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{
"cell_type": "code",
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"execution_count": 1,
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"source": [
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"#IMPORTS AND COMMON VARIABLES\n",
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"import matplotlib\n",
"import matplotlib.cm as cm\n",
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"import matplotlib.pyplot as plt\n",
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"from matplotlib.pyplot import savefig\n",
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"import numpy as np\n",
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"from math import sqrt\n",
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"\n",
"from constants import *\n",
"from maths import gaussian\n",
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"from markov import MarkovModel\n",
"from markovlog import LogMarkovModel\n",
"\n",
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"fig_dpi = 200\n",
"fig_export = False\n",
"\n",
"x = np.linspace(-4, 8, 300) # x values for figures\n",
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"x_label = \"Observation Space\"\n",
"y_label = \"Probability Density\""
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]
},
{
"source": [
"State Probability Functions (1)\n",
"==================="
],
"cell_type": "markdown",
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},
{
"cell_type": "code",
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"execution_count": 2,
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"state_1_y = [gaussian(i, state1.mean, state1.std_dev) for i in x]\n",
"state_2_y = [gaussian(i, state2.mean, state2.std_dev) for i in x]\n",
"\n",
"plt.plot(x, state_1_y, c='r', label=\"State 1\")\n",
"plt.plot(x, state_2_y, c='b', label=\"State 2\")\n",
"\n",
"plt.legend()\n",
"plt.title(\"State Probability Density Functions\")\n",
"\n",
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"plt.xlabel(x_label)\n",
"plt.ylabel(y_label)\n",
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"plt.grid(linestyle=\"--\")\n",
"\n",
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"fig = matplotlib.pyplot.gcf()\n",
"fig.set_dpi(fig_dpi)\n",
"fig.set_tight_layout(True)\n",
"if fig_export:\n",
" savefig(\"report/res/pdfs.png\")\n",
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"plt.show()"
]
},
{
"source": [
"Output Probability Densities (2)\n",
"=========="
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
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"3.8 -> State 1: 0.02185157424475792, State 2: 0.5471239427774459\n4.2 -> State 1: 0.009496655019831194, State 2: 0.5471239427774459\n3.4 -> State 1: 0.04499247209432338, State 2: 0.3947074079064296\n-0.4 -> State 1: 0.16833223796171576, State 2: 1.500652790137751e-09\n1.9 -> State 1: 0.2509478601290037, State 2: 0.006331212017054291\n3.0 -> State 1: 0.08289761566062391, State 2: 0.2054255182126689\n1.6 -> State 1: 0.2933877723035829, State 2: 0.001596702666402633\n1.9 -> State 1: 0.2509478601290037, State 2: 0.006331212017054291\n5.0 -> State 1: 0.0012852324969092556, State 2: 0.2054255182126689\n"
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]
}
],
"source": [
"for obs in observations:\n",
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" print(f'{obs} -> State 1: {gaussian(obs, state1.mean, state1.std_dev)},', \n",
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" f'State 2: {gaussian(obs, state2.mean, state2.std_dev)}')"
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]
},
{
"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"state_1_y = [gaussian(i, state1.mean, state1.std_dev) for i in x]\n",
"state_2_y = [gaussian(i, state2.mean, state2.std_dev) for i in x]\n",
"\n",
"plt.plot(x, state_1_y, c='r', label=\"State 1\")\n",
"plt.plot(x, state_2_y, c='b', label=\"State 2\")\n",
"\n",
"plt.legend()\n",
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"plt.title(\"State Probability Density Functions With Observations\")\n",
