{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "You can order print and ebook versions of *Think Bayes 2e* from\n", "[Bookshop.org](https://bookshop.org/a/98697/9781492089469) and\n", "[Amazon](https://amzn.to/334eqGo)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Classification" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "# install empiricaldist if necessary\n", "\n", "try:\n", " import empiricaldist\n", "except ImportError:\n", " !pip install empiricaldist\n", " import empiricaldist" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "# Get utils.py\n", "\n", "from os.path import basename, exists\n", "\n", "def download(url):\n", " filename = basename(url)\n", " if not exists(filename):\n", " from urllib.request import urlretrieve\n", " local, _ = urlretrieve(url, filename)\n", " print('Downloaded ' + local)\n", " \n", "download('https://github.com/AllenDowney/ThinkBayes2/raw/master/soln/utils.py')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "from utils import set_pyplot_params\n", "\n", "set_pyplot_params()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "from utils import Or70, Pu50, Gr30\n", "\n", "color_list3 = [Or70, Pu50, Gr30]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from cycler import cycler\n", "\n", "marker_cycle = cycler(marker=['s', 'o', '^'])\n", "color_cycle = cycler(color=color_list3)\n", "line_cycle = cycler(linestyle=['-', '--', ':'])\n", "\n", "plt.rcParams['axes.prop_cycle'] = (color_cycle + \n", " marker_cycle + \n", " line_cycle)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Classification might be the most well-known application of Bayesian methods, made famous in the 1990s as the basis of the first generation of [spam filters](https://en.wikipedia.org/wiki/Naive_Bayes_spam_filtering).\n", "\n", "In this chapter, I'll demonstrate Bayesian classification using data collected and made available by Dr. Kristen Gorman at the Palmer Long-Term Ecological Research Station in Antarctica (see Gorman, Williams, and Fraser, [\"Ecological Sexual Dimorphism and Environmental Variability within a Community of Antarctic Penguins (Genus *Pygoscelis*)\"](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0090081), March 2014).\n", "We'll use this data to classify penguins by species." ] }, { "cell_type": "markdown", "metadata": { "tags": [ "remove-cell" ] }, "source": [ "The following cell downloads the raw data." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "# Load the data files from \n", "# https://github.com/allisonhorst/palmerpenguins\n", "# With gratitude to Allison Horst (@allison_horst)\n", "\n", "download('https://github.com/allisonhorst/palmerpenguins/raw/main/inst/extdata/penguins_raw.csv')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Penguin Data\n", "\n", "I'll use Pandas to load the data into a `DataFrame`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(342, 17)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "df = pd.read_csv('penguins_raw.csv').dropna(subset=['Body Mass (g)'])\n", "df.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dataset contains one row for each penguin and one column for each variable." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/html": [ "
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studyNameSample NumberSpeciesRegionIslandStageIndividual IDClutch CompletionDate EggCulmen Length (mm)Culmen Depth (mm)Flipper Length (mm)Body Mass (g)SexDelta 15 N (o/oo)Delta 13 C (o/oo)Comments
0PAL07081Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN1A1Yes2007-11-1139.118.7181.03750.0MALENaNNaNNot enough blood for isotopes.
1PAL07082Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN1A2Yes2007-11-1139.517.4186.03800.0FEMALE8.94956-24.69454NaN
2PAL07083Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN2A1Yes2007-11-1640.318.0195.03250.0FEMALE8.36821-25.33302NaN
4PAL07085Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN3A1Yes2007-11-1636.719.3193.03450.0FEMALE8.76651-25.32426NaN
5PAL07086Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN3A2Yes2007-11-1639.320.6190.03650.0MALE8.66496-25.29805NaN
\n", "
" ], "text/plain": [ " studyName Sample Number Species Region \\\n", "0 PAL0708 1 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "1 PAL0708 2 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "2 PAL0708 3 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "4 PAL0708 5 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "5 PAL0708 6 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "\n", " Island Stage Individual ID Clutch Completion Date Egg \\\n", "0 Torgersen Adult, 1 Egg Stage N1A1 Yes 2007-11-11 \n", "1 Torgersen Adult, 1 Egg Stage N1A2 Yes 2007-11-11 \n", "2 Torgersen Adult, 1 Egg Stage N2A1 Yes 2007-11-16 \n", "4 Torgersen Adult, 1 Egg Stage N3A1 Yes 2007-11-16 \n", "5 Torgersen Adult, 1 Egg Stage N3A2 Yes 2007-11-16 \n", "\n", " Culmen Length (mm) Culmen Depth (mm) Flipper Length (mm) Body Mass (g) \\\n", "0 39.1 18.7 181.0 3750.0 \n", "1 39.5 17.4 186.0 3800.0 \n", "2 40.3 18.0 195.0 3250.0 \n", "4 36.7 19.3 193.0 3450.0 \n", "5 39.3 20.6 190.0 3650.0 \n", "\n", " Sex Delta 15 N (o/oo) Delta 13 C (o/oo) \\\n", "0 MALE NaN NaN \n", "1 FEMALE 8.94956 -24.69454 \n", "2 FEMALE 8.36821 -25.33302 \n", "4 FEMALE 8.76651 -25.32426 \n", "5 MALE 8.66496 -25.29805 \n", "\n", " Comments \n", "0 Not enough blood for isotopes. \n", "1 NaN \n", "2 NaN \n", "4 NaN \n", "5 NaN " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.head()" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "remove-cell" ] }, "source": [ "For convenience, I'll create a new column called `Species2` that contains a shorter version of the species names." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "def shorten(species):\n", " return species.split()[0]\n", "\n", "df['Species2'] = df['Species'].apply(shorten)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Three species of penguins are represented in the dataset: Adélie, Chinstrap and Gentoo." ] }, { "cell_type": "markdown", "metadata": { "tags": [ "remove-cell" ] }, "source": [ "These species are shown in this illustration (by Allison Horst, available under the [CC-BY](https://creativecommons.org/licenses/by/2.0/) license):\n", "\n", "\"Drawing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The measurements we'll use are:\n", "\n", "* Body Mass in grams (g).\n", "\n", "* Flipper Length in millimeters (mm).\n", "\n", "* Culmen Length in millimeters. \n", "\n", "* Culmen Depth in millimeters.\n", "\n", "If you are not familiar with the word \"culmen\", it refers to the [top margin of the beak](https://en.wikipedia.org/wiki/Bird_measurement#Culmen)." ] }, { "cell_type": "markdown", "metadata": { "tags": [ "remove-cell" ] }, "source": [ "The culmen is shown in the following illustration (also by Allison Horst):\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These measurements will be most useful for classification if there are substantial differences between species and small variation within species. To see whether that is true, and to what degree, I'll plot cumulative distribution functions (CDFs) of each measurement for each species. \n", "\n", "The following function takes the `DataFrame` and a column name.\n", "It returns a dictionary that maps from each species name to a `Cdf` of the values in the column named `colname`." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def make_cdf_map(df, colname, by='Species2'):\n", " \"\"\"Make a CDF for each species.\"\"\"\n", " cdf_map = {}\n", " grouped = df.groupby(by)[colname]\n", " for species, group in grouped:\n", " cdf_map[species] = Cdf.from_seq(group, name=species)\n", " return cdf_map" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "The following function plots a `Cdf` of the values in the given column for each species: " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [], "source": [ "from empiricaldist import Cdf\n", "from utils import decorate\n", "\n", "def plot_cdfs(df, colname, by='Species2'):\n", " \"\"\"Make a CDF for each species.\n", " \n", " df: DataFrame\n", " colname: string column name\n", " by: string column name\n", "\n", " returns: dictionary from species name to Cdf\n", " \"\"\"\n", " cdf_map = make_cdf_map(df, colname, by)\n", " \n", " for species, cdf in cdf_map.items():\n", " cdf.plot(label=species, marker='')\n", " \n", " decorate(xlabel=colname,\n", " ylabel='CDF')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the distributions look like for culmen length." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colname = 'Culmen Length (mm)'\n", "plot_cdfs(df, colname)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks like we can use culmen length to identify Adélie penguins, but the distributions for the other two species almost entirely overlap.\n", "\n", "Here are the distributions for flipper length." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colname = 'Flipper Length (mm)'\n", "plot_cdfs(df, colname)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using flipper length, we can distinguish Gentoo penguins from the other two species. So with just these two features, it seems like we should be able to classify penguins with some accuracy.\n", "\n", "All of these CDFs show the sigmoid shape characteristic of the normal distribution; I will take advantage of that observation in the next section." ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "Here are the distributions for culmen depth." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colname = 'Culmen Depth (mm)'\n", "plot_cdfs(df, colname)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "And here are the distributions of body mass." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colname = 'Body Mass (g)'\n", "plot_cdfs(df, colname)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "Culmen depth and body mass distinguish Gentoo penguins from the other two species, but these features might not add a lot of additional information, beyond what we get from flipper length and culmen length." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Normal Models\n", "\n", "Let's use these features to classify penguins. We'll proceed in the usual Bayesian way:\n", "\n", "1. Define a prior distribution with the three possible species and a prior probability for each,\n", "\n", "2. Compute the likelihood of the data for each hypothetical species, and then\n", "\n", "3. Compute the posterior probability of each hypothesis.\n", "\n", "To compute the likelihood of the data under each hypothesis, I'll use the data to estimate the parameters of a normal distribution for each species.\n", "\n", "The following function takes a `DataFrame` and a column name; it returns a dictionary that maps from each species name to a `norm` object.\n", "\n", "`norm` is defined in SciPy; it represents a normal distribution with a given mean and standard deviation." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "from scipy.stats import norm\n", "\n", "def make_norm_map(df, colname, by='Species2'):\n", " \"\"\"Make a map from species to norm object.\"\"\"\n", " norm_map = {}\n", " grouped = df.groupby(by)[colname]\n", " for species, group in grouped:\n", " mean = group.mean()\n", " std = group.std()\n", " norm_map[species] = norm(mean, std)\n", " return norm_map" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For example, here's the dictionary of `norm` objects for flipper length:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "dict_keys(['Adelie', 'Chinstrap', 'Gentoo'])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "flipper_map = make_norm_map(df, 'Flipper Length (mm)')\n", "flipper_map.keys()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose we measure a penguin and find that its flipper is 193 cm. What is the probability of that measurement under each hypothesis?\n", "\n", "The `norm` object provides `pdf`, which computes the probability density function (PDF) of the normal distribution. We can use it to compute the likelihood of the observed data in a given distribution." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.054732511875530694" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data = 193\n", "flipper_map['Adelie'].pdf(data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a probability density, so we can't interpret it as a probability. But it is proportional to the likelihood of the data, so we can use it to update the prior.\n", "\n", "Here's how we compute the likelihood of the data in each distribution." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.054732511875530694, 0.05172135615888162, 5.8660453661990634e-05]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hypos = flipper_map.keys()\n", "likelihood = [flipper_map[hypo].pdf(data) for hypo in hypos]\n", "likelihood" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we're ready to do the update." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Update\n", "\n", "As usual I'll use a `Pmf` to represent the prior distribution. For simplicity, let's assume that the three species are equally likely." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
probs
Adelie0.333333
Chinstrap0.333333
Gentoo0.333333
\n", "
" ], "text/plain": [ "Adelie 0.333333\n", "Chinstrap 0.333333\n", "Gentoo 0.333333\n", "dtype: float64" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from empiricaldist import Pmf\n", "\n", "prior = Pmf(1/3, hypos)\n", "prior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can do the update in the usual way." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
probs
Adelie0.513860
Chinstrap0.485589
Gentoo0.000551
\n", "
" ], "text/plain": [ "Adelie 0.513860\n", "Chinstrap 0.485589\n", "Gentoo 0.000551\n", "dtype: float64" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "posterior = prior * likelihood\n", "posterior.normalize()\n", "posterior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A penguin with a 193 mm flipper is unlikely to be a Gentoo, but might be either an Adélie or Chinstrap (assuming that the three species were equally likely before the measurement). \n", "\n", "The following function encapsulates the steps we just ran.\n", "It takes a `Pmf` representing the prior distribution, the observed data, and a map from each hypothesis to the distribution of the feature." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "def update_penguin(prior, data, norm_map):\n", " \"\"\"Update hypothetical species.\"\"\"\n", " hypos = prior.qs\n", " likelihood = [norm_map[hypo].pdf(data) for hypo in hypos]\n", " posterior = prior * likelihood\n", " posterior.normalize()\n", " return posterior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The return value is the posterior distribution.\n", "\n", "Here's the previous example again, using `update_penguin`:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
probs
Adelie0.513860
Chinstrap0.485589
Gentoo0.000551
\n", "
" ], "text/plain": [ "Adelie 0.513860\n", "Chinstrap 0.485589\n", "Gentoo 0.000551\n", "dtype: float64" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "posterior1 = update_penguin(prior, 193, flipper_map)\n", "posterior1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we saw in the CDFs, flipper length does not distinguish strongly between Adélie and Chinstrap penguins.\n", "\n", "But culmen length *can* make this distinction, so let's use it to do a second round of classification.\n", "First we estimate distributions of culmen length for each species like this:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "culmen_map = make_norm_map(df, 'Culmen Length (mm)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose we see a penguin with culmen length 48 mm.\n", "We can use this data to update the prior." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
probs
Adelie0.001557
Chinstrap0.474658
Gentoo0.523785
\n", "
