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@neila
Created December 9, 2019 16:40
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Generate fake data from a sample data, also Benford's law stuff
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fake Data Generation \n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Original data: \n",
" Date Amount\n",
"0 2016-05-25 54241.35\n",
"1 2017-05-29 54008.83\n",
"2 2017-06-30 54008.82\n",
"3 2017-01-05 52704.37\n",
"4 2017-02-23 52704.36\n",
"... ... ...\n",
"2513 2017-06-14 -26263.65\n",
"2514 2014-08-25 -27909.36\n",
"2515 2016-09-22 -28400.00\n",
"2516 2017-06-23 -35570.00\n",
"2517 2014-12-19 -41054.95\n",
"\n",
"[2518 rows x 2 columns]\n"
]
}
],
"source": [
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from sklearn.neighbors import KernelDensity\n",
"\n",
"dateparser = lambda x: pd.datetime.strptime(x, \"%d %m %Y\")\n",
"data = pd.read_csv(\"https://course-resources.minerva.kgi.edu/uploaded_files/mke/Y5GZpr/anonymized.csv\", sep=',')\n",
"data['Date'] = pd.to_datetime(data['Date'], format='%d%b%Y')\n",
"print(\"Original data: \\n\", data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's see if Benford's law holds for this original data."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First digit occurences in original data: [('0', 5), ('1', 810), ('2', 383), ('3', 347), ('4', 253), ('5', 201), ('6', 225), ('7', 114), ('8', 98), ('9', 82)]\n"
]
},
{
"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": [
"first_digits = {}\n",
"for i in data[\"Amount\"]:\n",
" if str(np.abs(i))[0] not in first_digits.keys():\n",
" first_digits[str(np.abs(i))[0]] = 1\n",
" else:\n",
" first_digits[str(np.abs(i))[0]] += 1\n",
"print(\"First digit occurences in original data:\", sorted(first_digits.items()))\n",
"x, y = zip(*sorted(first_digits.items()))\n",
"y = [i/sum(y) for i in y]\n",
"plt.plot(x, y)\n",
"plt.title(\"First digit occurences in original data\")\n",
"plt.xlabel(xlabel=\"First digit of transaction amount\")\n",
"plt.ylabel(ylabel=\"Probability\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Evidently, Benford's law holds strongly."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To find out the density model for the number of transactions that occur in a single month, the code segment below takes every distinct month in the dataset and counts how many times the month has occurred in a dictionary. It then takes a list with the number of transactions for every distinct month to plot it's density model."
]
},
{
"cell_type": "code",
"execution_count": 3,
"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": [
"monthly_transaction = {} #dictionary to store monthly transaction times\n",
"#for every different month in data, count how many times a transaction occurred.\n",
"for i in range(len(data[\"Date\"])):\n",
" yearmonth = str(data['Date'][i].year)+\"-\"+str(data['Date'][i].month)\n",
" if yearmonth not in monthly_transaction.keys():\n",
" monthly_transaction[yearmonth] = 1\n",
" else:\n",
" monthly_transaction[yearmonth] += 1\n",
"lists = sorted(monthly_transaction.items()) # sorted by key, return a list of tuples\n",
"trans_month, trans_times = zip(*lists) # unpack a list of pairs into two tuples\n",
"density_transtimes = pd.DataFrame(trans_times).plot(kind='density',\n",
" title=\"Transaction Times in a Month Density Model\", legend=False);\n",
"density_transtimes.set(xlabel='No of Transactions in a month', ylabel='Probability');\n",
"plt.show(density_transtimes)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To find out the density model for the day of the month that a transaction takes place in, the code segment below takes a record of the day of the month that a transaction took place on, and stores in a list. It then takes that list to plot it's density model."
]
},
{
"cell_type": "code",
"execution_count": 4,
"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": [
"day_of_transaction = []\n",
"for i in range(len(data[\"Date\"])):\n",
" day_of_transaction.append(data['Date'][i].day)\n",
"density_transdays = pd.DataFrame(day_of_transaction).plot(kind='density',\n",
" title=\"Transaction Day of the Month Density Model\", legend=False);\n",
"density_transdays.set(xlabel='Day of the Month', ylabel='Probability');\n",
"plt.show(density_transdays)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To find out the density model for the transaction size, the code segment simply takes the \"Amount\" column of the orignal dataset and plots it's density model using `pandas.plot()`."