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"\n",
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"plt.xlabel(x_label)\n",
"plt.ylabel(y_label)\n",
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"plt.grid(linestyle=\"--\", axis='y')\n",
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"\n",
"state1_pd = [gaussian(i, state1.mean, state1.std_dev) for i in observations]\n",
"state2_pd = [gaussian(i, state2.mean, state2.std_dev) for i in observations]\n",
"\n",
"#############################################\n",
"# Observation Marks \n",
"#############################################\n",
"\n",
"config = {\n",
" \"s\": 65,\n",
" \"marker\": 'x'\n",
"}\n",
"\n",
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"[plt.axvline(x=i, ls='--', lw=1.0, c=(0,0,0), alpha=0.4) for i in observations]\n",
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"plt.scatter(observations, state1_pd, color=(0.5, 0, 0), **config)\n",
"plt.scatter(observations, state2_pd, color=(0, 0, 0.5), **config)\n",
"\n",
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"fig = matplotlib.pyplot.gcf()\n",
"fig.set_dpi(fig_dpi)\n",
"fig.set_tight_layout(True)\n",
"if fig_export:\n",
" savefig(\"report/res/pdfs-w-obs.png\")\n",
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"plt.show()"
]
},
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{
"source": [
"# Forward Procedure (3)"
],
"cell_type": "markdown",
"metadata": {}
},
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{
"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
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"[[9.61469267e-03 2.00389806e-04 2.89433448e-04 4.30961030e-04\n 9.94968491e-05 7.58875028e-06 2.06308972e-06 4.76335758e-07\n 5.63267096e-10]\n [3.06389408e-01 1.56214298e-01 5.73475605e-02 8.00607227e-11\n 1.63710810e-07 1.25762776e-06 2.59451223e-09 7.98988065e-10\n 6.02373446e-09]]\n"
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]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
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"1.9197737567283167e-10"
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]
},
"metadata": {},
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"execution_count": 5
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}
],
"source": [
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"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition)\n",
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"model.populate_forward()\n",
"\n",
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"print(model.forward)\n",
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"\n",
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"forward = model.forward\n",
"model.calculate_p_obs_forward()\n"
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]
},
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{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 1200x800 with 1 Axes>",
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition).populate()\n",
"\n",
"state_x = np.arange(1, 10)\n",
"\n",
"from numpy import log as ln\n",
"\n",
"plt.plot(state_x, [ln(i) for i in model.forward[0, :]], c='r', label=\"State 1\")\n",
"plt.plot(state_x, [ln(i) for i in model.forward[1, :]], c='b', label=\"State 2\")\n",
"\n",
"plt.ylim(top=0)\n",
"\n",
"plt.legend()\n",
"plt.title(\"Forward Log-Likelihoods Over Time\")\n",
"\n",
"plt.xlabel(\"Observation (t)\")\n",
"plt.ylabel(\"Log Likelihood\")\n",
"plt.grid(linestyle=\"--\")\n",
"\n",
"fig = matplotlib.pyplot.gcf()\n",
"fig.set_dpi(fig_dpi)\n",
"fig.set_tight_layout(True)\n",
"if fig_export:\n",
" savefig(\"report/res/forward-logline.png\")\n",
"plt.show()"
]
},
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{
"source": [
"# Backward Procedure (4)"
],
"cell_type": "markdown",
"metadata": {}
},
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{
"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
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"[[6.57892066e-11 2.92661737e-09 6.89869860e-08 4.45463420e-07\n 1.92898428e-06 2.51074677e-05 9.30059204e-05 3.93414211e-04\n 2.00000000e-02]\n [6.24515168e-10 1.22518178e-09 2.99943420e-09 2.11439342e-08\n 3.02470605e-07 1.14745634e-06 3.77015860e-05 5.73240014e-03\n 3.00000000e-02]]\n"
