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Last active January 10, 2022 13:59
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Hidden Markov models sample
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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from hmmlearn import hmm"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Define variables\n",
"SAMPLE_NUM = 500"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"startprob = np.array([0.6, 0.3, 0.1, 0.0])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# The transition matrix, note that there are no transitions possible\n",
"# between component 1 and 3\n",
"transmat = np.array([[0.7, 0.2, 0.0, 0.1],\n",
" [0.3, 0.5, 0.2, 0.0],\n",
" [0.0, 0.3, 0.5, 0.2],\n",
" [0.2, 0.0, 0.2, 0.6]])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# The means of each component\n",
"means = np.array([[0.0, 0.0],\n",
" [0.0, 11.0],\n",
" [9.0, 10.0],\n",
" [11.0, -1.0]])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# The covariance of each component\n",
"covars = .5 * np.tile(np.identity(2), (4, 1, 1))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Build an HMM instance and set parameters\n",
"model = hmm.GaussianHMM(n_components=4, covariance_type=\"full\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Instead of fitting it from the data, we directly set the estimated\n",
"# parameters, the means and covariance of the components\n",
"model.startprob_ = startprob\n",
"model.transmat_ = transmat\n",
"model.means_ = means\n",
"model.covars_ = covars"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"X, Z = model.sample(SAMPLE_NUM)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x10a1d5b00>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a15eda0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot the sampled data\n",
"plt.plot(X[:, 0], X[:, 1], \".-\", label=\"observations\", ms=6,\n",
" mfc=\"orange\", alpha=0.7)\n",
"\n",
"# Indicate the component numbers\n",
"for i, m in enumerate(means):\n",
" plt.text(m[0], m[1], 'Component %i' % (i + 1),\n",
" size=17, horizontalalignment='center',\n",
" bbox=dict(alpha=.7, facecolor='w'))\n",
"plt.legend(loc='best')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"x_sample = np.array([[-1.2, -2.9], [2.3, 1.1], [0.3, 13.5], [7.6, 11.0], [13.1, 9.7]])\n",
"print('Predicted hidden sequence:')\n",
"print(model.predict(x_sample) + 1)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x10a7d3240>"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10a23cf98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot the sampled data\n",
"plt.plot(x_sample[:,0], x_sample[:, 1], \".-\", label=\"observations\", ms=6,\n",
" mfc=\"orange\", alpha=0.7)\n",
"\n",
"# Indicate the component numbers\n",
"for i, m in enumerate(means):\n",
" plt.text(m[0], m[1], 'Component %i' % (i + 1),\n",
" size=17, horizontalalignment='center',\n",
" bbox=dict(alpha=.7, facecolor='w'))\n",
"plt.legend(loc='best')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.6.8 64-bit ('sandbox-3L9k0fs7-py3.6': venv)",
"language": "python",
"name": "python36864bitsandbox3l9k0fs7py36venv11bd57b127ef47349f9f9f0428bb6601"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.8"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}
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