]
},
{
"cell_type": "code",
"execution_count": 5,
"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": [
"transaction_size = []\n",
"for i in range(len(data[\"Amount\"])):\n",
" transaction_size.append(data[\"Amount\"][i])\n",
"density_transsize = pd.DataFrame(transaction_size).plot(kind=\"density\",\n",
" title=\"Transaction Size Density Model\", legend=False);\n",
"density_transsize.set(xlabel='Transaction Amount', ylabel='Probability');\n",
"plt.show(density_transsize)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we have visualized the density models, we can use the models to generate fake data that resembles the original."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Fictious Month of Personal Transactions: \n",
" Fake-Date Fake-Amount\n",
"0 2019-10-30 43854.04\n",
"1 2019-10-2 15916.64\n",
"2 2019-10-25 10001.10\n",
"3 2019-10-12 2999.54\n",
"4 2019-10-22 999.08\n",
"5 2019-10-21 12.04\n",
"6 2019-10-19 4.11\n",
"7 2019-10-20 -7.49\n",
"8 2019-10-10 -8.64\n",
"9 2019-10-15 -10.22\n",
"10 2019-10-17 -30.83\n",
"11 2019-10-25 -38.24\n",
"12 2019-10-25 -38.60\n",
"13 2019-10-14 -39.08\n",
"14 2019-10-6 -41.15\n",
"15 2019-10-26 -43.38\n",
"16 2019-10-4 -43.49\n",
"17 2019-10-10 -46.35\n",
"18 2019-10-6 -48.34\n",
"19 2019-10-22 -64.74\n",
"20 2019-10-18 -65.33\n",
"21 2019-10-20 -65.91\n",
"22 2019-10-19 -67.39\n",
"23 2019-10-2 -68.94\n",
"24 2019-10-5 -73.84\n",
"25 2019-10-10 -81.59\n",
"26 2019-10-22 -100.22\n",
"27 2019-10-21 -105.83\n",
"28 2019-10-5 -117.45\n",
"29 2019-10-18 -121.81\n",
"30 2019-10-18 -137.56\n",
"31 2019-10-2 -141.32\n",
"32 2019-10-29 -167.91\n",
"33 2019-10-4 -181.15\n",
"34 2019-10-22 -198.54\n",
"35 2019-10-15 -199.07\n",
"36 2019-10-11 -199.49\n",
"37 2019-10-9 -200.23\n",
"38 2019-10-13 -200.40\n",
"39 2019-10-30 -202.22\n",
"40 2019-10-21 -215.89\n",
"41 2019-10-27 -248.94\n",
"42 2019-10-3 -250.07\n",
"43 2019-10-7 -275.59\n",
"44 2019-10-28 -279.64\n",
"45 2019-10-1 -301.47\n",
"46 2019-10-4 -321.21\n",
"47 2019-10-7 -349.55\n",
"48 2019-10-30 -349.68\n",
"49 2019-10-11 -360.23\n",
"50 2019-10-26 -379.70\n",
"51 2019-10-29 -400.20\n",
"52 2019-10-1 -400.97\n",
"53 2019-10-3 -422.58\n",
"54 2019-10-19 -428.20\n",
"55 2019-10-26 -456.74\n",
"56 2019-10-2 -498.85\n",
"57 2019-10-8 -629.53\n",
"58 2019-10-8 -630.11\n",
"59 2019-10-5 -712.41\n",
"60 2019-10-19 -717.66\n",
"61 2019-10-16 -864.70\n",
"62 2019-10-27 -901.56\n",
"63 2019-10-2 -988.41\n",
"64 2019-10-7 -999.02\n",
"65 2019-10-27 -999.82\n",
"66 2019-10-28 -1001.46\n",
"67 2019-10-25 -1016.22\n",
"68 2019-10-23 -1250.26\n",
"69 2019-10-12 -1356.67\n",
"70 2019-10-6 -1497.94\n",
"71 2019-10-3 -1498.64\n",
"72 2019-10-14 -1499.32\n",
"73 2019-10-23 -1542.85\n",
"74 2019-10-12 -1654.70\n",
"75 2019-10-25 -1681.10\n",
"76 2019-10-27 -1838.99\n",
"77 2019-10-16 -2099.76\n",
"78 2019-10-21 -2292.34\n",
"79 2019-10-23 -3469.91\n",
"80 2019-10-30 -3814.31\n",
"81 2019-10-10 -3816.29\n",
"82 2019-10-28 -5537.47\n",
"83 2019-10-29 -9998.31\n",
"84 2019-10-24 -16301.68\n",
"85 2019-10-3 -18456.75\n"
]
}
],
"source": [
"#pick a month randomly\n",
"month = np.random.choice([\"01\",\"02\",\"03\",\"04\",\"05\",\"06\",\"07\",\"08\",\"09\",\"10\",\"11\",\"12\"], size=1)[0]\n",