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]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
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"1.9197737567283167e-10"
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]
},
"metadata": {},
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"execution_count": 7
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}
],
"source": [
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"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition)\n",
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"model.populate_backward()\n",
"\n",
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"print(model.backward)\n",
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"\n",
"backward = model.backward\n",
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"model.calculate_p_obs_backward()\n"
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]
},
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{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 1200x800 with 1 Axes>",
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition).populate()\n",
"\n",
"state_x = np.arange(1, 10)\n",
"\n",
"from numpy import log as ln\n",
"\n",
"plt.plot(state_x, [ln(i) for i in model.backward[0, :]], c='r', label=\"State 1\")\n",
"plt.plot(state_x, [ln(i) for i in model.backward[1, :]], c='b', label=\"State 2\")\n",
"\n",
"plt.ylim(top=0)\n",
"\n",
"plt.legend()\n",
"plt.title(\"Backward Log-Likelihoods Over Time\")\n",
"\n",
"plt.xlabel(\"Observation (t)\")\n",
"plt.ylabel(\"Log Likelihood\")\n",
"plt.grid(linestyle=\"--\")\n",
"\n",
"fig = matplotlib.pyplot.gcf()\n",
"fig.set_dpi(fig_dpi)\n",
"fig.set_tight_layout(True)\n",
"if fig_export:\n",
" savefig(\"report/res/backward-logline.png\")\n",
"plt.show()"
]
},
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{
"source": [
"# Compare Forward/Backward Final"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
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"forward: 1.9197737567283167e-10\nbackward: 1.9197737567283167e-10\ndiff: 0.0\n"
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]
}
],
"source": [
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"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition)\n",
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"model.populate_forward()\n",
"model.populate_backward()\n",
"\n",
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"print(\"forward:\", model.calculate_p_obs_forward())\n",
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"print(\"backward:\", model.calculate_p_obs_backward())\n",
"\n",
"print(\"diff: \", model.p_obs_forward - model.p_obs_backward)\n"
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]
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},
{
"source": [
"# Occupation Likelihoods (5)"
],
"cell_type": "markdown",
"metadata": {}
},
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{
"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[[3.29488306e-03 3.05486147e-03 1.04007783e-01 9.99999991e-01\n 9.99742065e-01 9.92483109e-01 9.99490475e-01 9.76142401e-01\n 5.86805704e-02]\n [9.96705117e-01 9.96945139e-01 8.95992217e-01 8.81769869e-09\n 2.57935122e-04 7.51689067e-03 5.09524759e-04 2.38575993e-02\n 9.41319430e-01]]\n"
]
}
],
"source": [
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"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition).populate()\n",
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"\n",
"occupation = model.occupation\n",
"print(model.occupation)"
]
},
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{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 1200x1200 with 1 Axes>",
2021-01-05 11:10:29 +00:00
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2021-01-01 18:53:11 +00:00
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition).populate()\n",
"\n",
"fig = plt.figure(figsize=(6,6), dpi=fig_dpi, tight_layout=True)\n",
"ax = fig.add_subplot(1, 1, 1, projection=\"3d\", xmargin=0, ymargin=0)\n",
