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@adambear91
Created January 29, 2019 20:26
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Code and data for Templeton presentation 1/30/19.
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Templeton Presentation\n",
"\n",
"Load in some useful Python packages."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import scipy as sp\n",
"import scipy.stats as stats\n",
"import pandas as pd\n",
"\n",
"plt.style.use('ggplot') \n",
"sns.set_style('darkgrid')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loss Functions\n",
"\n",
"This covers Topic #1. \n",
"\n",
"### Generic Plots of Different Loss Functions\n",
"\n",
"Here I plot three different loss functions: standard squared error (L2 loss), absolute error (L1 loss), and a concave error function I made up, which is $|e|^\\frac{1}{10}$ (i.e., the tenth root of the absolute value). "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x241.2 with 3 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12,3.35))\n",
"x = np.linspace(-10, 10, 100)\n",
"\n",
"# Calculate loss functions and z-score them\n",
"mse = np.power(x,2); mse = stats.zscore(mse)\n",
"mae = np.abs(x); mae = stats.zscore(mae)\n",
"mce = np.power(np.abs(x), .1); mce = stats.zscore(mce)\n",
"\n",
"plt.subplot(131); plt.title('Convex (Squared) Loss')\n",
"plt.plot(x, mse - np.min(mse), linewidth=3, color=[0,0,1]);\n",
"plt.yticks([]);\n",
"plt.xlabel('Error'); plt.ylabel('Cost of Being Wrong')\n",
"\n",
"plt.subplot(132); plt.title('Absolute Loss')\n",
"plt.plot(x, mae - np.min(mae), linewidth=3, color=[.5,0,.5]);\n",
"plt.yticks([]);\n",
"plt.xlabel('Error')\n",
"\n",
"plt.subplot(133); plt.title('Concave Loss')\n",
"plt.plot(x, mce - np.min(mce), linewidth=3, color=[1,0,0]);\n",
"plt.yticks([]);\n",
"plt.xlabel('Error')\n",
"\n",
"plt.savefig('loss_plot.pdf')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Regression with Skewed Noise\n",
"\n",
"The code below generated the skewed data I plot later. I've commented it out here, but note that if it is run again, the data set will not be exactly the same as before."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"%%capture\n",
"\n",
"\"\"\"\n",
"n = 1000\n",
"x = np.linspace(0, 1, n)\n",
"b0 = 0; b1 = 2\n",
"y = b0 + b1*x + 2*np.random.exponential(1, size=n) + .5*np.random.normal(size=n)\n",
"\n",
"d = {'x': x, 'y': y}\n",
"df = pd.DataFrame(data=d)\n",
"df.to_csv('templeton_data.csv', index=False)\n",
"\"\"\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Load in the saved data and make a scatter plot."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"df = pd.read_csv('templeton_data.csv')\n",
"x = df['x']; y = df['y']\n",
"\n",
"plt.figure(figsize=(7,5))\n",
"plt.plot(x, y, 'k.', markersize=2, alpha=.5);\n",
"plt.ylim([-2,20]); plt.yticks([0,5,10,15,20], ['0','5','10','15','20']);\n",
"plt.savefig('data_plot.pdf')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's find the best fitting line for each of the loss functions. (I've added an extra loss function, \"lpt5\", here, which is the square root of the absolute loss, but I don't plot it.)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# Define generic loss function\n",
"def calc_loss(x, y, b0=0, b1=0, power=2):\n",
" est = b0 + b1*x\n",
" err = np.array((np.abs([y - est]) ** power))\n",
" loss = np.mean(err)\n",
" return loss\n",
" \n",
"# Define loss functions for different powers\n",
"l2 = lambda z: calc_loss(x, y, z[0], z[1], power=2)\n",
"l1 = lambda z: calc_loss(x, y, z[0], z[1], power=1)\n",
"lpt5 = lambda z: calc_loss(x, y, z[0], z[1], power=.5)\n",
"lpt1 = lambda z: calc_loss(x, y, z[0], z[1], power=.1)\n",
"\n",
"# Starting values for optimization\n",
"b0 = 0; b1 = 2\n",
"\n",
"# Minimize loss functions (use b0 and b1 as starting values for optimization)\n",
"l2_opt = sp.optimize.minimize(l2, x0=[b0, b1])\n",
"l1_opt = sp.optimize.minimize(l1, x0=[b0, b1])\n",
"lpt5_opt = sp.optimize.minimize(lpt5, x0=[b0, b1])\n",
"lpt1_opt = sp.optimize.minimize(lpt1, x0=[b0, b1])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Plot fits for each loss function\n",
