{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Statistics for Hackers\n", "\n", "### An Exploration of Statistics Through Computational Simulation\n", "\n", "#### A [talk][video] by [Jake VanDerPlas][jakevdp] for PyCon 2016\n", "#### [Slides][slides] available on speakerdeck\n", "\n", "\n", "## Motivation\n", "\n", "There's no shortage of absolutely magnificent material out there on the topics of data science and machine learning for an autodidact, such as myself, to learn from. In fact, so many great resources exist that an individual can be forgiven for not knowing where to begin their studies, or for getting distracted once they're off the starting block. I honestly can't count the number of times that I've started working through many of these online courses and tutorials only to have my attention stolen by one of the multitudes of amazing articles on data analysis with Python, or some great new [MOOC][mooc] on Deep Learning. But this year is different! This year, for one of my new year's resolutions, I've decided to create a personalized data science curriculum and stick to it. This year, I promise not to just casually sign up for another course, or start reading yet another textbook to be distracted part way through. This year, I'm sticking to the plan.\n", "\n", "As part of my personalized program of study, I've chosen to start with [Harvard's Data Science course][cs109]. I'm currently on week 3 and one of the suggested readings for this week is [Jake VanderPlas'][jakevdp] talk from PyCon 2016 titled \"Statistics for Hackers\". As I was watching the [video][video] and following along with the [slides][slides], I wanted to try out some of the examples and create a set of notes that I could refer to later, so I figured why not create a Jupyter notebook. Once I'd finished, I realized I'd created a decently-sized resource that could be of use to others working their way through the talk. The result is the article you're reading right now, the remainder of which contains my notes and code examples for Jake's excellent talk. \n", "\n", "So, enjoy the article, I hope you find this resource useful, and if you have any problems or suggestions of any kind, the full [notebook][notebook] can be found on [github][github], so please send me a [pull request][github_pulls], or submit an [issue][github_issues], or just message me directly on [Twitter][twitter].\n", "\n", "[mooc]: https://en.wikipedia.org/wiki/Massive_open_online_course\n", "[cs109]: http://cs109.github.io/2015/index.html\n", "[video]: https://youtu.be/Iq9DzN6mvYA\n", "[slides]: https://speakerdeck.com/jakevdp/statistics-for-hackers\n", "[jakevdp]: https://staff.washington.edu/jakevdp/\n", "[notebook]: http://nbviewer.jupyter.org/github/croach/statistics-for-hackers/blob/master/statistics-for-hackers.ipynb\n", "[github]: https://github.com/croach/statistics-for-hackers\n", "[github_pulls]: https://github.com/croach/statistics-for-hackers/pulls\n", "[github_issues]: https://github.com/croach/statistics-for-hackers/issues\n", "[twitter]: https://twitter.com/vthakr\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Preliminaries" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import seaborn as sns\n", "\n", "# Suppress all warnings just to keep the notebook nice and clean. \n", "# This must happen after all imports since numpy actually adds its\n", "# RankWarning class back in.\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "\n", "# Setup the look and feel of the notebook\n", "sns.set_context(\"notebook\", \n", " font_scale=1.5, \n", " rc={\"lines.linewidth\": 2.5})\n", "sns.set_style('whitegrid')\n", "sns.set_palette('deep')\n", "\n", "# Create a couple of colors to use throughout the notebook\n", "red = sns.xkcd_rgb['vermillion']\n", "blue = sns.xkcd_rgb['dark sky blue']\n", "\n", "from IPython.display import display\n", "\n", "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Warm-up\n", "\n", "The talk starts off with a motivating example that asks the question \"If you toss a coin 30 times and see 22 heads, is it a fair coin?\"\n", "\n", "We all know that a fair coin should come up heads roughly 15 out of 30 tosses, give or take, so it does seem unlikely to see so many heads. However, the skeptic might argue that even a fair coin could show 22 heads in 30 tosses from time-to-time. This could just be a chance event. So, the question would then be \"how can you determine if you're tossing a fair coin?\"\n", "\n", "### The Classic Method\n", "\n", "The classic method would assume that the skeptic is correct and would then test the hypothesis (i.e., the [*Null Hypothesis*][null_hypothesis]) that the observation of 22 heads in 30 tosses could happen simply by chance. Let's start by first considering the probability of a single coin flip coming up heads and work our way up to 22 out of 30. \n", "\n", "$$\n", "P(H) = \\frac{1}{2}\n", "$$\n", "\n", "As our equation shows, the probability of a single coin toss turning up heads is exactly 50% since there is an equal chance of either heads or tails turning up. Taking this one step further, to determine the probability of getting 2 heads in a row with 2 coin tosses, we would need to multiply the probability of getting heads by the probability of getting heads again since the two events are independent of one another.