"\n",
"y_width = 0.3\n",
"\n",
"X = np.arange(1, 10) - 0.5\n",
"Y = np.arange(1, 3) - 0.5*y_width\n",
"X, Y = np.meshgrid(X, Y)\n",
"Z = np.zeros(model.forward.size)\n",
"\n",
"dx = np.ones(model.forward.size)\n",
"dy = y_width * np.ones(model.forward.size)\n",
"\n",
"colours = [*[(1.0, 0.1, 0.1) for i in range(9)], *[(0.2, 0.2, 1.0) for i in range(9)]]\n",
"ax.bar3d(X.flatten(), Y.flatten(), Z, \n",
" dx, dy, model.occupation.flatten(), \n",
" color=colours, shade=True)\n",
"\n",
"ax.set_yticks([1, 2])\n",
"ax.set_zlim(top=1.0)\n",
"\n",
"ax.set_title(\"Occupation Likelihoods Over Time\")\n",
"ax.set_xlabel(\"Observation\")\n",
"ax.set_ylabel(\"State\")\n",
"ax.set_zlabel(\"Occupation Likelihood\")\n",
"ax.view_init(35, -72)\n",
"if fig_export:\n",
" savefig(\"report/res/occupation-bars.png\")\n",
"fig.show()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 1200x800 with 1 Axes>",
2021-01-05 11:10:29 +00:00
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition).populate()\n",
"\n",
"state_x = np.arange(1, 10)\n",
"\n",
"plt.plot(state_x, model.occupation[0, :], c='r', label=\"State 1\")\n",
"plt.plot(state_x, model.occupation[1, :], c='b', label=\"State 2\")\n",
"\n",
"plt.legend()\n",
"plt.title(\"Occupation Likelihoods Over Time\")\n",
"\n",
"plt.xlabel(\"Observation (t)\")\n",
"plt.ylabel(\"Occupation Likelihood\")\n",
"plt.grid(linestyle=\"--\")\n",
"\n",
"fig = matplotlib.pyplot.gcf()\n",
"fig.set_dpi(fig_dpi)\n",
"fig.set_tight_layout(True)\n",
"if fig_export:\n",
" savefig(\"report/res/occupation-line.png\")\n",
"plt.show()"
]
},
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{
"source": [
"# Re-estimate Mean & Variance (6)"
],
"cell_type": "markdown",
"metadata": {}
},
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{
"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
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"mean: [1, 4]\nvariance: [1.44, 0.49]\n\nmean: [1.6747846620246418, 4.089148442531048]\nvariance: [1.8465047320872243, 0.37804421554121403]\n"
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]
}
],
"source": [
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"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition).populate()\n",
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"\n",
"print(\"mean: \", [state1.mean, state2.mean])\n",
"print(\"variance: \", [state1.variance, state2.variance])\n",
"print()\n",
"\n",
"print(\"mean: \", model.reestimated_mean())\n",
"print(\"variance: \", model.reestimated_variance())\n"
]
},
{
"source": [
"New PDFs (7)\n",
"==================="
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
"outputs": [
{
"output_type": "display_data",
"data": {
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"text/plain": "<Figure size 1200x800 with 1 Axes>",
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
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"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition).populate()\n",
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"\n",
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"new_mean = model.reestimated_mean()\n",
"new_var = model.reestimated_variance()\n",
"new_std_dev = [sqrt(x) for x in new_var]\n",
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"\n",
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"state_1_y = [gaussian(i, new_mean[0], new_std_dev[0]) for i in x]\n",
"state_2_y = [gaussian(i, new_mean[1], new_std_dev[1]) for i in x]\n",
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"\n",
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"plt.plot(x, state_1_y, c='r', label=\"State 1\")\n",
"plt.plot(x, state_2_y, c='b', label=\"State 2\")\n",
"\n",
"plt.legend()\n",
"plt.title(\"Re-estimated Probability Density Functions\")\n",
"\n",
"plt.xlabel(x_label)\n",
"plt.ylabel(y_label)\n",
"plt.grid(linestyle=\"--\")\n",
"\n",
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"fig = matplotlib.pyplot.gcf()\n",
"fig.set_dpi(fig_dpi)\n",
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"plt.show()"
]
},
{
"source": [
"# Compare PDFs (7)"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
