<div id="readability-page-1" class="page"><div>
<p>Let me start by emphasizing that HMM’s core purpose is identifying the hidden states given observations. In such case, hidden state corresponds to labels, e.g., phonemes in the speech given features from speech data.</p>



<p>But it can also be used for output generation. In this case, we predict next observations, using hidden states and transition probs. From the predicted state, we sample next outputs. Example in this category would be predicting tomorrow’s stock price.</p>



<p>Since next state and output isn’t the core mission, hmmlearn doesn’t have predict method of next outputs. But it can be calculated as below.</p>


<div><pre title="">import numpy as np
from sklearn.utils import check_random_state

# Get the states from the input data
states = model.predict(X)

# We now want to predict the next state.
# It's done as in https://en.wikipedia.org/wiki/Inverse_transform_sampling
# 1) From state transition matrix, get the CDF.
transmat_cdf = np.cumsum(model.transmat_, axis=1)
random_state = check_random_state(model.random_state)
# 2) Get a random number. We use model's current random_state which can then be used to get a next
#    random number. If F(x) &gt;= random_state.rand(), x is the next state.
#    argmax() let us find the smallest state index when there's tie, btw.
next_state = (transmat_cdf[states[-1]] &gt; random_state.rand()).argmax()

# From the next state, generate sample.
next_obs = model._generate_sample_from_state(next_state, random_state)
</pre></div>


<p>Example)<br>states: I have 3 states.</p>


<div><pre title="">[1 0 1 2 2 1 0 1 0 1 0 1 2 2 0 1 0 1 0 1 0 1 0 1 2 2 2 1 0 1 2 1 2 1 0 1 0
 1 0 1 0 1 0 1 2 2 2 1 0 1 2 0 1 2 2 2 0 1 0 1 2 2 2 2 1 0 1 0 1 0 1 0 1 2
 2 1 0 1 0 1 0 1 0 1 2 2 2 2 1 0 1 0 1 2 2 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
 1 0 1 0 1 0 1 0 1 2 1 2 2 2 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 2 2 2 1 0
 1 0 1 0 1 2 0 1 2 2 2 1 0 1 2 0 1 0 1 0 1 2 2 1 0 1 0 1 2 0 1 2 2 1 0 1 2
 2 2 1 0 1 2 0 1 0 1 0 1 0 1 0]
</pre></div>


<p>model.transmat_: 3×3 state transition matrix. (i, j) = transition prob. of state i -&gt; state j.</p>


<div><pre title="">model.transmat_=array([[5.08198885e-34, 1.00000000e+00, 2.54323877e-10],
                       [7.09506733e-01, 7.07290542e-14, 2.90493267e-01],
                       [1.63093521e-01, 3.38933349e-01, 4.97973129e-01]])
</pre></div>


<p>transform_cdf</p>


<div><pre title="">transmat_cdf=array([[5.08198885e-34, 1.00000000e+00, 1.00000000e+00],
                    [7.09506733e-01, 7.09506733e-01, 1.00000000e+00],
                    [1.63093521e-01, 5.02026871e-01, 1.00000000e+00]])
</pre></div>


<p>To find the next state, Inverse transform sampling from the ith row where i=last state in my prediction<br></p>


<div><pre title="">(transmat_cdf[states[-1]] &gt; random_state.rand())=array([False,  True,  True])
next_state=1
</pre></div>


<p>And then you get next sample using emission prob.</p>
</div></div>

Passion is like genius; a miracle.

Let me start by emphasizing that HMM’s core purpose is identifying the hidden states given observations. In such case, hidden state corresponds to labels, e.g., phonemes in the speech given features from speech data. But it can also be used for output generation. In this case, we predict next observations, using hidden states and transition […]

Predicting next state and observation in hmmlearn

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