\n", "\n", "$$\n", "P(HH) = P(H) \\cdot P(H) = P(H)^2 = \\left(\\frac{1}{2}\\right)^2 = \\frac{1}{4}\n", "$$\n", "\n", "From the equation above, we can see that the probability of getting 2 heads in a row from a total of 2 coin tosses is 25%. Let's now take a look at a slightly different scenario and calculate the probability of getting 2 heads and 1 tails with 3 coin tosses.\n", "\n", "$$\n", "P(HHT) = P(H)^2 \\cdot P(T) = \\left(\\frac{1}{2}\\right)^2 \\cdot \\frac{1}{2} = \\left(\\frac{1}{2}\\right)^3 = \\frac{1}{8}\n", "$$\n", "\n", "The equation above tells us that the probability of getting 2 heads and 1 tails in 3 tosses is 12.5%. This is actually the exact same probability as getting heads in all three tosses, which doesn't sound quite right. The problem is that we've only calculated the probability for a single permutation of 2 heads and 1 tails; specifically for the scenario where we only see tails on the third toss. To get the actual probability of tossing 2 heads and 1 tails we will have to add the probabilities for all of the possible permutations, of which there are exactly three: HHT, HTH, and THH. \n", "\n", "$$\n", "P(2H,1T) = P(HHT) + P(HTH) + P(THH) = \\frac{1}{8} + \\frac{1}{8} + \\frac{1}{8} = \\frac{3}{8}\n", "$$\n", "\n", "Another way we could do this is to calculate the total number of permutations and simply multiply that by the probability of each event happening. To get the total number of permutations we can use the [binomial coefficient][binom_coeff]. Then, we can simply calculate the probability above using the following equation.\n", "\n", "$$\n", "P(2H,1T) = \\binom{3}{2} \\left(\\frac{1}{2}\\right)^{3} = 3 \\left(\\frac{1}{8}\\right) = \\frac{3}{8}\n", "$$\n", "\n", "While the equation above works in our particular case, where each event has an equal probability of happening, it will run into trouble with events that have an unequal chance of taking place. To deal with those situations, you'll want to extend the last equation to take into account the differing probabilities. The result would be the following equation, where $N$ is number of coin flips, $N_H$ is the number of expected heads, $N_T$ is the number of expected tails, and $P_H$ is the probability of getting heads on each flip.\n", "\n", "$$\n", "P(N_H,N_T) = \\binom{N}{N_H} \\left(P_H\\right)^{N_H} \\left(1 - P_H\\right)^{N_T}\n", "$$\n", "\n", "Now that we understand the classic method, let's use it to test our null hypothesis that we *are* actually tossing a fair coin, and that this is just a chance occurrence. The following code implements the equations we've just discussed above.\n", "\n", "\n", "\n", "[null_hypothesis]: https://en.wikipedia.org/wiki/Null_hypothesis\n", "[binom_coeff]: https://en.wikipedia.org/wiki/Binomial_coefficient" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def factorial(n):\n", " \"\"\"Calculates the factorial of `n`\n", " \"\"\"\n", " vals = list(range(1, n + 1))\n", " if len(vals) <= 0:\n", " return 1\n", "\n", " prod = 1\n", " for val in vals:\n", " prod *= val\n", " \n", " return prod\n", " \n", " \n", "def n_choose_k(n, k):\n", " \"\"\"Calculates the binomial coefficient\n", " \"\"\"\n", " return factorial(n) / (factorial(k) * factorial(n - k))\n", "\n", "\n", "def binom_prob(n, k, p):\n", " \"\"\"Returns the probability of see `k` heads in `n` coin tosses\n", " \n", " Arguments:\n", " \n", " n - number of trials\n", " k - number of trials in which an event took place\n", " p - probability of an event happening\n", " \n", " \"\"\"\n", " return n_choose_k(n, k) * p**k * (1 - p)**(n - k)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have a method that will calculate the probability for a specific event happening (e.g., 22 heads in 30 coin tosses), we can calculate the probability for every possible outcome of flipping a coin 30 times, and if we plot these values we'll get a visual representation of our coin's probability distribution." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 272, "width": 404 } }, "output_type": "display_data" } ], "source": [ "# Calculate the probability for every possible outcome of tossing \n", "# a fair coin 30 times.\n", "probabilities = [binom_prob(30, k, 0.5) for k in range(1, 31)]\n", "\n", "# Plot the probability distribution using the probabilities list \n", "# we created above.