"monthdays = {\"01\":31, \"02\":28, \"03\":31, \"04\":30, \"05\":31,\n",
" \"06\":30, \"07\":31, \"08\":31, \"09\":30, \"10\":31, \"11\":30, \"12\":31}\n",
"\n",
"# instantiate and fit the KDE models for different variables to generate fake data\n",
"kde_trans_times = KernelDensity(bandwidth=1.0, kernel='gaussian')\n",
"kde_trans_times.fit(np.array(trans_times).reshape(-1,1));\n",
"#generate fake transaction counts\n",
"generated_no_transactions = int(np.floor(kde_trans_times.sample(n_samples=1))[0][0])\n",
"\n",
"kde_trans_day = KernelDensity(bandwidth=1.0, kernel='gaussian')\n",
"kde_trans_day.fit(np.array(day_of_transaction).reshape(-1,1)); \n",
"generated_trans_day = np.floor(kde_trans_day.sample(\n",
" n_samples=generated_no_transactions))\n",
"#generate fake transactoin dates\n",
"generated_trans_day = generated_trans_day.reshape(1,-1)[0]\n",
"#resample invalid values from the distribution\n",
"while max(generated_trans_day) > monthdays[month] or min(generated_trans_day) < 1:\n",
" generated_trans_day = [int(kde_trans_day.sample(n_samples=1))\n",
" if i<1 or i>monthdays[month] else int(i) for i in generated_trans_day]\n",
"\n",
"kde_trans_amount = KernelDensity(bandwidth=1.0, kernel='gaussian')\n",
"kde_trans_amount.fit(np.array(transaction_size).reshape(-1,1));\n",
"#generate fake transaction amounts\n",
"generated_trans_amount = np.around(kde_trans_amount.sample(\n",
" n_samples=generated_no_transactions), decimals=2).reshape(1,-1)[0]\n",
"\n",
"\n",
"fake_date = [\"2019-\"+month+\"-\"+str(generated_trans_day[i])\n",
" for i in range(generated_no_transactions)]\n",
"fake_data = {'Fake-Date':fake_date, 'Fake-Amount':generated_trans_amount}\n",
"fake_data = pd.DataFrame(fake_data).sort_values(by=[\"Fake-Amount\"],ascending=False).reset_index(drop=True)\n",
"print(\"Fictious Month of Personal Transactions: \\n\", fake_data.to_string())\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We also want to find out whether the above fake output follows Benford's law."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First digit occurences in fake data: [('1', 28), ('2', 11), ('3', 13), ('4', 13), ('5', 1), ('6', 7), ('7', 4), ('8', 3), ('9', 6)]\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"first_digits_fake = {}\n",
"for i in fake_data[\"Fake-Amount\"]:\n",
" if str(np.abs(i))[0] not in first_digits_fake.keys():\n",
" first_digits_fake[str(np.abs(i))[0]] = 1\n",
" else:\n",
" first_digits_fake[str(np.abs(i))[0]] += 1\n",
"print(\"First digit occurences in fake data:\", sorted(first_digits_fake.items()))\n",
"x, y = zip(*sorted(first_digits_fake.items()))\n",
"y = [i/sum(y) for i in y]\n",
"plt.plot(x, y)\n",
"plt.title(\"First digit occurences in fake data\")\n",
"plt.xlabel(xlabel=\"First digit of transaction amount\")\n",
"plt.ylabel(ylabel=\"Probability\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we can see that albeit not perfect (small data size), overall there is a decreasing trend of occurences as the first digit goes higher."
]
}
],
"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": "3.7.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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