"plt.figure(figsize=(7,5))\n",
"\n",
"plt.plot(x, l2_opt.x[0] + x*l2_opt.x[1], '-', linewidth=3, color=[0,0,1]);\n",
"plt.plot(x, l1_opt.x[0] + x*l1_opt.x[1], '-', linewidth=3, color=[.5,0,.5]);\n",
"plt.plot(x, lpt1_opt.x[0] + x*lpt1_opt.x[1], '-', linewidth=3, color=[1,0,0]);\n",
"plt.legend(['Convex (Squared) Error', 'Absolute Error', 'Concave Error'])\n",
"plt.ylim([-2,20]); plt.yticks([0,5,10,15,20], ['0','5','10','15','20'])\n",
"\n",
"plt.plot(x, y, 'k.', markersize=2, alpha=.5);\n",
"\n",
"plt.savefig('data_with_fit_plot.pdf')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To get a better sense of the optimization procedure, here I plot loss values for different estimates of the intercept in the regression. I fix the slope term at the best-fitting values from above, since it doesn't vary much across loss functions anyway."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# Calculate losses across b0 test vals\n",
"nLosses = 5000; # number of losses to calculate\n",
"b0Vals = np.linspace(0, 5, nLosses)\n",
"l2_losses = np.array([])\n",
"l1_losses = np.array([])\n",
"lpt1_losses = np.array([])\n",
"\n",
"for i in b0Vals:\n",
" l2_losses = np.append(l2_losses, calc_loss(x, y, b0=i, b1=l2_opt.x[1], power=2))\n",
" l1_losses = np.append(l1_losses, calc_loss(x, y, b0=i, b1=l1_opt.x[1], power=1))\n",
" lpt1_losses = np.append(lpt1_losses, calc_loss(x, y, b0=i, b1=lpt1_opt.x[1], power=.1))\n",
" \n",
"# Z-score values\n",
"l2_losses = stats.zscore(l2_losses)\n",
"l1_losses = stats.zscore(l1_losses)\n",
"lpt1_losses = stats.zscore(lpt1_losses)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Plot Z-scored Losses\n",
"plt.figure(figsize=(7,5))\n",
"\n",
"plt.plot(b0Vals, l2_losses, color=[0,0,1]);\n",
"plt.plot(b0Vals, l1_losses, color=[.5,0,.5]);\n",
"plt.plot(b0Vals, lpt1_losses, color=[1,0,0]);\n",
"plt.legend(['Convex (Squared) Error', 'Absolute Error', 'Concave Error']);\n",
"plt.xlabel('Regression Intercept'); plt.ylabel('Z-scored Loss');\n",
"\n",
"plt.savefig('data_with_min_loss_plot.pdf')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Group Data from Qualtrics\n",
"\n",
"Here I load in the data from Qualtrics to see how you fit the data and compare to the loss functions above."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Unzip Complete\n"
]
}
],
"source": [
"import requests\n",
"import zipfile\n",
"import json\n",
"import io\n",
"\n",
"# Setting user Parameters\n",
"apiToken = \"aysjuKd0HUZiEyOmtXRPugaU6bKtinwaFghRSGcM\"\n",
"surveyId = \"SV_agWcCONrZ4LDaDP\"\n",
"fileFormat = \"csv\"\n",
"dataCenter = 'ca1'\n",
"\n",
"# Setting static parameters\n",
"requestCheckProgress = 0\n",
"progressStatus = \"in progress\"\n",
"baseUrl = \"https://az1.qualtrics.com/API/v3/responseexports/\".format(dataCenter)\n",
"headers = {\n",
" \"content-type\": \"application/json\",\n",
" \"x-api-token\": apiToken,\n",
" }\n",
"\n",
"# Step 1: Creating Data Export\n",
"downloadRequestUrl = baseUrl\n",
"downloadRequestPayload = '{\"format\":\"' + fileFormat + '\",\"surveyId\":\"' + surveyId + '\"}'\n",
"downloadRequestResponse = requests.request(\"POST\", downloadRequestUrl, data=downloadRequestPayload, headers=headers)\n",
"progressId = downloadRequestResponse.json()[\"result\"][\"id\"]\n",
"#print(downloadRequestResponse.text)\n",
"\n",
"# Step 2: Checking on Data Export Progress and waiting until export is ready\n",
"while requestCheckProgress < 100 and progressStatus is not \"complete\":\n",
" requestCheckUrl = baseUrl + progressId\n",
" requestCheckResponse = requests.request(\"GET\", requestCheckUrl, headers=headers)\n",
" requestCheckProgress = requestCheckResponse.json()[\"result\"][\"percentComplete\"]\n",
" #print(\"Download is \" + str(requestCheckProgress) + \" complete\")\n",
"\n",
"# Step 3: Downloading file\n",
"requestDownloadUrl = baseUrl + progressId + '/file'\n",
"requestDownload = requests.request(\"GET\", requestDownloadUrl, headers=headers, stream=True)\n",
"\n",
"# Step 4: Unzipping the file\n",
"zipfile.ZipFile(io.BytesIO(requestDownload.content)).extractall(\"MyQualtricsDownload\")\n",