\n", "plt.step(range(1, 31), probabilities, where='mid', color=blue)\n", "plt.xlabel('number of heads')\n", "plt.ylabel('probability')\n", "plt.plot((22, 22), (0, 0.1599), color=red);\n", "plt.annotate('0.8%', \n", " xytext=(25, 0.08), \n", " xy=(22, 0.08), \n", " multialignment='right',\n", " va='center',\n", " color=red,\n", " size='large',\n", " arrowprops={'arrowstyle': '<|-', \n", " 'lw': 2, \n", " 'color': red, \n", " 'shrinkA': 10});" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The visualization above shows the probability distribution for flipping a fair coin 30 times. Using this visualization we can now determine the probability of getting, say for example, 12 heads in 30 flips, which looks to be about 8%. Notice that we've labeled our example of 22 heads as 0.8%. If we look at the probability of flipping exactly 22 heads, it looks likes to be a little less than 0.8%, in fact if we calculate it using the `binom_prob` function from above, we get 0.5%" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probability of flipping 22 heads: 0.5%\n" ] } ], "source": [ "print(\"Probability of flipping 22 heads: %0.1f%%\" % (binom_prob(30, 22, 0.5) * 100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, then why do we have 0.8% labeled in our probability distribution above? Well, that's because we are showing the probability of getting **at least** 22 heads, which is also known as the p-value.\n", "\n", "#### What's a p-value?\n", "\n", "In [statistical hypothesis testing][hypothesis_test] we have an idea that we want to test, but considering that it's very hard to prove something to be true beyond doubt, rather than test our hypothesis directly, we formulate a competing hypothesis, called a [null hypothesis][null_hypothesis], and then try to disprove it instead. The null hypothesis essentially assumes that the effect we're seeing in the data could just be due to chance. \n", "\n", "In our example, the null hypothesis assumes we have a fair coin, and the way we determine if this hypothesis is true or not is by calculating how often flipping this fair coin 30 times would result in 22 or more heads. If we then take the number of times that we got 22 or more heads and divide that number by the total of all possible permutations of 30 coin tosses, we get the probability of tossing 22 or more heads with a fair coin. This probability is what we call the [p-value][p_value]. \n", "\n", "The p-value is used to check the validity of the null hypothesis. The way this is done is by agreeing upon some predetermined upper limit for our p-value, below which we will assume that our null hypothesis is false. In other words, if our null hypothesis were true, and 22 heads in 30 flips could happen often enough by chance, we would expect to see it happen more often than the given threshold percentage of times. So, for example, if we chose 10% as our threshold, then we would expect to see 22 or more heads show up at least 10% of the time to determine that this is a chance occurrence and not due to some bias in the coin. Historically, the generally accepted threshold has been 5%, and so if our p-value is less than 5%, we can then make the assumption that our coin may not be fair.\n", "\n", "The `binom_prob` function from above calculates the probability of a single event happening, so now all we need for calculating our p-value is a function that adds up the probabilities of a given event, or a more extreme event happening. So, as an example, we would need a function to add up the probabilities of getting 22 heads, 23 heads, 24 heads, and so on. The next bit of code creates that function and uses it to calculate our p-value.\n", "\n", "[null_hypothesis]: https://en.wikipedia.org/wiki/Null_hypothesis\n", "[hypothesis_test]: https://en.wikipedia.org/wiki/Statistical_hypothesis_testing\n", "[p_value]: https://www.statisticsdonewrong.com/data-analysis.html#the-power-of-p-values" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P-value: 0.8%\n" ] } ], "source": [ "def p_value(n, k, p):\n", " \"\"\"Returns the p-value for the given the given set \n", " \"\"\"\n", " return sum(binom_prob(n, i, p) for i in range(k, n+1))\n", "\n", "print(\"P-value: %0.1f%%\" % (p_value(30, 22, 0.5) * 100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Running the code above gives us a p-value of roughly 0.8%, which matches the value in our probability distribution above and is also less than the 5% threshold needed to reject our null hypothesis, so it does look like we may have a biased coin.\n", "\n", "### The Easier Method\n", "\n", "That's an example of using the classic method for testing if our coin is fair or not. However, if you don't happen to have at least some background in statistics, it can be a little hard to follow at times, but luckily for us, there's an easier method...\n", "\n", "Simulation!\n", "\n", "The code below seeks to answer the same question of whether or not our coin is fair by running a large number of simulated coin flips and calculating the proportion of these experiments that resulted in at least 22 heads or more." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Simulated P-value: 0.8%\n" ] } ], "source": [ "M = 0\n", "n = 50000\n", "for i in range(n):\n", " trials = np.random.randint(2, size=30)\n", " if (trials.sum() >= 22):\n", " M += 1\n", "p = M / n\n", "\n", "print(\"Simulated P-value: %0.1f%%\" % (p * 100))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result of our simulations is 0.8%, the exact same result we got earlier when we calculated the p-value using the classical method above. So, it definitely looks like it's possible that we have a biased coin since the chances of seeing 22 or more heads in 30 tosses of a fair coin is less than 1%.