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@kiko-datasparq
Created January 28, 2021 08:53
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Bayesian Estimation for Binary Classifiers
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.ticker as mtick"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Auxiliary functions"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Func formatter\n",
"def y_fmt(y, pos):\n",
" decades = [1e9, 1e6, 1e3, 1e0, 1e-3, 1e-6, 1e-9 ]\n",
" suffix = [\"G\", \"M\", \"k\", \"\" , \"m\" , \"u\", \"n\" ]\n",
" if y == 0:\n",
" return str(0)\n",
" for i, d in enumerate(decades):\n",
" if np.abs(y) >=d:\n",
" val = y/float(d)\n",
" signf = len(str(val).split(\".\")[1])\n",
" if signf == 0:\n",
" return '{val:d} {suffix}'.format(val=int(val), suffix=suffix[i])\n",
" else:\n",
" if signf == 1:\n",
" #print(val, signf)\n",
" if str(val).split(\".\")[1] == \"0\":\n",
" return '{val:d} {suffix}'.format(val=int(round(val)), suffix=suffix[i]) \n",
" tx = \"{\"+\"val:.{signf}f\".format(signf = signf) +\"} {suffix}\"\n",
" return tx.format(val=val, suffix=suffix[i])\n",
" return y\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Parameters"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Values\n",
"TP = 1900\n",
"FP = 5000\n",
"TN = 3000\n",
"FN = 100\n",
"N_total = TP + FP + TN + FN"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"TN frequentist probability: 0.3\n",
"FN frequentist probability: 0.01\n"
]
}
],
"source": [
"pTN = TN/N_total\n",
"pFN = FN/N_total\n",
"print(\"TN frequentist probability: {}\".format(pTN))\n",
"print(\"FN frequentist probability: {}\".format(pFN))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Bayes Posterior"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"deltaT = 2e-4\n",
"theta_TN_min = 28e-2\n",
"theta_TN_max = 32.1e-2\n",
"theta_FN_min = 6e-3\n",
"theta_FN_max = 14.1e-3\n",
"theta_TN = np.arange(theta_TN_min, theta_TN_max, deltaT)\n",
"theta_FN = np.arange(theta_FN_min, theta_FN_max, deltaT)\n",
"mesh_FN, mesh_TN = np.meshgrid(theta_FN, theta_TN)\n",
"posterior = FN*np.log10(mesh_FN) + (N_total-FN)*np.log10(1-mesh_FN) \\\n",
" + TN*np.log10(mesh_TN/(1-mesh_FN)) \\\n",
" + (N_total-FN-TN)*np.log10(1-mesh_TN/(1-mesh_FN)) \n",
"\n",
"posterior = 10**(posterior - posterior.max())"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"posterior_lim = np.log10(np.maximum(posterior, 1e-4))\n",
"plt.rcParams.update({'font.size': 13})\n",
"\n",
"fig, ax = plt.subplots()\n",
"#fig.set_figheight(6)\n",
"plt.imshow(posterior, origin='lower', extent=[theta_FN.min(), theta_FN.max(), theta_TN.min(), theta_TN.max()])\n",
"#plt.imshow(posterior, origin='lower')\n",
"plt.colorbar()\n",
"plt.xlabel('$θ_1$')\n",
"plt.xticks(np.arange(theta_FN_min, theta_FN_max, 4e-3))\n",
"plt.ylabel('$θ_2$')\n",
"plt.title('Posterior for $θ = (θ_1, θ_2)$')\n",
"ax.set_aspect(.2)\n",
"#plt.tight_layout()\n",
"#plt.savefig('figs_bayes/posterior.png', dpi=600)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sample from posterior"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def sample_posterior_parameters(n=1):\n",
" index = np.random.choice([i for i in range(posterior_prob.shape[0])], size=n, p=posterior_prob)\n",
" col_i = index % posterior.shape[1]\n",
" row_i = np.floor((index - col_i)/posterior.shape[1]).astype(int)\n",
" pTN = theta_TN_min + row_i*deltaT\n",
" pFN = theta_FN_min + col_i*deltaT\n",
" return pTN, pFN"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"posterior_prob = np.reshape(posterior, [posterior.shape[0]*posterior.shape[1]])/posterior.sum()\n",
"\n",
"N = int(2e6)\n",
"# Sample\n",
"sampled_posterior = np.random.choice([i for i in range(posterior_prob.shape[0])], size=N, p=posterior_prob)\n",
"# Convert to df\n",
"df = pd.DataFrame()\n",
"df['sampled_posterior'] = sampled_posterior\n",
"df['count'] = 0\n",
"df_count = df.groupby(by='sampled_posterior').count().reset_index().sort_values(by='sampled_posterior')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"sampled_mesh_posterior = 0*posterior\n",
"for i, row in df_count.iterrows():\n",
" col_i = row['sampled_posterior'] % posterior.shape[1]\n",
" row_i = np.floor((row['sampled_posterior'] - col_i)/posterior.shape[1]).astype(int)\n",
" sampled_mesh_posterior[row_i, col_i] = row['count']"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"plt.imshow(sampled_mesh_posterior, origin='lower', extent=[theta_FN.min(), theta_FN.max(), theta_TN.min(), theta_TN.max()])\n",
"plt.colorbar()\n",
"plt.xlabel('$θ_1$')\n",
"plt.ylabel('$θ_2$')\n",
"ax.set_aspect(.2)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Error\n",
"error_sampling = sampled_mesh_posterior/sampled_mesh_posterior.max() - posterior\n",
"fig, ax = plt.subplots()\n",
"plt.imshow(error_sampling, origin='lower', extent=[theta_FN.min(), theta_FN.max(), theta_TN.min(), theta_TN.max()])\n",
