|

This can be done by creating a hidten.tf.hmm.TFHMM object. The hidten.tf.hmm.TFHMM derives from tf.keras.Layer. Under the hood, two important components are created automatically (if the user does not provide them specifically), that are used by all HidTen algorithms: The hidten.emitter.Emitter and the hidten.transitioner.Transitioner.

The Emitter computes emission scores from observations. The Transitioner implements the state transition graph and computes timesteps in a Markov chain.

Let’s see this in action:

# Create a new HMM with 4 states
hmm = TFHMM(states=4)

# Always start in the first state (IR)
hmm.transitioner.allow_start = [0]

# Define the state transition graph
hmm.transitioner.allow = [
    (0, 0),     # IR -> IR
    (0, 1),     # IR -> E0
    (1, 2),     # E0 -> E1
    (2, 3),     # E1 -> E2
    (3, 0),     # E2 -> IR
    (3, 1),     # E2 -> E0
]

# Initialize the transition probabilities
# The initialize has the same order as used above for allow
p_enter_E0, p_enter_IR = 0.1, 0.5
hmm.transitioner.initializer = [
    1-p_enter_E0,
    p_enter_E0,
    1.,
    1.,
    p_enter_IR,
    1-p_enter_IR,
]

# The default emitter is a Categorical Emitter over a discrete observation space.
# Let the alphabet be {0, 1, 2, 3}.
# We define emission probabilities:
hmm.emitter[0].initializer = [
    0.25, 0.25, 0.25, 0.25,   # IR
    0.4, 0.2, 0.2, 0.2,       # E0
    0.4, 0.2, 0.2, 0.2,       # E1
    0.4, 0.2, 0.2, 0.2,       # E2
]
# Note that HidTen supports multiple emitters, which is why the emitter property
# is a list of emitters - by default only containing the CategoricalEmitter.

In TensorFlow, a layer has to be built to be used. Run:

hmm.build((None, None, 4))

We can now inspect the transition- and emission-matrices that we’ve just defined:

hmm.transitioner.matrix()

hmm.emitter[0].matrix()

Next, we’ll see how to use the hmm for inference.