\n", "\n", "## Four Recipes for Hacking Statistics\n", "\n", "We've just seen one example of how our hacking skills can make it easy for us to answer questions that typically only a statistician would be able to answer using the classical methods of statistical analysis. This is just one possible method for answering statistical questions using our coding skills, but Jake's talk describes four recipes in total for \"hacking statistics\", each of which is listed below. The rest of this article will go into each of the remaining techniques in some detail.\n", "\n", "1. [Direct Simulation](#Warm-up)\n", "2. [Shuffling](#Shuffling)\n", "3. [Bootstrapping](#Bootstrapping)\n", "4. [Cross Validation](#Cross-Validation)\n", "\n", "In the [Warm-up](#Warm-up) section above, we saw an example direct simulation, the first recipe in our tour of statistical hacks. The next example uses the Shuffling method to figure out if there's a statistically significant difference between two different sample populations. \n", "\n", "### Shuffling\n", "\n", "In this example, we look at the Dr. Seuss story about the Star-belly Sneetches. In this Seussian world, a group of creatures called the Sneetches are divided into two groups: those with stars on their bellies, and those with no \"stars upon thars\". Over time, the star-bellied sneetches have come to think of themselves as better than the plain-bellied sneetches. As researchers of sneetches, it's our job to uncover whether or not star-bellied sneetches really are better than their plain-bellied cousins.\n", "\n", "The first step in answering this question will be to create our experimental data. In the following code snippet we create a dataframe object that contains a set of test scores for both star-bellied and plain-bellied sneetches. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " score star\n", "0 84 1\n", "1 72 1\n", "2 57 1\n", "3 46 1\n", "4 63 1\n", "5 76 1\n", "6 99 1\n", "7 91 1\n", "8 81 0\n", "9 69 0\n", "10 74 0\n", "11 61 0\n", "12 56 0\n", "13 87 0\n", "14 69 0\n", "15 65 0\n", "16 66 0\n", "17 44 0\n", "18 62 0\n", "19 69 0" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "df = pd.DataFrame({'star': [1, 1, 1, 1, 1, 1, 1, 1] + \n", " [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n", " 'score': [84, 72, 57, 46, 63, 76, 99, 91] +\n", " [81, 69, 74, 61, 56, 87, 69, 65, 66, 44, 62, 69]})\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we then take a look at the average scores for each group of sneetches, we will see that there's a difference in scores of **6.6** between the two groups. So, on average, the star-bellied sneetches performed better on their tests than the plain-bellied sneetches. But, the real question is, is this a significant difference?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Star-bellied Sneetches Mean: 73.5\n", "Plain-bellied Sneetches Mean: 66.9\n", "Difference: 6.6\n" ] } ], "source": [ "star_bellied_mean = df[df.star == 1].score.mean()\n", "plain_bellied_mean = df[df.star == 0].score.mean()\n", "\n", "print(\"Star-bellied Sneetches Mean: %2.1f\" % star_bellied_mean)\n", "print(\"Plain-bellied Sneetches Mean: %2.1f\" % plain_bellied_mean)\n", "print(\"Difference: %2.1f\" % (star_bellied_mean - plain_bellied_mean))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To determine if this is a signficant difference, we could perform a [t-test][t_test] on our data to compute a p-value, and then just make sure that the p-value is less than the target 0.05. Alternatively, we could use simulation instead. \n", "\n", "Unlike our first example, however, we don't have a generative function that we can use to create our probability distribution. So, how can we then use simulation to solve our problem?\n", "\n", "Well, we can run a bunch of simulations where we randomly shuffle the labels (i.e., star-bellied or plain-bellied) of each sneetch, recompute the difference between the means, and then determine if the proportion of simulations in which the difference was at least as extreme as 6.6 was less than the target 5%. If so, we can conclude that the difference we see is, in fact, one that doesn't occur strictly by chance very often and so the difference is a significant one. In other words, if the proportion of simulations that have a difference of 6.6 or greater is less than 5%, we can conclude that the labels really do matter, and so we can conclude that star-bellied sneetches are \"better\" than their plain-bellied counterparts.\n", "\n", "[t_test]: https://en.wikipedia.org/wiki/Student's_t-test" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "df['label'] = df['star']\n", "\n", "num_simulations = 10000\n", "\n", "differences = []\n", "for i in range(num_simulations):\n", " np.random.shuffle(df['label'])\n", " star_bellied_mean = df[df.label == 1].score.mean()\n", " plain_bellied_mean = df[df.label == 0].score.mean()\n", " differences.append(star_bellied_mean - plain_bellied_mean)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we've ran our simulations, we can calculate our p-value, which is simply the proportion of simulations that resulted in a difference greater than or equal to 6.6.