"plt.colorbar()\n",
"plt.xlabel('$θ_1$')\n",
"plt.ylabel('$θ_2$')\n",
"ax.set_aspect(.2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Monte Carlo simulation"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# Random sample for given parameters\n",
"def random_sample(n, tn, fn):\n",
" sample = np.random.choice([0, 1, 2], size=n, p=[(n-tn-fn)/n, tn/n, fn/n])\n",
" sample_tn_norm = sum(sample == 1)\n",
" sample_fn_norm = sum(sample == 2)\n",
" return sample_tn_norm, sample_fn_norm\n",
"\n",
"# Parameters\n",
"M_total = 1e6\n",
"factor = 10"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Multinomial Sampling"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"N = int(1e5)\n",
"tn_vector = np.zeros(N)\n",
"fn_vector = np.zeros(N)\n",
"profit_vector = np.zeros(N)\n",
"\n",
"RUN_COMPUTATION = False\n",
"if RUN_COMPUTATION:\n",
" # Loop over range\n",
" # Run MC\n",
" for i in range(N):\n",
" if i % 100 == 0:\n",
" print(i)\n",
" pTN, pFN = sample_posterior_parameters()\n",
" tn_vector[i], fn_vector[i] = random_sample(N_total, float(pTN)*N_total, float(pFN)*N_total)\n",
" \n",
" # Save vectors\n",
" with open('profit_bayes.npy', 'wb') as f:\n",
" np.save(f, tn_vector)\n",
" np.save(f, fn_vector)\n",
"\n",
"else:\n",
" # Save vectors\n",
" with open('profit_bayes.npy', 'rb') as f:\n",
" tn_vector = np.load(f)\n",
" fn_vector = np.load(f)\n",
"\n",
"\n",
"\n",
"profit_vector = M_total*(tn_vector - factor*fn_vector)/N_total"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.xaxis.set_major_formatter(mtick.FuncFormatter(y_fmt))\n",
"plt.hist(profit_vector, bins=np.arange(140e3, 260e3, 1e3))\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"MEAN profit: 199056.82\n",
"MEDIAN profit: 199500.0\n",
"CI p2.5 profit: 166800.0\n",
"CI p97.5 profit: 229000.0\n",
"2STD profit: 15901.38777866888\n"
]
}
],
"source": [
"mean_profit = profit_vector.mean()\n",
"p25 = np.percentile(profit_vector, 2.5)\n",
"p975 = np.percentile(profit_vector, 97.5)\n",
"median_profit = np.percentile(profit_vector, 50)\n",
"std_profit = profit_vector.std()\n",
"print(\"MEAN profit: {:}\".format(mean_profit))\n",
"print(\"MEDIAN profit: {}\".format(median_profit))\n",
"print(\"CI p2.5 profit: {}\".format(p25))\n",
"print(\"CI p97.5 profit: {}\".format(p975))\n",
"print(\"2STD profit: {}\".format(std_profit))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Central Limit Theorem"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"def sample_opv(pFN, pTN):\n",
" # False negatives Gaussian\n",
" mu_fn = pFN*M_total\n",
" sigma_fn = np.sqrt((1-pFN)*pFN*M_total)\n",
" # True negatives Gaussian\n",
" mu_tn = pTN*M_total\n",
" sigma_tn = np.sqrt((1-pTN)*pTN*M_total)\n",
" # Profit\n",
" mu_opv = mu_tn - factor*mu_fn\n",
" sigma_opv = np.sqrt(sigma_tn**2 + factor*factor*sigma_fn**2)\n",
" #return np.random.normal(loc=mu_opv, scale=sigma_opv)\n",
" return np.random.normal(size=N)*sigma_opv + mu_opv"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"N = int(1e5)\n",
"# Run MC\n",
"pTN, pFN = sample_posterior_parameters(n=N)\n",
"profit_vector_CLT = sample_opv(pFN, pTN)\n"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.xaxis.set_major_formatter(mtick.FuncFormatter(y_fmt))\n",
"plt.hist(profit_vector_CLT, bins=np.arange(1.4e5, 2.6e5, 1e3))\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"MEAN profit: 199023.54693769367\n",
"MEDIAN profit: 199347.75148559044\n",
"CI p2.5 profit: 176170.53065987944\n",
"CI p97.5 profit: 220341.37486451754\n",
"2STD profit: 11302.285680490933\n"
]
}
],
"source": [
"mean_profit = profit_vector_CLT.mean()\n",
"p25 = np.percentile(profit_vector_CLT, 2.5)\n",
"p975 = np.percentile(profit_vector_CLT, 97.5)\n",
"median_profit = np.percentile(profit_vector_CLT, 50)\n",
"std_profit = profit_vector_CLT.std()\n",
"print(\"MEAN profit: {:}\".format(mean_profit))\n",
"print(\"MEDIAN profit: {}\".format(median_profit))\n",
"print(\"CI p2.5 profit: {}\".format(p25))\n",
"print(\"CI p97.5 profit: {}\".format(p975))\n",
"print(\"2STD profit: {}\".format(std_profit))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Combination"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'count')"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.xaxis.set_major_formatter(mtick.FuncFormatter(y_fmt))\n",
"plt.hist(profit_vector, bins=np.arange(1.4e5, 2.6e5, 1e3), alpha=0.5)\n",
"plt.hist(profit_vector_CLT, bins=np.arange(1.4e5, 2.6e5, 1e3), alpha=0.5)\n",
"plt.legend(['Multinomial Sampling', 'CLT Approximation'])\n",
"ax.axis([1.4e5, 2.6e5, 0, 5000])\n",
"ax.set_xlabel('Overall Profit Variation (OPV) (£)')\n",
"ax.set_ylabel('count')\n",
"#plt.savefig('figs_bayes/comparison_OPV.png', dpi=600)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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