"outputs": [
{
"output_type": "display_data",
"data": {
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"text/plain": "<Figure size 1200x800 with 1 Axes>",
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
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"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition).populate()\n",
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"\n",
"new_mean = model.reestimated_mean()\n",
"new_var = model.reestimated_variance()\n",
"new_std_dev = [sqrt(x) for x in new_var]\n",
"\n",
"#######################################\n",
"# Original\n",
"#######################################\n",
"state_1_y = [gaussian(i, state1.mean, state1.std_dev) for i in x]\n",
"state_2_y = [gaussian(i, state2.mean, state2.std_dev) for i in x]\n",
"plt.plot(x, state_1_y, '--', c='r', label=\"State 1\", linewidth=1.0)\n",
"plt.plot(x, state_2_y, '--', c='b', label=\"State 2\", linewidth=1.0)\n",
"\n",
"#######################################\n",
"# Re-Estimated\n",
"#######################################\n",
"state_1_new_y = [gaussian(i, new_mean[0], new_std_dev[0]) for i in x]\n",
"state_2_new_y = [gaussian(i, new_mean[1], new_std_dev[1]) for i in x]\n",
"plt.plot(x, state_1_new_y, c='r', label=\"New State 1\")\n",
"plt.plot(x, state_2_new_y, c='b', label=\"New State 2\")\n",
"\n",
"plt.legend()\n",
"plt.title(\"Re-estimated Probability Density Functions\")\n",
"\n",
"plt.xlabel(x_label)\n",
"plt.ylabel(y_label)\n",
"plt.grid(linestyle=\"--\")\n",
"\n",
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"fig = matplotlib.pyplot.gcf()\n",
"fig.set_dpi(fig_dpi)\n",
"fig.set_tight_layout(True)\n",
"if fig_export:\n",
" savefig(\"report/res/re-est-pdfs.png\")\n",
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"plt.show()"
]
},
{
"source": [
"# Multiple Iterations"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
2021-01-05 11:10:29 +00:00
"execution_count": 16,
2020-12-31 19:30:39 +00:00
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
2021-01-05 11:10:29 +00:00
"mean (0): [1.6747846620246418, 4.089148442531048]\n",
"var (0): [1.8465047320872243, 0.37804421554121403]\n",
"[[0.70176362 0.57084996]\n",
" [1.6956088 0.26442637]]\n",
"\n",
"mean (1): [1.8732627187085478, 4.1264787288916045]\n",
"var (1): [1.741702511836495, 0.3397362903623662]\n",
"[[0.8060609 0.14928497]\n",
" [0.3747969 0.38642879]]\n",
"\n",
"mean (2): [1.9467921888680977, 4.144829018638114]\n",
"var (2): [1.802927096107906, 0.3244337549372125]\n",
"[[0.82078158 0.13830527]\n",
" [0.34355999 0.40237225]]\n",
"\n",
"mean (3): [1.998417533036004, 4.146391356501866]\n",
"var (3): [1.8794907388957407, 0.31336829013095496]\n",
"[[0.82382934 0.12631664]\n",
" [0.34908171 0.40883355]]\n",
"\n",
"mean (4): [2.0403185801109194, 4.137443801197436]\n",
"var (4): [1.9532263949235384, 0.30316834940556364]\n",
"[[0.82663329 0.11372608]\n",
" [0.35679246 0.4179057 ]]\n",
"\n",
"mean (5): [2.0768416135288152, 4.120742753858993]\n",
"var (5): [2.026102075205389, 0.291798571474891]\n",
"[[0.82952161 0.1002526 ]\n",
" [0.36446428 0.43140289]]\n",
"\n",
"mean (6): [2.11194659437116, 4.096434012657846]\n",
"var (6): [2.1032895125514766, 0.2773354097864741]\n",
"[[0.83266361 0.08482054]\n",
" [0.37298205 0.45042633]]\n",
"\n",
"mean (7): [2.149792870100123, 4.062396551986207]\n",
"var (7): [2.191678450688613, 0.2568529817420179]\n",
"[[0.8363706 0.0660714 ]\n",
" [0.3837438 0.47744431]]\n",
"\n",
"mean (8): [2.194489793285685, 4.014103644960269]\n",
"var (8): [2.2986239066545524, 0.22514847051325343]\n",
"[[0.84098808 0.04298428]\n",
" [0.39835926 0.51702684]]\n",
"\n",
"mean (9): [2.246078108416006, 3.9478836679900287]\n",
"var (9): [2.423237858945465, 0.17533830729899114]\n",
"[[0.84636913 0.01806124]\n",
" [0.41572836 0.57245506]]\n",
"\n",
"mean (10): [2.2856592028959346, 3.882184182166453]\n",
"var (10): [2.527476010893805, 0.11675401844606319]\n",
"[[0.85009354 0.00251453]\n",
" [0.420065 0.6209139 ]]\n",
"\n",
"mean (11): [2.290643073016055, 3.8598915740419946]\n",
"var (11): [2.5588220300129474, 0.09296081385828549]\n",
"[[8.49474403e-01 6.94178508e-05]\n",