\n", "\n", "$$\n", "p = \\frac{N_{>6.6}}{N_{total}} = \\frac{1512}{10000} = 0.15\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p-value: 0.16\n" ] } ], "source": [ "p_value = sum(diff >= 6.6 for diff in differences) / num_simulations\n", "print(\"p-value: %2.2f\" % p_value)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "The following code plots the distribution of the differences we found by running the simulations above. We've also added an annotation that marks where the difference of 6.6 falls in the distribution along with its corresponding p-value." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 272, "width": 400 } }, "output_type": "display_data" } ], "source": [ "plt.hist(differences, bins=50, color=blue)\n", "plt.xlabel('score difference')\n", "plt.ylabel('number')\n", "plt.plot((6.6, 6.6), (0, 700), color=red);\n", "plt.annotate('%2.f%%' % (p_value * 100), \n", " xytext=(15, 350), \n", " xy=(6.6, 350), \n", " multialignment='right',\n", " va='center',\n", " color=red,\n", " size='large',\n", " arrowprops={'arrowstyle': '<|-', \n", " 'lw': 2, \n", " 'color': red, \n", " 'shrinkA': 10});" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see from the histogram above---and from our simulated p-value, which was greater than 5%---that the difference that we are seeing between the populations can be explained by random chance, so we can effectively dismiss the difference as not statistically significant. In short, star-bellied sneetches are no better than the plain-bellied ones, at least not from a statistical point of view.\n", "\n", "For further discussion on this method of simulation, check out John Rauser's keynote talk [\"Statistics Without the Agonizing Pain\"][rauser] from Strata + Hadoop 2014. Jake mentions that he drew inspiration from it in his talk, and it is a really excellent talk as well; I wholeheartedly recommend it.\n", "\n", "[rauser]: https://youtu.be/5Dnw46eC-0o\n", "\n", "### Bootstrapping\n", "\n", "In this example, we'll be using the story of Yertle the Turtle to explore the bootstrapping recipe. As the story goes, in the land of Sala-ma-Sond, Yertle the Turtle was the king of the pond and he wanted to be the most powerful, highest turtle in the land. To achieve this goal, he would stack turtles as high as he could in order to stand upon their backs. As observers of this curious behavior, we've recorded the heights of 20 turtle towers and we've placed them in a dataframe in the following bit of code." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "df = pd.DataFrame({'heights': [48, 24, 51, 12, 21, \n", " 41, 25, 23, 32, 61, \n", " 19, 24, 29, 21, 23, \n", " 13, 32, 18, 42, 18]})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The questions we want to answer in this example are: what is the mean height of Yertle's turtle stacks, and what is the uncertainty of this estimate?\n", "\n", "#### The Classic Method\n", "\n", "The classic method is simply to calculate the sample mean...\n", "\n", "$$\n", "\\bar{x} = \\frac{1}{N} \\sum_{i=1}^{N} x_i = 28.9\n", "$$\n", "\n", "...and the standard error of the mean.\n", "\n", "$$\n", "\\sigma_{\\bar{x}} = \\frac{1}{\n", " \\sqrt{N}}\\sqrt{\\frac{1}{N - 1}\n", " \\sum_{i=1}^{N} (x_i - \\bar{x})^2\n", "} = 3.0\n", "$$\n", "\n", "But, being hackers, we'll be using simulation instead.\n", "\n", "Just like in our last example, we are once again faced with the problem of not having a generative model, but unlike the last example, we're not comparing two groups, so we can't just shuffle around labels here, instead we'll use something called [bootstrap][bootstrap] [resampling][resampling].\n", "\n", "Bootstrap resampling is a method that simulates several random sample distributions by drawing samples from the current distribution with replacement, i.e., we can draw the same data point more than once. Luckily, pandas makes this super easy with its `sample` function. We simply need to make sure that we pass in `True` for the `replace` argument to sample from our dataset with replacement.\n", "\n", "[bootstrap]: https://en.wikipedia.org/wiki/Bootstrapping_(statistics)\n", "[resampling]: https://en.wikipedia.org/wiki/Resampling_(statistics)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " heights\n", "1 24\n", "9 61\n", "10 19\n", "15 13\n", "7 23\n", "1 24\n", "17 18\n", "9 61\n", "3 12\n", "15 13\n", "11 24\n", "3 12\n", "7 23\n", "11 24\n", "9 61\n", "14 23\n", "14 23\n", "10 19\n", "15 13\n", "7 23" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Mean: 25.65\n", "Standard Error: 3.55\n" ] } ], "source": [ "sample = df.sample(20, replace=True)\n", "display(sample)\n", "print(\"Mean: %2.2f\" % sample.heights.mean())\n", "print(\"Standard Error: %2.2f\" % (sample.heights.std() / np.sqrt(len(sample))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More than likely the mean and standard error from our freshly drawn sample above didn't exactly match the one that we calculated using the classic method beforehand. But, if we continue to resample several thousand times and take a look at the average (mean) of all those sample means and their standard deviation, we should have something that very closely approximates the mean and standard error derived from using the classic method above." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean: 28.8\n", "Standard Error: 2.9\n" ] } ], "source": [ "xbar = []\n", "for i in range(10000):\n", " sample = df.sample(20, replace=True)\n", " xbar.append(sample.heights.mean())\n", " \n", "\n", "print(\"Mean: %2.1f\" % np.mean(xbar))\n", "print(\"Standard Error: %2.1f\" % np.std(xbar))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cross Validation\n", "\n", "For the final example, we dive into the world of the Lorax. In the story of the Lorax, a faceless creature sales an item that (presumably) all creatures need called a Thneed. Our job as consultants to Onceler Industries is to project Thneed sales. But, before we can get started forecasting the sales of Thneeds, we'll first need some data. \n", "\n", "Lucky for you, I've already done the hard work of assembling that data in the code below by \"eyeballing\" the data in the scatter plot from the slides of the talk. So, it may not be exactly the same, but it should be close enough for our example analysis." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "df = pd.DataFrame({\n", " 'temp': [22, 36, 36, 38, 44, 45, 47,\n", " 43, 44, 45, 47, 49,\n", " 52, 53, 53, 53, 54, 55, 55, 55, 56, 57, 58, 59,\n", " 60, 61, 61.5, 61.7, 61.7, 61.7, 61.8, 62, 62, 63.4, 64.6,\n", " 65, 65.6, 65.6, 66.4, 66.9, 67, 67, 67.4, 67.5, 68, 69, \n", " 70, 71, 71, 71.5, 72, 72, 72, 72.7, 73, 73, 73, 73.3, 74, 75, 75, \n", " 77, 77, 77, 77.4, 77.9, 78, 78, 79,\n", " 80, 82, 83, 84, 85, 85, 86, 87, 88,\n", " 90, 90, 91, 93, 95, 97,\n", " 102, 104],\n", " 'sales': [660, 433, 475, 492, 302, 345, 337,\n", " 479, 456, 440, 423, 269,\n", " 331, 197, 283, 351, 470, 252, 278, 350, 253, 253, 343, 280,\n", " 200, 194, 188, 171, 204, 266, 275, 171, 282, 218, 226, \n", " 187, 184, 192, 167, 136, 149, 168, 218, 298, 199, 268,\n", " 235, 157, 196, 203, 148, 157, 213, 173, 145, 184, 226, 204, 250, 102, 176,\n", " 97, 138, 226, 35, 190, 221, 95, 211,\n", " 110, 150, 152, 37, 76, 56, 51, 27, 82,\n", " 100, 123, 145, 51, 156, 99,\n", " 147, 54]\n", "})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have our sales data in a pandas dataframe, we can take a look to see if any trends show up. Plotting the data in a scatterplot, like the one below, reveals that a relationship does seem to exist between temperature and Thneed sales." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 277, "width": 400 } }, "output_type": "display_data" } ], "source": [ "# Grab a reference to fig and axes object so we can reuse them\n", "fig, ax = plt.subplots()\n", "\n", "# Plot the Thneed sales data\n", "ax.scatter(df.temp, df.sales)\n", "ax.set_xlim(xmin=20, xmax=110)\n", "ax.set_ylim(ymin=0, ymax=700)\n", "ax.set_xlabel('temperature (F)')\n", "ax.set_ylabel('thneed sales (daily)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see what looks like a relationship between the two variables temperature and sales, but how can we best model that relationship so we can accurately predict sales based on temperature? \n", "\n", "Well, one measure of a model's accuracy is the [Root-Mean-Square Error (RMSE)][rmse]. This metric represents the sample standard deviation between a set of predicted values (from our model) and the actual observed values. \n", "\n", "[rmse]: https://en.wikipedia.org/wiki/Root-mean-square_deviation" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def rmse(predictions, targets):\n", " return np.sqrt(((predictions - targets)**2).mean())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now use our `rmse` function to measure how well our models' accurately represent the Thneed sales dataset. And, in the next cell, we'll give it a try by creating two different models and seeing which one does a better job of fitting our sales data." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 277, "width": 424 } }, "output_type": "display_data" } ], "source": [ "# 1D Polynomial Fit\n", "d1_model = np.poly1d(np.polyfit(df.temp, df.sales, 1))\n", "d1_predictions = d1_model(range(111))\n", "ax.plot(range(111), d1_predictions, \n", " color=blue, alpha=0.7)\n", "\n", "# 2D Polynomial Fit\n", "d2_model = np.poly1d(np.polyfit(df.temp, df.sales, 2))\n", "d2_predictions = d2_model(range(111))\n", "ax.plot(range(111), d2_predictions, \n", " color=red, alpha=0.5)\n", "\n", "ax.annotate('RMS error = %2.1f' % rmse(d1_model(df.temp), df.sales),\n", " xy=(75, 650),\n", " fontsize=20,\n", " color=blue,\n", " backgroundcolor='w')\n", "\n", "ax.annotate('RMS error = %2.1f' % rmse(d2_model(df.temp), df.sales),\n", " xy=(75, 580),\n", " fontsize=20,\n", " color=red,\n", " backgroundcolor='w')\n", "\n", "display(fig);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the figure above, we plotted our sales data along with the two models we created in the previous step. The first model (in blue) is a simple linear model, i.e., a [first-degree polynomial][degree]. The second model (in red) is a second-degree polynomial, so rather than a straight line, we end up with a slight curve. \n", "\n", "We can see from the RMSE values in the figure above that the second-degree polynomial performed better than the simple linear model. Of course, the question you should now be asking is, is this the best possible model that we can find?