"print('Unzip Complete')"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sample size: N = 2\n"
]
}
],
"source": [
"# Templeton data\n",
"td = pd.read_csv('MyQualtricsDownload/Templeton Demo.csv')\n",
"td = td.iloc[2:] # get rid of extra header lines\n",
"\n",
"# Convert to numeric\n",
"myNumericVars = ('b0','b1')\n",
"\n",
"for i in myNumericVars:\n",
" td[i] = pd.to_numeric(td[i],errors='coerce') \n",
"\n",
"# Remove incomplete responses\n",
"td = td[~td['b0'].isnull()]\n",
"\n",
"print('Sample size: N =', len(td))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(7,5))\n",
"\n",
"plt.plot(x, np.mean(td['b0']) + np.mean(td['b1'])*x, 'k--', linewidth=5)\n",
"plt.plot(x, l2_opt.x[0] + x*l2_opt.x[1], '-', linewidth=3, color=[0,0,1]);\n",
"plt.plot(x, l1_opt.x[0] + x*l1_opt.x[1], '-', linewidth=3, color=[.5,0,.5]);\n",
"plt.plot(x, lpt1_opt.x[0] + x*lpt1_opt.x[1], '-', linewidth=3, color=[1,0,0]);\n",
"plt.legend(['Your Mean Responses','Convex (Squared) Error', 'Absolute Error', 'Concave Error'])\n",
"plt.ylim([-2,20]); plt.yticks([0,5,10,15,20], ['0','5','10','15','20'])\n",
"\n",
"plt.plot(x, y, 'k.', markersize=2, alpha=.5);\n",
"\n",
"plt.savefig('group_data_plot.pdf')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Risky decisions over time\n",
"\n",
"This is topic #2.\n",
"\n",
"## Median returns on two investments\n",
"\n",
"Consider an investment that alternates gains and losses each year over 50 years. How does a gain of 10% and loss of 5% (_safe_ investment) compare to a gain of 40% and a loss of 30% (_risky_ investment)?"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Create plot for safe vs. risky investment returns\n",
"P = 100 # principal investment ($)\n",
"t = np.linspace(1, 50, 50) # time\n",
"safe = np.matlib.repmat([1.10, .95], 1, 25); safe = np.cumprod(safe)\n",
"risky = np.matlib.repmat([1.40, .70], 1, 25); risky = np.cumprod(risky)\n",
"\n",
"# Plot 'median' path of alternating gains & losses\n",
"plt.figure(figsize=(7,5))\n",
"plt.plot(t, P*safe, linewidth=2, color='green');\n",
"plt.plot(t, P*risky, linewidth=2, color='red');\n",
"plt.xlim([0,51]); plt.xticks([1,10,20,30,40,50],['1','10','20','30','40','50'])\n",
"plt.yscale('log', basey=2); plt.ylim([50, 500]); \n",
"plt.yticks([50,100,250,500], ['$50','$100','$250','$500']);\n",
"plt.xlabel('Year'); plt.ylabel('Value of Investment')\n",
"plt.legend(['Safe Investment','Risky Investment']);\n",
"\n",
"plt.plot(t, 100*np.ones(50), 'k');\n",
"\n",
"plt.savefig('investment_returns.pdf')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Monte Carlo simulations of returns on investments\n",
"\n",
"Now let's get a better sense of the _distribution_ of returns by simulating different gain/loss trajectories. We suppose that, each year, a gain and a loss are equally likely (50% each), and that the two investments are perfectly correlated."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Plot Monte Carlo sims\n",
"N = 50 # number of simulated paths for each investment\n",
"t = np.linspace(1, 50, 50) # time\n",
"gains = np.random.choice([0, 1], size=(N, len(t)), p=[.5, .5]) # simulate yrs with gains\n",
"safeGains = 1.10*gains + .95*(1-gains); safeGains = np.cumprod(safeGains, axis=1)\n",
"riskyGains = 1.40*gains + .70*(1-gains); riskyGains = np.cumprod(riskyGains, axis=1)\n",
"\n",
"plt.figure(figsize=(8,5))\n",
"plt.xlim([0,51]); plt.xticks([1,10,20,30,40,50],['1','10','20','30','40','50'])\n",
"plt.yscale('log', basey=10); plt.ylim([0.01, 100000]); \n",
"plt.yticks([.01,.1,1,10,100,1000,10000,100000], ['$.01','$.10','$1','$10','$100','$1000','$10000','$100000'])\n",
"plt.xlabel('Year'); plt.ylabel('Value of Investment')\n",
"\n",
"for i in range(N):\n",
" plt.plot(t, P*safeGains[i,:], color='green', alpha=.3)\n",
" plt.plot(t, P*riskyGains[i,:], color='red', alpha=.3)\n",
" plt.legend(['Safe Investment','Risky Investment']);\n",
" \n",
"plt.plot(t, 100*np.ones(len(t)), 'k');\n",
"\n",
"plt.savefig('investment_returns_monte_carlo.pdf')"
]
}
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