" [4.04708642e-01 6.12273377e-01]]\n",
"\n",
"mean (12): [2.2914144510257906, 3.8594038663696892]\n",
"var (12): [2.559782940361538, 0.09129358424097164]\n",
"[[8.48816419e-01 2.56744984e-06]\n",
" [4.07814693e-01 5.92792027e-01]]\n",
"\n",
"mean (13): [2.2920722638916136, 3.8597894517174827]\n",
"var (13): [2.559397203251749, 0.09112610156222908]\n",
"[[8.48468970e-01 1.38599620e-07]\n",
" [4.08641855e-01 5.91369797e-01]]\n",
"\n",
"mean (14): [2.2923368298535873, 3.85996676996849]\n",
"var (14): [2.559213392145394, 0.0910669910055963]\n",
"[[8.48421180e-01 7.64719574e-09]\n",
" [4.08579843e-01 5.91420888e-01]]\n",
"\n",
"mean (15): [2.2924457175066317, 3.860041202681166]\n",
"var (15): [2.559136099327699, 0.09104297025788764]\n",
"[[8.48413724e-01 4.22240186e-10]\n",
" [4.08544019e-01 5.91456046e-01]]\n",
"\n",
"mean (16): [2.2924909067581587, 3.8600721725675933]\n",
"var (16): [2.559103947613575, 0.09103301880870453]\n",
"[[8.48411387e-01 2.33175631e-11]\n",
" [4.08528360e-01 5.91471648e-01]]\n",
"\n",
"mean (17): [2.2925096881606515, 3.8600850494050714]\n",
"var (17): [2.5590905823972907, 0.09102888377407325]\n",
"[[8.48410459e-01 1.28774690e-12]\n",
" [4.08521812e-01 5.91478189e-01]]\n",
"\n",
"mean (18): [2.292517496754187, 3.860090403678976]\n",
"var (18): [2.55908502565561, 0.09102716461059344]\n",
"[[8.48410077e-01 7.11193032e-14]\n",
" [4.08519090e-01 5.91480910e-01]]\n",
"\n",
"mean (19): [2.292520743671027, 3.860092630150436]\n",
"var (19): [2.559082715100272, 0.09102644975438301]\n",
"[[8.48409918e-01 3.92779179e-15]\n",
" [4.08517958e-01 5.91482042e-01]]\n",
"\n",
"mean (20): [2.2925220938511153, 3.860093556010955]\n",
"var (20): [2.5590817542930737, 0.09102615249086479]\n",
"[[8.48409852e-01 2.16925735e-16]\n",
" [4.08517488e-01 5.91482512e-01]]\n",
"\n",
"mean (21): [2.292522655314822, 3.8600939410271335]\n",
"var (21): [2.5590813547477076, 0.09102602887540412]\n",
"[[8.48409824e-01 1.19804846e-17]\n",
" [4.08517292e-01 5.91482708e-01]]\n",
"\n",
"mean (22): [2.2925228887980498, 3.8600941011356555]\n",
"var (22): [2.5590811885978098, 0.09102597747017212]\n",
"[[8.48409813e-01 6.61664720e-19]\n",
" [4.08517211e-01 5.91482789e-01]]\n",
"\n",
"mean (23): [2.2925229858918237, 3.8600941677167215]\n",
"var (23): [2.5590811195045364, 0.09102595609334513]\n",
"[[8.48409808e-01 3.65427891e-20]\n",
" [4.08517177e-01 5.91482823e-01]]\n",
"\n",
"mean (24): [2.2925230262682406, 3.8600941954044554]\n",
"var (24): [2.559081090772119, 0.09102594720379605]\n",
"[[8.48409806e-01 2.01820581e-21]\n",
" [4.08517163e-01 5.91482837e-01]]\n",
"\n",
"mean (25): [2.2925230430587726, 3.860094206918401]\n",
"var (25): [2.559081078823743, 0.09102594350707681]\n",
"[[8.48409805e-01 1.11462617e-22]\n",
" [4.08517157e-01 5.91482843e-01]]\n",
"\n",
"mean (26): [2.292523050041117, 3.8600942117064783]\n",
"var (26): [2.55908107385501, 0.0910259419697957]\n",
"[[8.48409805e-01 6.15592084e-24]\n",
" [4.08517154e-01 5.91482846e-01]]\n",
"\n",
"mean (27): [2.2925230529447265, 3.8600942136976]\n",
"var (27): [2.559081071788762, 0.09102594133051709]\n",
"[[8.48409805e-01 3.39982702e-25]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (28): [2.2925230541521926, 3.860094214525609]\n",
"var (28): [2.559081070929512, 0.09102594106467299]\n",
"[[8.48409805e-01 1.87767584e-26]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (29): [2.292523054654318, 3.860094214869936]\n",
"var (29): [2.5590810705721925, 0.09102594095412166]\n",
"[[8.48409805e-01 1.03701351e-27]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (30): [2.2925230548631266, 3.8600942150131257]\n",
"var (30): [2.5590810704236024, 0.09102594090814888]\n",
"[[8.48409805e-01 5.72727731e-29]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (31): [2.29252305494996, 3.8600942150726705]\n",
"var (31): [2.55908107036181, 0.09102594088903106]\n",
"[[8.48409805e-01 3.16309335e-30]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (32): [2.292523054986069, 3.8600942150974324]\n",
"var (32): [2.559081070336114, 0.09102594088108093]\n",
"[[8.48409805e-01 1.74693122e-31]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (33): [2.292523055001086, 3.8600942151077295]\n",