\n", "\n", "To find out, let's take a look at the RMSE of a few more models to see if we can do any better.\n", "\n", "[degree]: https://en.wikipedia.org/wiki/Degree_of_a_polynomial" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 278, "width": 489 } }, "output_type": "display_data" } ], "source": [ "rmses = []\n", "for deg in range(15):\n", " model = np.poly1d(np.polyfit(df.temp, df.sales, deg))\n", " predictions = model(df.temp)\n", " rmses.append(rmse(predictions, df.sales))\n", " \n", "plt.plot(range(15), rmses)\n", "plt.ylim(45, 70)\n", "plt.xlabel('number of terms in fit')\n", "plt.ylabel('rms error')\n", "\n", "plt.annotate('$y = a + bx$', \n", " xytext=(14.2, 70), \n", " xy=(1, rmses[1]), \n", " multialignment='right',\n", " va='center',\n", " arrowprops={'arrowstyle': '-|>',\n", " 'lw': 1,\n", " 'shrinkA': 10,\n", " 'shrinkB': 3})\n", "\n", "plt.annotate('$y = a + bx + cx^2$', \n", " xytext=(14.2, 64), \n", " xy=(2, rmses[2]), \n", " multialignment='right',\n", " va='top',\n", " arrowprops={'arrowstyle': '-|>',\n", " 'lw': 1,\n", " 'shrinkA': 35,\n", " 'shrinkB': 3})\n", "\n", "\n", "plt.annotate('$y = a + bx + cx^2 + dx^3$', \n", " xytext=(14.2, 58), \n", " xy=(3, rmses[3]), \n", " multialignment='right',\n", " va='top',\n", " arrowprops={'arrowstyle': '-|>',\n", " 'lw': 1,\n", " 'shrinkA': 12,\n", " 'shrinkB': 3});" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see, from the plot above, that as we increase the number of terms (i.e., the degrees of freedom) in our model we decrease the RMSE, and this behavior can continue indefinitely, or until we have as many terms as we do data points, at which point we would be fitting the data perfectly.\n", "\n", "The problem with this approach though, is that as we increase the number of terms in our equation, we simply match the given dataset closer and closer, but what if our model were to see a data point that's not in our training dataset?\n", "\n", "As you can see in the plot below, the model that we've created, though it has a very low RMSE, it has so many terms that it matches our current dataset too closely." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 277, "width": 409 } }, "output_type": "display_data" } ], "source": [ "# Remove everything but the datapoints\n", "ax.lines.clear()\n", "ax.texts.clear()\n", "\n", "# Changing the y-axis limits to match the figure in the slides\n", "ax.set_ylim(0, 1000)\n", "\n", "# 14 Dimensional Model\n", "model = np.poly1d(np.polyfit(df.temp, df.sales, 14))\n", "ax.plot(range(20, 110), model(range(20, 110)),\n", " color=sns.xkcd_rgb['sky blue'])\n", "\n", "display(fig)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The problem with fitting the data too closely, is that our model is so finely tuned to our specific dataset, that if we were to use it to predict future sales, it would most likely fail to get very close to the actual value. This phenomenon of too closely modeling the training dataset is well known amongst machine learning practitioners as [overfitting][overfitting] and one way that we can avoid it is to use [cross-validation][cv]. \n", "\n", "Cross-validation avoids overfitting by splitting the training dataset into several subsets and using each one to train and test multiple models. Then, the RMSE's of each of those models are averaged to give a more likely estimate of how a model of that type would perform on unseen data.\n", "\n", "So, let's give it a try by splitting our data into two groups and randomly assigning data points into each one.\n", "\n", "[overfitting]: https://en.wikipedia.org/wiki/Overfitting\n", "[cv]: https://en.wikipedia.org/wiki/Cross-validation_(statistics)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "df_a = df.sample(n=len(df)//2)\n", "df_b = df.drop(df_a.index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can get a look at the data points assigned to each subset by plotting each one as a different color." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 277, "width": 400 } }, "output_type": "display_data" } ], "source": [ "plt.scatter(df_a.temp, df_a.sales, color='red')\n", "plt.scatter(df_b.temp, df_b.sales, color='blue')\n", "plt.xlim(0, 110)\n", "plt.ylim(0, 700)\n", "plt.xlabel('temprature (F)')\n", "plt.ylabel('thneed sales (daily)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, we'll find the best model for each subset of data. In this particular example, we'll fit a second-degree polynomial to each subset and plot both below." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 332, "width": 735 } }, "output_type": "display_data" } ], "source": [ "# Create a 2-degree model for each subset of data\n", "m1 = np.poly1d(np.polyfit(df_a.temp, df_a.sales, 2))\n", "m2 = np.poly1d(np.polyfit(df_b.temp, df_b.sales, 2))\n", "\n", "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, \n", " sharex=False, sharey=True,\n", " figsize=(12, 5))\n", "\n", "x_min, x_max = 20, 110\n", "y_min, y_max = 0, 700\n", "x = range(x_min, x_max + 1)\n", "\n", "# Plot the df_a group\n", "ax1.scatter(df_a.temp, df_a.sales, color='red')\n", "ax1.set_xlim(xmin=x_min, xmax=x_max)\n", "ax1.set_ylim(ymin=y_min, ymax=y_max)\n", "ax1.set_xlabel('temprature (F)')\n", "ax1.set_ylabel('thneed sales (daily)')\n", "ax1.plot(x, m1(x),\n", " color=sns.xkcd_rgb['sky blue'],\n", " alpha=0.7)\n", "\n", "# Plot the df_b group\n", "ax2.scatter(df_b.temp, df_b.sales, color='blue')\n", "ax2.set_xlim(xmin=x_min, xmax=x_max)\n", "ax2.set_ylim(ymin=y_min, ymax=y_max)\n", "ax2.set_xlabel('temprature (F)')\n", "ax2.plot(x, m2(x),\n", " color=sns.xkcd_rgb['rose'], \n", " alpha=0.