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Description:

mchmm 0.4.3

mchmm is a Python package implementing Markov chains and Hidden Markov models in pure NumPy and SciPy.
It can also visualize Markov chains (see below).

Dependencies

NumPy
SciPy

Installation

Install from PyPi:

$ pip install mchmm

Clone a GitHub repository:

$ git clone https://github.com/maximtrp/mchmm.git
$ cd mchmm
$ pip install . --user

Features

Discrete Markov chains
Initializing a Markov chain using some data.
>>> import mchmm as mc
>>> a = mc.MarkovChain().from_data('AABCABCBAAAACBCBACBABCABCBACBACBABABCBACBBCBBCBCBCBACBABABCBCBAAACABABCBBCBCBCBCBCBAABCBBCBCBCCCBABCBCBBABCBABCABCCABABCBABC')
Now, we can look at the observed transition frequency matrix:
>>> a.observed_matrix
array([[ 7., 18., 7.],
[19., 5., 29.],
[ 5., 30., 3.]])
And the observed transition probability matrix:
>>> a.observed_p_matrix
array([[0.21875 , 0.5625 , 0.21875 ],
[0.35849057, 0.09433962, 0.54716981],
[0.13157895, 0.78947368, 0.07894737]])
You can visualize your Markov chain. First, build a directed graph with graph_make() method of MarkovChain object.
Then render() it.
>>> graph = a.graph_make(
format="png",
graph_attr=[("rankdir", "LR")],
node_attr=[("fontname", "Roboto bold"), ("fontsize", "20")],
edge_attr=[("fontname", "Iosevka"), ("fontsize", "12")]
)
>>> graph.render()
Here is the result:

Pandas can help us annotate columns and rows:
>>> import pandas as pd
>>> pd.DataFrame(a.observed_matrix, index=a.states, columns=a.states, dtype=int)
A B C
A 7 18 7
B 19 5 29
C 5 30 3
Viewing the expected transition frequency matrix:
>>> a.expected_matrix
array([[ 8.06504065, 13.78861789, 10.14634146],
[13.35772358, 22.83739837, 16.80487805],
[ 9.57723577, 16.37398374, 12.04878049]])
Calculating Nth order transition probability matrix:
>>> a.n_order_matrix(a.observed_p_matrix, order=2)
array([[0.2782854 , 0.34881028, 0.37290432],
[0.1842357 , 0.64252707, 0.17323722],
[0.32218957, 0.21081868, 0.46699175]])
Carrying out a chi-squared test:
>>> a.chisquare(a.observed_matrix, a.expected_matrix, axis=None)
Power_divergenceResult(statistic=47.89038802624337, pvalue=1.0367838347591701e-07)
Finally, let’s simulate a Markov chain given our data.
>>> ids, states = a.simulate(10, start='A', seed=np.random.randint(0, 10, 10))
>>> ids
array([0, 2, 1, 0, 2, 1, 0, 2, 1, 0])
>>> states
array(['A', 'C', 'B', 'A', 'C', 'B', 'A', 'C', 'B', 'A'], dtype='<U1')
>>> "".join(states)
'ACBACBACBA'

Hidden Markov models
We will use a fragment of DNA sequence with TATA box as an example. Initializing a hidden Markov model with sequences of observations and states:
>>> import mchmm as mc
>>> obs_seq = 'AGACTGCATATATAAGGGGCAGGCTG'
>>> sts_seq = '00000000111111100000000000'
>>> a = mc.HiddenMarkovModel().from_seq(obs_seq, sts_seq)
Unique states and observations are automatically inferred:
>>> a.states
['0' '1']
>>> a.observations
['A' 'C' 'G' 'T']
The transition probability matrix for all states can be accessed using tp attribute:
>>> a.tp
[[0.94444444 0.05555556]
[0.14285714 0.85714286]]
There is also ep attribute for the emission probability matrix for all states and observations.
>>> a.ep
[[0.21052632 0.21052632 0.47368421 0.10526316]
[0.57142857 0. 0. 0.42857143]]
Converting the emission matrix to Pandas DataFrame:
>>> import pandas as pd
>>> pd.DataFrame(a.ep, index=a.states, columns=a.observations)
A C G T
0 0.210526 0.210526 0.473684 0.105263
1 0.571429 0.000000 0.000000 0.428571
Directed graph of the hidden Markov model:

Graph can be visualized using graph_make method of HiddenMarkovModel object:
>>> graph = a.graph_make(
format="png",
graph_attr=[("rankdir", "LR"), ("ranksep", "1"), ("rank", "same")]
)
>>> graph.render()

Viterbi algorithm
Running Viterbi algorithm on new observations.
>>> new_obs = "GGCATTGGGCTATAAGAGGAGCTTG"
>>> vs, vsi = a.viterbi(new_obs)
>>> # states sequence
>>> print("VI", "".join(vs))
>>> # observations
>>> print("NO", new_obs)
VI 0000000001111100000000000
NO GGCATTGGGCTATAAGAGGAGCTTG

Baum-Welch algorithm
Using Baum-Welch algorithm to infer the parameters of a Hidden Markov model:
>>> obs_seq = 'AGACTGCATATATAAGGGGCAGGCTG'
>>> a = hmm.HiddenMarkovModel().from_baum_welch(obs_seq, states=['0', '1'])
>>> # training log: KL divergence values for all iterations
>>> a.log
{
'tp': [0.008646969455670256, 0.0012397829805491124, 0.0003950986109761759],
'ep': [0.09078874423746826, 0.0022734816599056084, 0.0010118204023946836],
'pi': [0.009030829793043593, 0.016658391248503462, 0.0038894983546756065]
}
The inferred transition (tp), emission (ep) probability matrices and
initial state distribution (pi) can be accessed as shown:
>>> a.ep, a.tp, a.pi
This model can be decoded using Viterbi algorithm:
>>> new_obs = "GGCATTGGGCTATAAGAGGAGCTTG"
>>> vs, vsi = a.viterbi(new_obs)
>>> print("VI", "".join(vs))
>>> print("NO", new_obs)
VI 0011100001111100000001100
NO GGCATTGGGCTATAAGAGGAGCTTG