"var (33): [2.559081070325428, 0.09102594087777484]\n",
"[[8.48409805e-01 9.64805129e-33]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (34): [2.2925230550073303, 3.8600942151120115]\n",
"var (34): [2.559081070320984, 0.09102594087640002]\n",
"[[8.48409805e-01 5.32848074e-34]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (35): [2.2925230550099274, 3.860094215113793]\n",
"var (35): [2.5590810703191362, 0.09102594087582833]\n",
"[[8.48409805e-01 2.94284371e-35]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (36): [2.292523055011007, 3.8600942151145334]\n",
"var (36): [2.5590810703183675, 0.09102594087559052]\n",
"[[8.48409805e-01 1.62529049e-36]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (37): [2.292523055011456, 3.8600942151148416]\n",
"var (37): [2.559081070318048, 0.09102594087549164]\n",
"[[8.48409805e-01 8.97624695e-38]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (38): [2.292523055011643, 3.860094215114969]\n",
"var (38): [2.5590810703179154, 0.09102594087545052]\n",
"[[8.48409805e-01 4.95745282e-39]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (39): [2.2925230550117206, 3.8600942151150224]\n",
"var (39): [2.5590810703178604, 0.09102594087543343]\n",
"[[8.48409805e-01 2.73793029e-40]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (40): [2.2925230550117526, 3.860094215115045]\n",
"var (40): [2.5590810703178373, 0.09102594087542634]\n",
"[[8.48409805e-01 1.51211974e-41]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (41): [2.2925230550117663, 3.860094215115054]\n",
"var (41): [2.559081070317828, 0.09102594087542336]\n",
"[[8.48409805e-01 8.35122109e-43]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (42): [2.2925230550117717, 3.8600942151150575]\n",
"var (42): [2.559081070317824, 0.09102594087542212]\n",
"[[8.48409805e-01 4.61225997e-44]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (43): [2.292523055011774, 3.860094215115059]\n",
"var (43): [2.5590810703178217, 0.09102594087542162]\n",
"[[8.48409805e-01 2.54728522e-45]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (44): [2.292523055011775, 3.8600942151150592]\n",
"var (44): [2.5590810703178217, 0.09102594087542144]\n",
"[[8.48409805e-01 1.40682920e-46]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (45): [2.2925230550117752, 3.8600942151150592]\n",
"var (45): [2.5590810703178213, 0.09102594087542136]\n",
"[[8.48409805e-01 7.76971646e-48]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (46): [2.2925230550117752, 3.86009421511506]\n",
"var (46): [2.5590810703178213, 0.09102594087542135]\n",
"[[8.48409805e-01 4.29110328e-49]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (47): [2.2925230550117752, 3.86009421511506]\n",
"var (47): [2.559081070317821, 0.0910259408754213]\n",
"[[8.48409805e-01 2.36991497e-50]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (48): [2.2925230550117757, 3.86009421511506]\n",
"var (48): [2.5590810703178213, 0.09102594087542129]\n",
"[[8.48409805e-01 1.30887015e-51]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n",
"mean (49): [2.2925230550117752, 3.8600942151150606]\n",
"var (49): [2.5590810703178213, 0.09102594087542129]\n",
"[[8.48409805e-01 7.22870263e-53]\n",
" [4.08517153e-01 5.91482847e-01]]\n",
"\n"
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]
},
{
"output_type": "display_data",
"data": {
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},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
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"iterations = 50\n",
"\n",
"fig = plt.figure(dpi=fig_dpi, tight_layout=True)\n",
"ax = fig.add_subplot(1, 1, 1, xmargin=0, ymargin=0)\n",
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"\n",
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"iter_mean = [state1.mean, state2.mean]\n",
"iter_var = [state1.variance, state2.variance]\n",
"iter_state_transitions = state_transition\n",
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"\n",
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"ax.plot(x, [gaussian(i, iter_mean[0], sqrt(iter_var[0])) for i in x], '--', c='r', linewidth=1.0)\n",