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we'll compare models across subsets by calculating the RMSE for each model using the training set for the other model. This will give us two RMSE scores which we'll then average to get a more accurate estimate of how well a second-degree polynomial will perform on any unseen data." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMS = 50.5\n", "RMS = 57.8\n", "RMS estimate = 54.1\n" ] } ], "source": [ "print(\"RMS = %2.1f\" % rmse(m1(df_b.temp), df_b.sales))\n", "print(\"RMS = %2.1f\" % rmse(m2(df_a.temp), df_a.sales))\n", "print(\"RMS estimate = %2.1f\" % np.mean([rmse(m1(df_b.temp), df_b.sales),\n", " rmse(m2(df_a.temp), df_a.sales)]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, we simply repeat this process for as long as we so desire. \n", "\n", "The following code repeats the process described above for polynomials up to 14 degrees and plots the average RMSE for each one against the non-cross-validated RMSE's that we calculated earlier." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "image/png": { "height": 277, "width": 509 } }, "output_type": "display_data" } ], "source": [ "rmses = []\n", "cross_validated_rmses = []\n", "for deg in range(15):\n", " # df_a the model on the whole dataset and calculate its\n", " # RMSE on the same set of data\n", " model = np.poly1d(np.polyfit(df.temp, df.sales, deg))\n", " predictions = model(df.temp)\n", " rmses.append(rmse(predictions, df.sales))\n", " \n", " # Use cross-validation to create the model and df_a it\n", " m1 = np.poly1d(np.polyfit(df_a.temp, df_a.sales, deg))\n", " m2 = np.poly1d(np.polyfit(df_b.temp, df_b.sales, deg))\n", " \n", " p1 = m1(df_b.temp)\n", " p2 = m2(df_a.temp)\n", " \n", " cross_validated_rmses.append(np.mean([rmse(p1, df_b.sales), \n", " rmse(p2, df_a.sales)]))\n", "\n", " \n", "plt.plot(range(15), rmses, color=blue, \n", " label='RMS')\n", "plt.plot(range(15), cross_validated_rmses, color=red, \n", " label='cross validated RMS')\n", "plt.ylim(45, 70)\n", "plt.xlabel('number of terms in fit')\n", "plt.ylabel('rms error')\n", "plt.legend(frameon=True)\n", "\n", "plt.annotate('Best model minimizes the\\ncross-validated error.', \n", " xytext=(7, 60), \n", " xy=(2, cross_validated_rmses[2]), \n", " multialignment='center',\n", " va='top',\n", " color='blue',\n", " size=25,\n", " backgroundcolor='w',\n", " arrowprops={'arrowstyle': '-|>',\n", " 'lw': 3,\n", " 'shrinkA': 12,\n", " 'shrinkB': 3,\n", " 'color': 'blue'});" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to the graph above, going from a 1-degree to a 2-degree polynomial gives us quite a large improvement overall. But, unlike the RMSE that we calculated against the training set, when using cross-validation we can see that adding more degrees of freedom to our equation quickly reduces the effectiveness of the model against unseen data. This is overfitting in action! In fact, from the looks of the graph above, it would seem that a second-degree polynomial is actually our best bet for this particular dataset.\n", "\n", "#### 2-Fold Cross-Validation\n", "\n", "Several different methods for performing cross-validation exist, the one we've just seen is called [2-fold cross-validation][2-fold-cv] since the data is split into two subsets. Another close relative is a method called [$k$-fold cross-validation][k-fold-cv]. It differs slightly in that the original dataset is divided into $k$ subsets (instead of just 2), one of which is reserved strictly for testing and the other $k - 1$ subsets are used for training models. This is just one example of an alternate cross-validation method, but more do exist and each one has advantages and drawbacks that you'll need to consider when deciding which method to use.\n", "\n", "[2-fold-cv]: https://en.wikipedia.org/wiki/Cross-validation_(statistics)#2-fold_cross-validation\n", "[k-fold-cv]: https://en.wikipedia.org/wiki/Cross-validation_(statistics)#k-fold_cross-validation\n", "\n", "## Conclusion\n", "\n", "Ok, so that covers nearly everything that Jake covered in his talk. The end of the talk contains a short overview of some important areas that he didn't have time to cover, and there's a nice set of Q&A at the end, but I'll simply direct you to the [video][video] for those parts of the talk. Hopefully, this article/notebook has been helpful to anyone working their way through Jake's talk, and if for some reason, you've read through this entire article and haven't watched the video of the talk yet, I encourage you to take 40 minutes out of your day and go [watch it now][video]---it really is a fantastic talk!\n", "\n", "[video]: https://youtu.be/Iq9DzN6mvYA" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 1 }