hidden-markov-model-tf
v4.0.0
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A trainable Hidden Markov Model with Gaussian emissions using TensorFlow.js
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hidden-markov-model-tf
A trainable Hidden Markov Model with Gaussian emissions using TensorFlow.js
Install
$ npm install hidden-markov-model-tf
Require: Node v12+
Usage
const assert = require('assert'):
require('@tensorflow/tfjs-node'); // Optional, enable native TensorFlow backend
const tf = require('@tensorflow/tfjs');
const HMM = require('hidden-markov-model-tf');
const [observations, time, states, dimensions] = [5, 7, 3, 2];
// Configure model
const hmm = new HMM({
states: states,
dimensions: dimensions
});
// Set parameters
await hmm.setParameters({
pi: tf.tensor([0.15, 0.20, 0.65]),
A: tf.tensor([
[0.55, 0.15, 0.30],
[0.45, 0.45, 0.10],
[0.15, 0.20, 0.65]
]),
mu: tf.tensor([
[-7.0, -8.0],
[-1.5, 3.7],
[-1.7, 1.2]
]),
Sigma: tf.tensor([
[[ 0.12, -0.01],
[-0.01, 0.50]],
[[ 0.21, 0.05],
[ 0.05, 0.03]],
[[ 0.37, 0.35],
[ 0.35, 0.44]]
])
});
// Sample data
const sample = hmm.sample({observations, time});
assert.deepEqual(sample.states.shape, [observations, time]);
assert.deepEqual(sample.emissions.shape, [observations, time, dimensions]);
// Your data must be a tf.tensor with shape [observations, time, dimensions]
const data = sample.emissions;
// Fit model with data
const results = await hmm.fit(data);
assert(results.converged);
// Predict hidden state indices
const inference = hmm.inference(data);
assert.deepEqual(inference.shape, [observations, time]);
states.print();
// Compute log-likelihood
const logLikelihood = hmm.logLikelihood(data);
assert.deepEqual(logLikelihood.shape, [observations]);
logLikelihood.print();
// Get parameters
const {pi, A, mu, Sigma} = hmm.getParameters();
pi.print();
A.print();
mu.print();
Sigma.print();
Documentation
hidden-markov-model-tf
is TensorFlow.js based, therefore your input must
be povided as a tf.tensor
. Likewise most outputs are also provided as a
tf.tensor
. You can always get a TypedArray
with await tensor.data()
.
hmm = new HMM({states, dimensions})
The constructor takes two integer arguments. The number of hidden states
and
the number of dimensions
in the Gaussian emissions.
result = await hmm.fit(tensor, {maxIterations = 100, tolerance = 0.001, seed})
The fit
method, takes an required tf.tensor
object. That must have the
shape [observations, time, dimensions]
. If you only have one observation
it should have the shape [1, time, dimensions]
.
The fit
method, returns a Promise
for the results
. The results
is
an object with the following properties:
const {
// the number of iterations used, will at most be `maxIterations`
iterations,
// if the training coverged, given the `tolerance`,
// before `maxIterations` was reached
converged,
// The achived tolerance, after the number of iterations. This can be
// useful if the optimizer did not converge, but you want to know how
// good the fit is.
tolerance
} = await hmm.fit(tensor);
The fit
method uses a KMeans initialization. This initialization algorithm is
random but can be seeded with the optional seed
parameter.
After initialization, the model is optimized using an EM-algorithm called the Baum–Welch algorithm.
states = hmm.inference(tensor)
The inference
method, takes an required tf.tensor
object. That must have
the shape [observations, time, dimensions]
.
It uses the Viterbi algorithm
for infering the hidden state. Which is returned as tf.tensor
with the
shape [observations, time]
.
const states = hmm.inference(tensor);
states.print();
console.log(await states.data());
logLikelihood = hmm.logLikelihood(tensor)
The inference
method, takes an required tf.tensor
object. That must have
the shape [observations, time, dimensions]
.
It uses the forward procedure of the
Baum–Welch algorithm
to compute the logLikelihood for each observation. This is returned as a
tf.tensor
with the shape [observations]
.
{states, emissions} = hmm.sample({ observations, time, seed })
The sample
method, samples data from the Hidden Markov Model distribution
and returns both the sampled states and Gaussian emissions, as two tf.tensor
objects.
the states
tensor has the shape [observations, time]
. While the emissions
tensor has the shape
[observations, time, dimensions].
The sampling can be seed with the optional seed
parameter.
{pi, A, mu, Sigma} = hmm.getParameters()
Return the underlying parameters:
pi
: the hidden state prior distribution.shape = [states]
A
: the hidden state transfer distribution.shape = [states, states]
mu
: the mean of the Gaussian emission distribution.shape = [states, dimensions]
Sigma
: the covariance matrix of the Gaussian emission distribution.shape = [states, dimensions, dimensions]
await hmm.setParameters({pi, A, mu, Sigma})
Set the underlying parameters of the Hidden Markov Model. Note that some
internal properties related to the Gaussian distribution will be precomputed.
Therefore this returns a Promise
. Be sure to wait for the promise to
resolve before calling any other method.