"ax.plot(x, [gaussian(i, iter_mean[1], sqrt(iter_var[1])) for i in x], '--', c='b', linewidth=1.0)\n",
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"\n",
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"label1=None\n",
"label2=None\n",
"\n",
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"for i in range(iterations):\n",
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" iter_model = MarkovModel(states=[State(iter_mean[0], iter_var[0], state1.entry, state1.exit), \n",
" State(iter_mean[1], iter_var[1], state2.entry, state2.exit)],\n",
" observations=observations,\n",
" state_transitions=iter_state_transitions).populate()\n",
"\n",
" # NEW PARAMETERS\n",
" iter_mean = iter_model.reestimated_mean()\n",
" iter_var = iter_model.reestimated_variance()\n",
" iter_state_transitions[1:3, 1:3] = iter_model.reestimated_state_transitions()\n",
"\n",
" print(f\"mean ({i}): \", iter_mean)\n",
" print(f\"var ({i}): \", iter_var)\n",
" print(iter_model.reestimated_state_transitions())\n",
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" print()\n",
"\n",
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" state_1_y = [gaussian(i, iter_mean[0], sqrt(iter_var[0])) for i in x]\n",
" state_2_y = [gaussian(i, iter_mean[1], sqrt(iter_var[1])) for i in x]\n",
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"\n",
" style = '--'\n",
" linewidth = 1.0\n",
" if i == iterations - 1:\n",
" style = '-'\n",
" linewidth = 2.0\n",
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" label1='State 1'\n",
" label2='State 2'\n",
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"\n",
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" ax.plot(x, state_1_y, style, c='r', label=label1, linewidth=linewidth)\n",
" ax.plot(x, state_2_y, style, c='b', label=label2, linewidth=linewidth)\n",
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"\n",
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"ax.set_title(\"Probability Density Function Iterations\")\n",
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"\n",
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"ax.set_xlabel(x_label)\n",
"ax.set_ylabel(y_label)\n",
"ax.grid(linestyle=\"--\")\n",
"ax.legend()\n",
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"\n",
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"if fig_export:\n",
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" savefig(\"report/res/iterated-pdfs.png\")\n",
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"fig.show()\n"
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]
},
{
"source": [
"# Baum-Welch State Transition Re-estimations"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
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"execution_count": 17,
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"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
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"[[0.92 0.06]\n [0.04 0.93]]\n[[8.37336439e-01 6.15623114e-50]\n [3.50509494e-01 6.49490506e-01]]\n"
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]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
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"array([[8.37336439e-01, 6.15623114e-50],\n",
" [3.50509494e-01, 6.49490506e-01]])"
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]
},
"metadata": {},
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"execution_count": 17
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}
],
"source": [
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"model = MarkovModel(states=[state1, state2], \n",
" observations=observations, \n",
" state_transitions=state_transition).populate()\n",
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"\n",
"print(a_matrix)\n",
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"print(model.reestimated_state_transitions())\n",
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"model.reestimated_state_transitions()"
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]
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},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
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}
]
}