" ], "text/plain": [ "Adelie 0.001557\n", "Chinstrap 0.474658\n", "Gentoo 0.523785\n", "dtype: float64" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "posterior2 = update_penguin(prior, 48, culmen_map)\n", "posterior2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A penguin with culmen length 48 mm is about equally likely to be a Chinstrap or Gentoo.\n", "\n", "Using one feature at a time, we can often rule out one species or another, but we generally can't identify species with confidence.\n", "We can do better using multiple features." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Naive Bayesian Classification\n", "\n", "To make it easier to do multiple updates, I'll use the following function, which takes a prior `Pmf`, a sequence of measurements and a corresponding sequence of dictionaries containing estimated distributions." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "def update_naive(prior, data_seq, norm_maps):\n", " \"\"\"Naive Bayesian classifier\n", " \n", " prior: Pmf\n", " data_seq: sequence of measurements\n", " norm_maps: sequence of maps from species to distribution\n", " \n", " returns: Pmf representing the posterior distribution\n", " \"\"\"\n", " posterior = prior.copy()\n", " for data, norm_map in zip(data_seq, norm_maps):\n", " posterior = update_penguin(posterior, data, norm_map)\n", " return posterior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It performs a series of updates, using one variable at a time, and returns the posterior `Pmf`.\n", "\n", "To test it, I'll use the same features we looked at in the previous section: culmen length and flipper length." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "colnames = ['Flipper Length (mm)', 'Culmen Length (mm)']\n", "norm_maps = [flipper_map, culmen_map]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now suppose we find a penguin with flipper length 193 mm and culmen length 48.\n", "Here's the update:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
probs
Adelie0.003455
Chinstrap0.995299
Gentoo0.001246
\n", "
" ], "text/plain": [ "Adelie 0.003455\n", "Chinstrap 0.995299\n", "Gentoo 0.001246\n", "dtype: float64" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data_seq = 193, 48\n", "posterior = update_naive(prior, data_seq, norm_maps)\n", "posterior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is almost certain to be a Chinstrap." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'Chinstrap'" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "posterior.max_prob()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can loop through the dataset and classify each penguin with these two features." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "df['Classification'] = \"None\"\n", "\n", "for i, row in df.iterrows():\n", " data_seq = row[colnames]\n", " posterior = update_naive(prior, data_seq, norm_maps)\n", " df.loc[i, 'Classification'] = posterior.max_prob()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This loop adds a column called `Classification` to the `DataFrame`; it contains the species with the maximum posterior probability for each penguin.\n", "\n", "So let's see how many we got right." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "342" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(df)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "342" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "valid = df['Classification'].notna()\n", "valid.sum()" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "324" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "same = df['Species2'] == df['Classification']\n", "same.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are 344 penguins in the dataset, but two of them are missing measurements, so we have 342 valid cases.\n", "Of those, 324 are classified correctly, which is almost 95%." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9473684210526315" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "same.sum() / valid.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following function encapsulates these steps." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "def accuracy(df):\n", " \"\"\"Compute the accuracy of classification.\"\"\"\n", " valid = df['Classification'].notna()\n", " same = df['Species2'] == df['Classification']\n", " return same.sum() / valid.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The classifier we used in this section is called \"naive\" because it ignores correlations between the features. To see why that matters, I'll make a less naive classifier: one that takes into account the joint distribution of the features." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Joint Distributions\n", "\n", "I'll start by making a scatter plot of the data." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def scatterplot(df, var1, var2):\n", " \"\"\"Make a scatter plot.\"\"\"\n", " grouped = df.groupby('Species2')\n", " for species, group in grouped:\n", " plt.plot(group[var1], group[var2],\n", " label=species, ls=\"None\", alpha=0.3)\n", " \n", " decorate(xlabel=var1, ylabel=var2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's a scatter plot of culmen length and flipper length for the three species." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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EspCowShaRLxWftmMg59bkJ2biqzsVDgcbhz6vBGTp+fC5ZRkzwNAtTF4o4hPHG2Fw+GGyaTH7PJ8xSjioe5rnU6A2+Wpk5woQWihGI3pX6GItnZwIqw/hhpDNEFbkeyTaBWrQrqIv/rVr+LZZ5/FVVddhX/961/o7u5GVVUVnnjiCTgcDqxZswZ/+9vfYjVWIolIxDU5b9s1h92NjvZ+OOzuqK1rt1vC8SMtyM5NhcnkeY41mfTIzk1Fa5MNk6blyq7nqtn6zRtFPH32eJy3YCKmzx7viyKWH7MIp9ONPqsDVSfbceZkO6pOtqPP6oDD4U7oikhqFQJJFKIpsqDV+mMk66nDjSEa13Ek+yRaxaqQFuxzzz2H0tJSv22ZmZlYvHgxFi9ejP/+7/9GU1OTpgMkiHgw0r9Hu90Fp1NEVnaq33aTSQ9rrx05eWkoKsmWteKjtfCHukcBnLNG9TpIogSDUYfMLKZojer1Ogz0u9DV2Y/MDBNSUg0Q3RIsDT3IG6delSm1SfT0r2iIxhLTqmNOJJHMocYwp3h6xK7jRHB5j4SQAhsorgD8aqUKgoCioiL1R0UQccAvfSbTNKL1x5QUA4xGnc8168X7c0qKIeR6biRrvXLu0fyJmXA6PUFTnW39cIsS9DoBeRPSfcUz5I/Pvf/z/nTuhwQl0dO/vETi6oymyMJI1h+VxhapwHnHUNfWhOrWekzNL4VBr/eMwYKI3deJ4PIeCWH91m3ZsgUPPvggWlpaAHj+oBljGBgY0HRwBBEr1LaC9HoBc+YV+NZgTSY9HA43eroGsWBpMfR6QbWAHLnApLqqLnS09XmaCGSakJKqh9stobG+B3kKNY/dbhHpGSakphnR1d4Pu90Ng17wRXgnilAFEquSjCNF65zWkaw/HqypxCufbIXJYMTy2Yt82yNdT/WO4UDVUVgH+7B81kIsnFYOu9OBV/+9NaKgrdHcJN5LWGk6//3f/42//e1vGBgYwMDAAAYHB0lciaRCi8L0c+cXYsHSYjjsbrS39cFhd2PB0mKUnVcwbCpMuHmoSg8GGVkpsFrtnofhs59lvv/47+89j1eoMs0mTJ01HjNmj8fUWeORaTYllFAFksjpX16izWmNhGjXHwcddvx9/0foG+zD3/d/5BtbNOupjDE4XE4crKnE1PwSHKyphMPlxInGqojTZxIt5SYawnocLS4uxuzZs7UeC0FEzUitQS2sIEEQMG9BEebMK4Td7kJKiqcHbHNjr2IqTMFEc0TRsEruUZ3AIAieiO2e7kHY7S7o9DoUl2QDDHC53OjqGAg6T1FpFqpPdY66ovmJmv7lJVpXZyxKJR6sqURNawNKxk9ETWsDDtZUYvnsRVGvp8pdazTu60RLuYmGsAT28ccfx0033YTLLrsMJpPJt/22227TbGAEEQ5qpWdoWZjes57qEf7hXNGcc5/AhZOHqvRgIEocKSkGmLNTkDc+HZIoQdAJEEUJLqeIzvZ+2fNMnZmHabPGJaxQKZGo6V/AyFydWruVvdZrWkoqUo0pSEtJxd/3f4QFU+aGFjiF9VTvtZrTMnC49jgmTyjB/qojuHnltbiiYmXQ+UP9jSZayk00hCWwTz/9NGpqarBnzx4IgserzBgbVmAnT56M9PR0GAwGAMBrr72GsrIyPPjgg3jnnXcgCAIee+wxXH/99SO8DGKsomZhBLWtIKXgI6WAnD6rA3XVyqUS5daBlR4M+q0OzC7PR2+3PeiBYcqMPDTW98qep6mhFwuXlSakUIVDItYijja6d9Bhx+6TB9BvH8DukwfCXnuMxOr1Wq9F4wogcQk5GVmobvFYsUoC511PDRTROcXTfdfa2tuBE5YqpJpSkaI34URjVcQPCNEEenlJlCYJYf0mHjlyBJWVlVGd4MMPP0RxcbHv523btmHPnj04ceIEWltbcf7552P16tXIzIxNCy0ieVA7MEltK0gp+MhudyE9wxjkitbpBYgih8Ggg8ThszqHi4ZVejDIL8xEa7MtaHvuuDTUVXcNG3WbaEIVD9S4UUfr6jxuOYPGzhY0dLaAcx62WzkSq/dA1RGIEoe1v8+3TeISDlYfxfLZi2QFzrueGiiiXlewU3Rhf9URGHVG7K86gqUzKmLu1k2UJglh/QUtWLAADQ0NKCkpGfEJ33nnHdx+++3Q6/UoKirCRRddhG3btmHDhg0jPjYxttAqPSMaKyhwDVhJ/M3ZKXC0umHttcOclSJjWfagrbUPvV2DvtSarNxUpGcYFdeBQz0YyG2XJD4qom4TATVu1NG4Or3Wa1dfD/Kz8tDV1xOWFRtpWs20gskQWPD3PbVA+V4fSkRXL1iF8eZcGHR6FOUWoLGrBctmzMfCafMUjzcS5B6Azln+gxFZ/loQ1l2kpqYGc+fOxYIFC/zWYLdt2zbsvmvXroUkSVi7di0effRRWCwWPzEtLS2FxWIJ2m/z5s3YvHmz7+fu7u5whkqMIbRKz4gkYEppDTh3XJqi+KemGVAyOQdtzbYgV3RXRz9OHG1Fdm4qMlKNcDjcqK/uwoKlxcOORenBIHB7LBuhj2bUKnIQjavzuOUMLB3NABhSjCb02QfQ0NGseqnEKxdGLv6hRNTbi3VCVh4EgWFCVp6mPVnlHoDOWf7N4FyKa+5sWAL72GOPRXXwnTt3ori4GDabDbfccgueeuopAP5fnlKXjo0bN2Ljxo2+n8vKyqIaA5G8qC0U0QRMKa0Bc56nKP4mkx7FpTkoLs0JsiwHB1yYNDUXPd2D6O9zQKfXYdLUXNgHXZAkHvKaInkwSPSo20RA7SIHkbibGzqaUd/RhLSUVHTaeiByEQ0dTbB0tCiOIZpgqmjEP5SIeudM4hyHao5jVtFUVapJySH3AAQAu08eQGdfD/Kzx6EzTMtfK8IS2FWrVkV1cO/aa2ZmJr71rW/hj3/8I0pKSlBfX+/7jMViwbJly6I6PkGoKRSRBkyFWgNuaujFxJIs1JwOnfIy1LJ0u0W43RLG52f4Rf4KAkNP96CiyzuaB4NEjrpNBLQochCJu7k4rwDLZy/CxLwJvm2NHa0oyssPeXwtSiUqnUfiEr6sPY6ZE6f4zuNdbz5YXYljDacx4BhE6fiJmqzBHrecwYDDjrbeTmSkpPvyYxs7W8AAmAxG9A32wxKG5a8VYQnszp078T//8z+ora2F2+32VXIaKpSB9Pf3QxRFmM1muN1uvP322zjvvPNw0UUXYdOmTfjGN76B1tZW7Ny5E88//7xqF0SMLdQSimgCpoZbAx53tixhuOIf6PIWBM84hnN5jySSWsmtnCxt36JFbbGKdF2w3doJQRDQ0t3h26bT6dBh61LcJ1Z5o97zHKo+hsqG0xiwD6LkrIiuXrAKA/ZBvPLvv2Bu6Qz02wdwy8rrkJaSOvyBI8D7AOQpYlGNeaWzsL/qCLLSMlHX0Yg0Yyq6bL0QJQn1nU2wdDYnrsDecccd+M1vfoOKigpfms5wtLa2Yv369ZAkCaIo4sILL8RDDz2E1NRUbN++HbNmzQJjDE899RRFEBMjZqTpGdEETA0VRG9BfUEnQHR7BNFg0Eck/tG4vNWOpE62tm/RorZYDbcuGOg+jiYwKlZ5o+dEdCvKSmai3zGAW1Zei7SUVDDGcLKpGpLEkZWWCdtAP042Vasubl7rta7dggnmXNS1W2DUT0GaKRXLZy3CxNxzln5jVwuK8wpUPX+4hHVHmjBhAtasWRPRgadOnYpDhw7JvvfEE0/giSeeiOh4BKEl0QRMCQJDUWkWDn1hgX3QDQ5PJcKUVD0qlpwLSopE/CN1easdST3aG66rhZpi5bVeQ60LBrqPo1kbDWcfNdKOzomohKz0DNgG+3wiGqv6wW29HWjpaUdXXw+y07PQ09+L1t4O9Dn6kZeZg5aedt9ndYIO7VZly19LwvrL+9GPfoQHHngAq1ev9osiXrkyuDIHQYxGRhQwxRnAAMa5p88dj95iiNTlrWYkdTK0fYvGtd0/OIhdx/fjwjmLkJ7qcWWOpMhBIF7rVWldUO2WbKFEVI20o1AiqsU6sNz1rCxbhrr2RiyYWgaTwQiHy4nuvl7csvI62blLyH6wXj7++GO8/vrrOHjwoF8lp3DSdAhitBCp9ShJHI31vSialAWdTvArR9jU0IuCiVlRC1K4Vq+akdSjpe2bHNG4tr37/HPv5/i0ag/aagfxlWVLVXeHN3Q0oa6jESa9EUfqTmJcZo7fuqDa0cpKIqqWkIcSUS3WgeWu50RjFSSJw2Tw/K6aDEaIoqSJO3okhPXX8t5776GqqsrPeiWIZCNS6zFQkLxBSYIQW0FSK5J6tLR9kyMa13ZLkxXHKhtxqvM0phWW4lTnaRRWFoXcJxpKxhVi+axFGHQ6cPBsOkuK0YjivALVXaqhRFQtIQ8lomqvAytdz2hpBBDWX39ZWRkcDgcJLDEmCNd6TBRBUiuSerQWoIjGte3dp93ZAjCOdFMa+ux9aHe2oLE+XVV3eFtvJ0TJU37QZDDiYPVRLJu5wLMuqLJLVUlEhxPySNZmQ4momq71UNczWhoBhCWwoihi3rx5uPjii/1E9ne/+51mAyOIRCfRBEmNQveJVIAi3Jv+UE+C3eXAlw1HMb+kHCkGk6Inwe0W0Tc4gJNtp5CTngMAyEnPwcm2U8hPLVTV+7B6wSqMy8yFThBQPK4Alo4WLJtRgUXT5+HDg5+oZomNZG30UE0lXv1kK1IMRlwwpOG6HGqLaDTXk2pKSTgxlSOs36ANGzZQrWBiVKJ1PmciCZIaJFIBinADcoZ6Eqrba/Gl5SgyUzIwY/x0RU+CXq9DY68FTpcL+gwdJC5Br9PB4XKh0WqBXq9e/2u704GDNZXIzx4HgQnIzx6HgzWVmFs6U1VLLNq10UGHHX/b/xGsg/342/6PUDFlblw70HgZScDUqOqm841vfEPrcRCEqsQqnzORBElN4t32LZKAHK8n4VhlIw43HMPE7EIcbjiGHGECyuYWyX4fgsAgZLjgaBDR0tMOnY5BFDmcdhFChkvV73A4oVCrJZtXRGvbGlHT2oAp+SUw6g3Dro3uOXkANa0WlI4rRE2rBYdqKoe1YmPBSNZZR0U3ne9973v4wQ9+gMmTJwe9J4oitm7dCrfbjRtvvFGr8RFEVMQ6nzPegqQ28bYAIg3IKZhoxpGG43C6XIBeB6fLBdFsRcHEOYr73HTZlVg15wI0NvTA6fSsmxeVZPv9fsSzXd1wBIqIV0R3nziAL2uOY/HUebhg9sKQa6Ne6zXNlIJUUwrSTCkJY8VGa92rnfY0EkLeEa699lrcfvvtGBwcxOLFizFhwgQ4HA6cOnUKR44cwYYNG/CjH/0oVmMliLBIhnzOeBNPCyCayFq704E6aw0WnjcDep0ObjEXddYa2J0VISxfAUUlOSgsylb0PsSrXd1wKImI3enAPw5+jD77AP5x8GMsnFYeUlwOnW24XpxXCM45cjOyUd3akBBWbLRrvWqnPY2EkHUPL7nkEl8O7LJly2AymZCfn4977rkHhw8fxmOPPUZlDomEwxv0MjSyF/CIrNMpwu0W4zSykSNJHE6nG5Ik34VKDQJv3oMOu2bnkiOUS3W4fcAkHLOcApg07D5evN6HQHFVax4YYxAEIeg1EoEdKiJuUfRdp0cw/d29gdf00ZHdvmvZV3UUEpdgHbSh09YN66ANkiRhf1Vl0DlHA0oPZ7H+HfYSlk9rypQpmDJlitZjIQhVSJT0GTWJZY3geFsAw7lU5dy2oQrQR0u850EJJRGZPKF4WHdvoEU+vaBU1pszLb80ptekFrHqKBQuybNoRBBnSbT0GTWI1ZpyrGrJhmI4l6qc2zZUAfpoSIR5UEJJRN79fHtId6+cW/nKhRePinzScEm0AhQksERSkkzpM7FcU04ECyDU2pvS2mOoAvTRkAjzoISSiOw9/aXP3evF6+69YPYiRYt8tIqpHIlWgIIElkhKkil9JpY1ghPNAggk2kpFkTKSedA6AltJRD448DFq2i1B26fllya0Ra4msSqCES5h/VU6nU68/fbbqKmpgdvt9m3/n//5H80GRhBqEKv0GS0LWsRyTTnRLIChxLKLy0jmIVSxfTWEV0lE1iy6RHHMB6srE9YiT2bCuvOsX78ejDEsWbIEOt3oCxAhCK2IRfDR0DXldLMJOoFBlDj6reqvKSeaBTCUWHZxiXYevL1f++0Dw/Z8VZtQY050z0SyEpbAVldX49ixY1qPhSBGHbEKPsovzERHWx9OHG2Fw+GGyaTH7PJ85BeOnTQ5r0jUtTWhurUeU/NLYdDrR9zFRU2Xrrf3a0NnCzjnI+75qtbYEtkzkcyEJbCLFi1CXV0dJk2apPV4CGLUEMvgo9ZmG3q77Zg+e7zPgu3ttqO12aZJZapExCsSB6qOwjrYh+WzFvqCdEZieUdS6D4UXuu1q68H+Vl56Orr8Vmx0ab8qGX1JrJnIpkJKbCXX345GGMYGBhAeXk5Fi5c6NdNhxquE2OZWAUfyQm5Hh7X8ViqTMUY8xXOn5pf4iuYPxLLTs1C98ctZ2DpaAbAkGI0oc8+gIaOZhysqURl/SmY0zJwuPY4Jk8oCcuKjWXJv3iXxkxWQv71P/LII7EaB0GMOmIVfBTLKOJER+3iD3KVj8KxYuUEqaGjGfUdTTAaDPiy9gTGmbPR0NGEvScPIcVoQmtvB05YqpBqSkWK3jTs2GNZ6CJRiuMnGyFLJa5atQqrVq3CkSNHfP/2viorR2cpLUJ9YlG+LxHxBh/Zeh1wuTzlF70FLYpKs1WzKocK+VBGc2WqaFC7DJ5SoftwjucVpKGlGIvzCrB89iKUl86EOS0d5aUzccGshdDrdHCKLuyvOgK9zoD9VUfgktwhA4xiWfIv3qUxk5mQAuvlhRdeCNr20ksvqT0WYpTBOUdzYy/276nHvt312L+nHs2NvbLBFImIGg8GBRPNmDZrHFxOET3dg3A5RdULWsRKyBOdaGoUh8Jb6D43Izuo8lEolASp3doJtyTiQHUljDojDlRXQuQSZkycjItmL8KFsxfj2mVX4MLZi3HR7EW4omJlzK41FEp1jYmRE9Kv9N577+Hdd99FQ0MD7r77bt92m81G6TpEzFvCqZVrqmZqTawKWiRTZapoUTvVZGihey9DKx8poeS6Xb1gFcabc2HQ6VGUW4DGrhYsmzEfc4pn4NV/b8WErDwIAsOErDwcqK5EWYny+nGs0mq8DwuRrg8T4RFSYEtLS3HRRRdh27ZtuPDCC33bzWYzLr30Us0HRyQusYygVTvXNNYPBmqQTJWpokXtVJNoCt2HKnYBAAeqK6ETdHjug1dw7fmrcaC6Ek63K+IiD7FKq/E+LES6PkyER0iBnT9/PubPn48NGzYgIyMjVmMiRgGxDLxRUxDDeTAAELaIxbLLDZB8jd0jQe1Uk2gK3Q/nunWLInYe34dDtceRm5mDC2cvwr6qo9DrdBFZo+Fcq1rN4L3rw0adEfurjmDpjAoqQKESYf2lXnfddUFfttlsxpIlS/Dd734XqanRdawgRi+xiqBV21Ie+mAgcUASJQg6wfdgYKnvRmuTLWyxHI3WcDITiehEI9ihXLecc/T0W/HZiX3ISsvEZyf2obx0JhZMLZNdbx3pw4JazeDl3NoLp80b0dgID2EJ7Lx582CxWHDLLbcAAF599VWUlpaipqYGd999N15++WVNB0kkHrFqCReupay0Phu4Xa/XQa8X0Nbah96uQbhFCXqdgKzcVLicbtRVdcGcnRKWWMbSTU6Eh1pFI7wECvZwrtsvTh9BXmY2phZMQnVLHdyiiNULVg0rpl22Hrz0ry24/dLrkZuZHda41MiRtTsdOFBdGdH6MBE+YUUR79q1C2+++SbWrVuHdevW4fXXX8fnn3+O5557Dvv379d6jESCEosI2uFSVHQ6QTaSWZIk2e2MAalpBtRXd4EJQEaGEUwA6qq6YLM6YM5OkRVLuUhjr/gPteC9+zmdItxuMWgfQjsCi0aokW4SmI7DGIMgCEEvxhiaulrx/v5/ojA337NmnpuP9/f/E01drb7xfXRkt+y4/nHgE3xw8BP848AnYY8rmsjfwDHEMlp5LBKWwHZ3d6O9vd33c3t7O1paWgAABoNBm5ERCY838GbhslIsvqAUC5eVorAoKyzXV7gpMsOlqLS12FB1sgNGkw7ZOakwmnSoOtmByi+bZbc3N/ZicMCFSVNzwTnQ3+cA50Dx5Cw4Bl3Q6cMXS8pPTSzkikaMhEjzQ1/859sej4igQ3NXG/SCDi63Gy/+820A8rmzgMd6/eDAx5hROBkfHPgYXbaesMYVTY5s4BiGury9L2oCoB5huYgffvhhVFRUYMWKFQCAnTt34he/+AX6+/tx9dVXazrAsYaWbc+0IpLAm2iCgpRSVCYUZOLA3oYgF216phHHj7RgRll+kDVaX9MN0S1hfH4G8san+9ZgAaCtuQ9OuwspqeceGkOJZazc5IQ/cuusSkUjRlr6UKmSktwYTjZVgYHjZGM1egf60GHtQpopFadbqkO6dP9x4BPYXU5gwAa7y4V/HPgEN6+6ZthxRdp6Tq7TDzUB0Jaw7orf+MY3cMUVV+Dzzz8HAPz6179GYWEhAOAXv/iFdqMbQ8Q6GjVeRBMUpJSi4nS6ZddndQKD0ylCFyBwBoMOfaITgk7wzbEgeITT5RIxPj8D/f1O6PRC2GJJ+amxRy64x1s0ojivMKhoxAWzF0UccTtcg3K5Mbz0n0+ib6AfL3y8Ba1d7cjPHY9vXnw9MtLS8WXtcVmx9lqvJoMRlq4WFOUW4IMDH2PNwlWKa7HR5sgqdfpJpvtLohF2vP+ECROwZMkSuN1uuFwu1NfXo7RUOV+MiIyxEI060qCgQEtZKZJZlDiMRh1Eifv9grtcIkwmHQqLs1BzujPI6iw7rwCMMVmx5JwDchWqzor/+PxM2O0upKQYoNeHtfJCRIGSJThc0YhII25DWYlziqfLjkGn06GqrR7tPR1o7G6BIDBUtdX7Pi8n1v848AkGnU70O/pgTklHp60Laca0kFZsNFZnqE4/FMykHWEJ7DPPPIOHH34Yubm5EATPzYMxhlOnTmk6uLHCWIlGVTt3VrERuc2JOfMK0NtthyDjui2YaPZ1ogkUUsZYkKXMOYdY+SF4X1fwINJz0J5zARrre5Pa85AoKLltQxWNiCbiNqSVaIHsGLwi1tnXg/zsceg8K2IOl0NRrKtb62EbtKKzrwdpxlQMOAeRlyGhtr1BcWzRpBcpdfqhghLaEtbd7KmnnkJlZSUmTpyo9XjGJGOlW4oWubNKjcjLzitAW0ufooiGqooUtKbMOXhfF1jmBGDofY0DzfXtqGvvQGZWeKk9nsMpW8MkysqEctuGKhpxsLoy4q40Slai3enAq//eKjsGrwuWATAZjOgb7IeloxkS54qFJu5feyfGZ+YiJ8MMk8EIh8uJ7j4rbr34uhHMVDDeTj9pKanotPVA5CIaOppg6WghgdWQsO7axcXFJK4aEquiDfFGi6AgpUbkbS19w5YWVArOUgw0YwBj59y/oiSisUNAxhwTdDoBbpcInU4I6XkIZQ2zjFzo5q4mkVVguOAexljQWutwa6lKKFmJJxqrFMfQ0NGEuo5GpBlT0WXrhShJqO9swvmzFmDtkstkz3GwuhIcHCln+2ynmEyQbBJONlUPK3yRrCt7O/1MzJvg29bY0YqivPyQ+xEjIyyBnT9/PtatW4frrrvOr+H617/+dc0GNpYYS9GoagYFhWpEbqnvwYT8DAgCg0EvAODgEg9pJSoFmuUXZPid0y0Ceh3gFgGnG3DbHOhs64coStDpBIybkAEwyHseQljD3NbmsWxJYGUJJ7gncK012ojb4cZQ19aE6tZ6TM0vhUGvR7u1EyXjCrF81iJMzD0nWo1dLSgZV+hbWovmmpSIZF253doJQRDQ0t3h26bT6dBhk1n2IFQjLIG12WzIy8vDv//9b982xhgJrIqMlWhUNYvWK7nW9XodbKcOwS7uQqC+hbISlQLNOOcYx4HWThGNrRxukUOvYygcDww4GHrqe2DOTEFKqgGiW4KloQd549J9noehFrHvrAHWMIcU1RyMJYYL7pFba1W7K413DAeqjsI62Iflsxb6rOcPD37iEbGeczUDdIIO7VZlEYs2TSbSdWVKx4kPYQnsiy++qPU4xjxjrVtKqNzZcHOBlV3rbhjEfhiyxoPphuwfwkocLtDM1c1Q1ysiI50hLZXB5eaosUjotzOwVICfO4XvB0+/XH+LuKg0C+O4v/FKhMdwwT3HLWcw4LCjrbcDGSkZOG45E5awRFq/2O50YO/pQxh0DGLv6UOYWzozrDKK0VyTEpHm6KrdKIEIj7DyCRobG3HTTTdh5UpPweqjR4/i2Wef1XRgYxWv8CSzuCoRaQN3pSpPfVYHJuZJEHQMjAm+VyhVC1n20CHCYs1EhmCD3mkFH+iF3mlFKvrg4CYUFmdBdEvo63NCdEsoKs1GWroRjQ09QdWkqk91oLVn7H23WuO16BwuJ040VsPhcmJ/1RHYnQ4IggCHy4lPKvfC4XL6Sht6UaqwpIQ3mKm+oxmNnS1hlVHU4lqVKjlFej2EdoQlsN/85jexfv16WK1WAMCcOXPwzDPPaDowYuzhddEGljdsabIq7iNXD3nqzHHIz/aIsiRxOF182JKMocoe6vQCUDAHpjkroJt57pVadhFY9kRkZJgwddZ4zJg9HlNnjUem2QS9QYcWizXIIs4wm9DUKUASOTiXfC8EDC/cUpLJTKjavYF4rdeqllrYnQ5UtdSi3z7oExkl0Ym0HKJSPqkadY/DJdS6cqTXQ2hLWALb1dWFG264wfckptPpoNeP/rQRInEYzkWrJDSy9ZDPrlu3dIo4cNyFA8edOHDchZZOUTY7Bghd87hkcg6MJj3cbsnnamOMQZK4r/qT6Bah1wsQ3Z59CiZmwi1KMhaxHi5dOly97eDWtnMvWxtYRi44EJEVn8xEYom19XagtacdtW2NqO9oQm1bI9p6O9Bu7QwpOl5hrmmtx4DDPuy5AvNJAebLJ/XSZevBr/76h2FrCkdLqPrB0TYBCEUkDzqEP2GpZEpKCmw2m09gKysrkZISfvWP73znO/jd734Ht9uNjz/+GGvXrsW0adMAANOnT8eWLVuiGDqRTIw0F3jomi6XOFp7GGq6/ddMqxsk8ByGYoVjhAo0EwQmG+WtVP1pQkGmX1/ZoddpmjwPKUuKg5cBGBsTFb2GorT+GWkQz8qyZTjTVIfWvHZkpmYgKy0dE3PysWLOUsX1ykC38rzS2cOeK5x80nc/347X/v1X5GZk4favfE3dCUN0ObojqdakRt/ZsUpYArtp0yasXr0a9fX1WL9+PT7//HP8+c9/DusEn376Kfr7+/22LVu2DDt27Ih8tETSomYusMSBxj7vminAnZ5f9AwBaO7LxEQOyB0tVKBZKPGVq/4EIGTqVWDXHmDsVPQaitLNO1QQjxwnGqvQ2NWCnoE+dNm6wcFh6WrBl7XHcLT+lGJhiAGHHXXtFozPykVduwVG/ZSQ5xoun7TL1oO3Pvs7dDo93vrs71i39PKw+rtGwnA5uhLnOFRzHLOKpo4oJQlQr+/sWCUsgV21ahX+9re/4bPPPgPnHL///e/98mGVcDgceOihh7B161a8+uqrIx4skbyomQssihKkCWUwZfvfCHQA7D12X75qqLEEWssRV39C5KlXY6Wilxelm3c0xSEaOppR3dqA1t4OmPRGtPZ2QC/osOfUQaQYUmTXK71u5XZrF+wuB1IMJmSlZfql8ARa2MPlk777+Xa09XahOC8fls5WvPv5dk2sWDm8ruOD1ZU41nAaA45BlI6fOKLWc5E+6BD+hP3XmpOTg6uuusr3c2lpKerr60Pu8/Of/xx33nknxo8f77d9//79qKiogNlsxsMPP4zVq1dHOGwiGVErF9hrDbvdkuqVsSJpzRdp6tVYqejlRenmHU1xiOK8AkzJL0Z2RibyMnPQaetGdpoZekGnmAe7smwZ6tqbkJWWiSP1pzCvdCayM7KwYs5SvzEOtbBDpeJ4rVdzWjqMBiPMaemaWbFyrF6wCgP2Qbzy779gbukM9NsHcMvK65CWkhrV8aKtgkWcI+rH4eGCLg4fPoy9e/di06ZNftsXLlyIuro6mM1mHDp0CF/96lexe/duTJo0ye9zmzdvxubNm30/d3d3RztUYpSgVi5wolXGCleUE23cWhLq5h1NcQhLZzMaOpuRZkxFd5/V427vasHy2YtClim0Ox2o72hCflYe6juaYDKYcKKxym+NNtDCVkq78VivnSjJK4QkSchKzUR9Z3PMrFjGGE42VUOSOLLSMmEb6A+r5KISalfBGotELbDD5Xbt2rULx44dw5QpUwAAoihi8uTJOHjwIHJycgAAFRUVWL58OQ4dOhQksBs3bsTGjRt9P5eVlUU7VGKUEYmVqMRorYw1WscdKaFu3tEUbIi2TGFLTzu6+nqQnZ6Fnv5etJ6NPB46xnDdo3tPfwnOOTps54wBzjk+P304JgKrtsWpdhWssUjIu9hrr70mu51zjoGBgZAHvvfee3HvvfeeO5Fej9raWjQ3N4NzDsYYLBYL9u7di1/+8pdRDJ0glBmtlbFG67gjJdTNO5qqQ229nRGXKfS4iBuxYGrZkE42vVgxZ+mwYiUX/bx28aUoK50edJ7p+R7jIVTFqEgbwsuhtsVJ5RVHTkiB3b59u+J7a9eujeqEb7/9Np599lkYDAYAwOOPP44ZM2ZEdSyCGA41rOF4MFrHHS5q37yjOd6JxipIEofJ4AkqMxmMEEUJJxqrACCkWMlFP69ZdEnIMYRKd4kmFSZQlNW2OKm84sgJ+ResZg1it9sNALjvvvtw3333qXZcgiBGH2rfvKOzepUFiXOu+F6otVmlMYRKd4k2FSaSACwiPiTvIzJBxBlqrB47opnr4QRJzQbuodZzo0mFiTQAi4gPJLAEoQHUWD12RDvXw1m9cu9FE0gUah8AUQUmUX7q6CCsWsQEQUTIkMbqzDzklTnBIwRjsLZwpIRdAzeGcx0qkCiafaI53nDddIjEIWwLtqmpCbW1tb61VAC+9nUEQShAjdWjJuLAnxjMdTSBRNGu9SpB+amjh7AE9uGHH8YLL7yAOXPmQKfzVJNhjGHbtm2aDo4giLGJty1cv30Qu08eSJjqQdEEEkW71qsE5aeOHsIS2DfffBNVVVVIS0vTejwEQRC+puYNnc3gXEoY6yyaaOVo1npDQdHCo4ew1mAnT55M/V8JIho4QjZWjzeJ2Njda7129vUgP3scOsNtap7gcx2KSHquMsYgCELQiwQ28QhLNYuLi7F8+XJcddVVfl10fvzjH2s2MIIY1TDmaaBuawt+KyMXiPPNkHOOliYrLHU9vuYCxZOyfe334onXemXwFH/oG+yH5WxTc1krVsO5VqPCUjio2XM1VmMmhicsgZ08eTImT54MAHC5XFqOhyCSAsYYdHNXJ2webCI3dm/oaEJdRyPSjKnosvVClCTUdzbB0tksKz5aznUsmo0PV4QiUrGkBumJQ1gC+9Of/lTrcRBjDEnicau1G6sCEIwxWeuJcw4uyUS4xkh4E72xu7dwf15mDk411WDmxCnosHWhOK8AgLzoKM31SIhVs/HhilBEIpbUID2xCEtgKysrceedd6K1tRU1NTX48ssv8fbbb+PnP/+51uMjkox4uybjXQCCcw730Q/A+4IjPllGHvTlV2o+D4ne2N1buH9/1RHsOrEftsE+TC0o9RXuj5WFFotiDuEUoYhELKkARWIRVpDTPffcg9/85jfIzs4GAMyfPx/vvPOOluMikhSva9Jo0iE7JxVGkw5VJzvQ0mSNzQDiXACCSxKk07vAW04FvaTTu+QtW5UZ2th9KInS2H31glW4bdV6GPUGFOcWwKg34LZV63FFxcogC02r4gqxKuYQThGKzNR0uEUxZPGJWI6ZCJ+wBNZut2Pp0qV+27zdcAgiXIZzTcY0kvVsUQLvCxoYjV5XsN9LFAFnH5BmBkvL8b2QZgac/TGp8ORt7G7rdfhE1tvYvag0O+7t8RhjOFx3HLVtjSgdPxG1bY04XHccjLGIRSdaoqmwFA1Dc1q9LyYwWDqbIxbLWI2ZCJ+w/EBmsxnNzc0+19U///lPX9N0ggiXRHdNRoPSei4HIB3bFuSKliQRUk8LWHaJn5BxHltRS+TG7oMOO/62/yOkmVKQakpBmikFf9v/EWYVTVO1oXgoRlLMIZLAJKWc1kM1lWjsbI2oWhMVoEg8wrqbPf3001i/fj3OnDmDhQsXwmazYevWrRoPjUg2hromvRYskDiuyUgJtZ6L9GyfK9rPOhbdgNuBeCdpJnJj90M1lahpbUBxXiE458jNyEZ1awP++vl2uEUREpfwZe1xzJw4RbMSgSMp5hDJGrFSEYq23s6IxZIKUCQeYQnsvHnz8Omnn+LkyZPgnGP27NlUeIKIGK9r0pse4hVbW68D02aNi+0NngfUqo1G74as5/qJKAfE3mag+QS4cMrvBsclERi0evYd6flVIBEbu++rOgqJS+js60FrTwfys8dBkiR8cfpLzJs8G4eqj6Gy4TQG7IMoGT9REwst2n61akXxRiOW1CA98Yio2H9nZyfcbjfa2jxPVZdeeqlmAyOSE68Lsr66C10DA0hLM8TWNalFUQKlIvPOfiC3GMA5y5xLnmYZfKAHEhsaAsHBjGlxL0CRCEwvKIUgMDS0N6OtpwPjMnOwYGoZpk4owcqyZXjl31tRVjIT/Y4B3LLyWqSlpGo2lkjzUNWK4iWxTA7CEtgHHngAb731FmbPng1B8NwUGGMksAlOPHNNleCco6OtD3U1XbDb3UhJ0SMtw4j8wsyY3FBiXwAi8JgMEHSAvQ8I/E7M+SSwAK5ceDEG7IN45d9/Qfmkmei3D+CWldchLSUVB6srIUkSstIzYBvsw8mmas1TdcJ190bTK5ZIbsIS2Pfeew+nT5+G0Wgc/sNE3Il3rmkoKr9sxsHPLcjOTUVWdiocDjcOfm4BAMxbUKTaeYYtJhGreeAAZ+dcwQwAN6ZBmLcagk7v/zlbuxbBzKMOxhhONlVDkjiy0jJhG+jHyaZqzCmeHlMBi9TdS23kiEDCEtjZs2djcHCQBDbBUBKR5iYrqk91JlwZPLdbwvEjLcjOTYXJ5PnVM5n0yM5NxYmjrZgzrxB6fViZYyGJeTEJ2fVcBpjSwQd7/cVckgBDylmhpz6xcihZgnaXI6YCFqm7l6J4iUDCEthNmzZh6dKlWLx4sV+x/xdeeEGzgRGhURIRSQLqG83ImFKRcGXw7HYXnE4RWdn+a2Ymkx7WXjvsdhcyMkwKe0dAiOAjbmvzPJSoIbCMAek5kKwtwW9l5ACFZRAyx/uNgYsSxLbT4Kc/gyQMEVjOAS6Bcz7mrVglS/BA1RHodPqYCFg07l6K4iUCCUtg77jjDlx99dWoqKjwrcEScUZBREQnh6u/C5kG/+8pEXJNU1IMMBp1cDjcPgsWgO/nlJTIi5fIWfGeakhcOfhIRdiQ/wa+wzJywfs6/Dd7KzWlmQE29HsQge7GqApNxKq2cqxQsgSnT5iMKypWBn1ei2uMxt1LgUlEIGHdaQ0GA5566imtx0JEQ4CI6PUiDDpvbum5rzcRck31egFz5hX41mBNJj0cDjd6ugaxYGlxxO5hJSuecwm85TiEzAnaLrVyDt7fDWbOl7WUhSU3Bt1wJbcbUt0+MAgAGyKKUnQDjXdtZS0IZQkOdy1qtWojdy+hBmEJ7JVXXol33nkH1157LVmwCY4gMBSNk1BndSAzi8U311SGufMLAQAnjrbC2muHyaTHgqXFvu0RoeQKliTwuv2IWXKpgqXMGAML+HthOh1YSvDaLOcczJQGDkTWaSdW7vAYMhJLUK1GAOTuJdQg7DVYURQhCAIEQfDcDBiD0+nUenxEFORnc+hKxqGpoTfhyuAJgoB5C4owZ14h7HYXUlIMIw9sChQ4b9Qu91iz594Y2WnUgDEGobAMyBzvP2YugVvbIR3fBqm/J3i/4azRGLjDEx01W7WRu5dQg7AElpqsJzAyEayMAYUTzSiYmJVwebBe9HpBnYAmWRhgTAds7eABN0mWkevR2Tj2YwWYx0Xst8XzM+/rgmAuSBprNJYct5zBgMOOtt4OZKRkUHoMEXcSq0YaET5hVCQSWOKVwYsFjDGwwjnQLbkxyEWrVIQfiG7NknPucUkz/4ccOffi2cGF/N54X5dq1mi8G7vHEq/16nA5caKxGvNKZ1ORByLuhLz7GgwGMMb8bhben8lFHF9iX5EogYmkrrCKa5YcAO9uAK/bF/ymOR8cwfHFob43zjn4F2+EdW65wQydAy5x8ObjEL94I+h6WEYuhLIr5NOBRunvjtd6rWu3YHxWLuraLTDqp5AVS8SVkAJLruHEJqYViRIRBWuQcw7e3QBx3xsIkrj0bESTwiObCiNJYNklQPGCILFGf4diPqvi9xZNs3XFOZA8UcqZE8CGLg9wgNtaIVZ+AESz1pugtPV2oLWnHV19vchON6On34q23g6K+iXiytjzHxJJg5I1yCUJ4r43wDKD02ckawtYhKUcQqUDice2g+WW+rmiPcUixOiLRkRgkQ87B4JMxSiefGu9K8uWoa69CRVT5sJkMMLhcqK7vxcr5iyN99CIMUzYebBe17D3pdPpyEU8CpEkSd5SOhshHk9CNS9XcmcqH8vztpyVyj25MAGfP1ucQuFgcm5lLroBuxVIzQLTDZk7iQM9lsiLRkTZ6UfZkzGMSKq41hvvpYoTjVWQJAkmowEAh8logGgVcaKxilzERNyIOIrY5XLhL3/5C06dOqXZoAhtkCQJrg+eAKytwW+a82G48sG4iayylehx9wq5JQh29+Z4iuf3dwceDLz5OLg5uNAE5wBajkFqFRBovjEMU6owQJB8H2TwiwrmTAx1qYokxrp6ZIFRiVLoggpDEIlIxC5ig8GAG264ARdeeCEeeeQRLcZEaIUkecQ1u8jf4uEc6Gn0vC8jsFpYKEGt9EIWjdgHlC70jwg+6+4FWFAlJS5J4LVfgHMRnA8t5iCBcwmMyxUMYACPVgh4QNRw9Am3qq+rR+Bu5pxDaj4G/sXr/g8SCCGWCVLoggpDEIlIWAL72Wef+f4tSRL27duH/v5+zQZFaAxjENi5kokSlC0utS0UpVZ6+QUZZw+qUDQilDsz4D0JEnhvC6RTu4LyYCG5gYI5ELLzZQs9RHZDZoDeCAz2gGNoCUoOxLt5ejjpQEHiywHHAFjmhKCHmWHFUsVCF9E80MW6MIRaJRmJ5CYsgX344YfP7aDXY8qUKXjrrbc0GxSRQKhsobQ0WVF1siOolR7nHOOjGh6XX0/lHDxo9ZZ71mXPBv4EWmnDXkeQIDHPNgngzN+CZXEuGxUyHQgAjm0LFl/OPQU64thKL1FczsOhVklGIrkJS2A/+ugjrcdBxBlvUYLA9Tef200FC0WSOBpqu5FhNkKv95Tc1OsFZJiNsNT1II8BkbQi4JwDzSfAW0/533S5BDBAmHEhdDrDkM9L4L3tUPaTyq8/ckDeGpQ4YEw5K9ZDb/psJF5i+ZFFadXJPTQwAEwh8ph/8UZ8BSxBXM6hULMkI5HchBTY1157DTabDd/+9rf9tv/ud7+D2WzGTTfdpOngiNBEvTbKuZ9bmEscvLcF4r43/XqUAjiXN6oCLpcbzvojSNH1+zmlBQAOdxpcJRw6pTVDpbrCzn4gp9jPFcwlCXA7z7oNA63Us7vKFGYItf4oV5iBSxI4OISsCSq4m5XRwqpTFN9oxxxJsY9wSODaypE2YifGLiEF9le/+hV27NgRtP2mm27CV77yFRLYOBLVTVcQAHO+J6DJ/2CAwegpSqALDiSKNG9UCZ3AoOs4DaeOY2jXPLcI6CUGQ9lM2aIRMOcDfe0IjO9lGbngpnTwQav/tUoSoDdBNk2FASxdxhrlHOAMLDNfpjBDm8fqkwkAEwQhOndzJMTaqotELKNMLRqtRNOInRi7DFvJKTs7O2i72WymHNh4E8VNVxAEGK58MCgPlksSxP1vQtAJylaDChaKwICJaR2osU+B2SBBr+Nwiwx9bgFTUmugn/ufEHTBTmKlPFjOOcSBnqDONJIoQnLYwMBkrF4GXVnww4fPPSpXmCEk3P8c8Fra3FenOIhoA3K0tuqiEMvESC2KHdE0YifGLiEF1mazwel0wmg0+m13OByw2WyaDmy0EvOk+whvuoIgBKXicEmCFGiBDTmBmhZKftogkDmIlt5U9DsZjDqOKeMHkS8OQq5/qmcECkiSZ3wBFiQTuKfnqq0NkHH3MiFwzfQccmKpVLjfl9bSHJxTCy4ClR8CAz3B16NysI5aQh6tWGpSslNtl7NKUL4tEQkhBfbqq6/GnXfeiWeffRYZGZ40ir6+PmzcuBFXX311TAY4mhgtEZCRwBjzrD/KjTuKhwbGgIIsFwqyJLhFBr2OAxCB7nOBVhGfJ+BmzODpuapbHNxNJ1TBBN58HLzlpN/73ihlxQIUXO54DJwz8L5uCFnB5RrVdOtyzj3dgQKLbSC637m417dOcJcz5dsSkRBSYP/v//2/+Na3voWJEydi+vTpYIzhzJkzWLduHR5//PFYjXH0MAoiIEOiYDUoWZYjOREDh0HHz/7kcadKx7dBGugN+rSiUIS8GeeB6XTh3/g49wRMZRf55856i3Ao3FRZ4Rwwc3DzdKm3zfNVq+nWlf1+zv7OmbUV8liR6C5nasROREJIgU1LS8Orr76KmpoaVFZWgnOO8vJyTJkyJaKTfOc738Hvfvc7uN1uAMCDDz6Id955B4Ig4LHHHsP1118f/RUkIrGMgFTDlRYrq4ExT57lgDV4mMa0sxZf+AXoVb0ZMwaY0oICpjjnYCblohHeSOWgyGM178HDfT/93QkddRspcbeiCUIlwsqDnTJlSsSi6uXTTz/1q/q0bds27NmzBydOnEBrayvOP/98rF69GpmZmVEdf8yioigOJ1QAVGnczQQBwowLwfuC16tYeg7YQE/EQqHWzZgxj1s5MGCKcwmwqZdyE+3YQvWQFaPtIUsQhKZo2q7O4XDgoYcewtatW/Hqq68CAN555x3cfvvt0Ov1KCoqwkUXXYRt27Zhw4YNWg4l6VDblaYkVJxzuI9+IC+KGXnQl18Z9rkYY9CXX6mqUKgZVMY5PMUjhlRl8hx/uB1DeBFUCtZRtYcsQRAxQVOB/fnPf44777wT48efK4JnsVj8xLS0tBQWiyVo382bN2Pz5s2+n7u7g4M4EpYYRUDGwpXGJQnS6V1B0bjA2QjbsivAZFJrIm6LF4VQcM4hHv1ANqgM6TnK67YycyZJEsTKbYAok36mM0K35Ebo5AKmQqwBAwCX6VykSbBOgkbdEsRYRjOBPXz4MPbu3YtNmzYFvRcUpSnDxo0bsXHjRt/PZWVl6g9SbUbgtk2EnpqyeIN/corAhhQy5BCBbvngH0mS4PrH48pt8db8t0JbvLPlGllwII/s0CQJ4pmd4PBPk+FcArrrwfu6/YtGIETAFOeA23G2SL/fkADngGKQU6h6v2Llh2frIWtIgkfdEsRYRjOB3bVrF44dO+ZbuxVFEZMnT8aaNWtQX1/v+5zFYsGyZcu0GkZMidZtOzrSe1jAg1GIhwVRhNTwJWBMRZBa9baAi2JwLi4AqasBqN0XfEBzvnyxCW/3l+xiPyGVRAm8qRLIGAc2tGTUMAFTLKsAyCn27zTERaDbEnkOqCQB/d0QzOEHbUVDokfdEsRYRjOBvffee3HvvfeeO5Fej9raWmzfvh2bNm3CN77xDbS2tmLnzp14/vnntRpGzInKbTva03sC8VqDGeP8LFVJkjyFF+SsQQAspwSsdKHMHLSHKNbo6ZoztJyjz2qMMmBqqCgxjNANH4PoXoq6JYjERNM1WDkuv/xybN++HbNmzQJjDE899RRFEHtJ5FQLDhnXbTgMtVSHFzgmBJRr5JKieHDOIXU3A/29EIeuEUsiMNAbySCjRsm171n6UC6jSBBE8hMzgfXmwALAE088gSeeeCJWpx5zqLqe68sP7Qkoth86PzQWcEkC+toBU6a/1StxwNEHLkUhZAGdhmTn0feWsmufp2WBNx0DZzoExhwwiMqVoQiCSBpibsES2qL2ei4TBOimX6QYqQsE58ieC1zjkKShjem0sNwYzprX/psAcC5Cks492Hla3imMQanTEODZLheUFcK1L/U2A45+sJxiv4cQFqIyFEEQyQUJbCKhRqoF55BsnWCZ44Nv+rZ26CJcz2WMQSeTu+qtgSuXuyqlZHnWYJtPBh/QaPIvRRg0/vDngAkCkDEOMKR5WvV4EUXA1gleuR2SLkAYFQKmlDoNnX1TIerZOxAF174xHZCpDAVjOq2ZEsQYgAQ2EYgy1ULOFSyJIqSmY2BCsGsyZNH6kMOTCaKRJPD+blnrjfW2AsXz4SvGO+RNBsiLVbTpJgyAwP2vVQBgMIKVXQGmH/IrzgH0dyhev1ynoWhhjAGFc8A0bsZOEETiQgKbAESTaqHkCuaSBN5eBUxeBMaGfr3KeasjG3yw9cYYoCuaC2YOFhelsoNRzYEkAbYOwJTubxWLEjDQDV79Gbju3Bxosf7pfXDx3yaBc0BQqFNM1itBjA1IYBOEiFMtFNb/uFv0uGcjyFvVCjlx0Sy0hwf8IHHAZAYMQ37FJQ70WlR7yBja4i7oPUkELywDU6nCUsIWIiEIQhES2NFOgAUJdjaoaJSVzosmOMuzBpvnWdMMXIPtbgBajgdYsBK4c0A50CkaGD+bdxvoJ+dgGTmqVFgaHYVICIIIhAQ22WAM0JvAB3vBhaHuWY3SatQqdB91sQ3m+R8faq3D47Y1pgK6oWuwHBjoVs2CHa4Dj6LwRWp1JlshEoIYI5DAJhmMAUJ2AdiMC/2bpHMAfSoG1wwXlAREZ73JRuRy2XZ5XJI8xfmN4+FX0EJye352DoDpDP7H0ptUFiP5dVZ+1kWvaqP6RC5EQhBEECSwo50gK5EBpnSgrwOBHXBYRp5q4sIYg1B2hWJaC2NMlTVDzjmk5mPgX7weLGKpZkBnBBz9/kFOkgTojUDhHM/73lOfDfQidypBELGABHa0EsKCFKZdCGHO5cFC4hU+FfDmwYZcF5Sx3jhXsEYV3bZnC/pnTgiyyKXeZsBg9HS78RNYflZ4+8CEocX+OWDKiK2bPNJDyQQzcSm69CqCIOILCewoRSmtxSt80v63gvfJyAVTKyAminXBkME66TkeEVESKxn3KOcA3M6zLeaGhlJLgMEENu0CMP05FzHzNg6IlZs84obvCvPjjVbOnAAIoydwjSDGOmNGYJMxzSHSAhCaBMREsi4YUpRb5aNuvZWPZO037hHYjPH+KUnS2Wvs6/QPcgIgZCq7ySP9HVG9VZxS6pXEgZZj4LZWGbc/9XwliERlTAhstGkOiS7KSu5ET5pIfANiOOdB67Ohx8agKwv+HrgkgX/xhvJ862RcxJwDGeOgX3wjdAaD/+dDFO5wH/0AvK8z6D2WkQd9+ZWKIqu6wAWmXgkShMIy6BbfGOx2T5DfRYIgghkTAqu6OzMBcg+VBIFzDrScgJA5IcK6FWo+THCIxz4E+nsCziGBtxxXHJtS1K0nYCpUOlBAHurZ62CCEHYUL5ckSKd3BVmIvnGXXQGm08nsqS6hKkNFcj0EQcSfsSGwXlRzZ8Y/91BJEDjn4G1VYDNW+EXWhupDOiILX5KC+sRyiQN9XRDMBf5zJ0ngdfsVxyFLyHXObHDRCZgC0nQgAYM9keW7cg44+4GcIjCcE1J+NvKYS5J8kwIVLcihlaHUqiNNEET8GFsCGw2J4GqVa+gtSbKCIEkuwNYO6fSnkNhQi4uDQeEmHY2FD4B3N4DX7QsedOYEIKckeO68Qsy9gj/kYAqEWucU3W5Iu1+TdxFHne8qV2KSQzz+IaQBa/Cn1fRmeEU+u8hfzDkH77aAi2KwyJOLmCASFhLYBCaUZYnU7LNiGXiD9QgCOAvQFwYMV484gocJBkDILQFKFwaLsrXdE7Irt5cxHbC1BwlFqGAdpXVOQacDmzAVHLoggWUQ1XOncoD3dUPIKtTWm8HY2eb2/i3uJEkCBrog7nsLkhA8b/FeriAIQp6xJbCjrD5v6IbeLbK7MMbAU8xgMy6EbkiKijZt0jxrpkFlApn81DLGwArnQLdEnWAdxhh0E+cqliqM6lo5glze506orTdDqfQik9zgR21g5vFBucCJsFxBEIQ8Y0NgR5KvmAiiHOrGLicIidImTWbuvIFM6gXrMDAEpK5A8Liw5apMeedAJn8YxjTwwZ6Ajj8czKSUJqQFwd8dY2evhweOTHldnSCI+DMmBDaqfEWViwgMR8iUG1m87kR/QeB8BPV2FR4mlFJuFINuGMDSYzB3it8Rh9TVIJ/ek57jcaL3d/vvcbbKk5BTGjy89Jygz2tKwPfAJQ6ppwXs9KfgQypTadHfliAI9RgTAgtEnq+oehGBECg2Tw+R1sIEQDf9QplUGE/7NAYWdiBRyIeJ9ByIx7YBgQITsrqQfE6r71wq1kOWrWZ1NndWMOcHu9atLQAYWMB7jAMSAL2M+5pzDvGLN7T3Zih9D96Hm9QcMF1AScge9frbEgShLmNGYKNBkyICciittXrTWjiXEUsG3dzg4gfnagS3B93/lazHUA8TXnGRqy7Emyoh9bYEjYFl5J5dm9V+7pS+I8/2EK51mfcU3decx8SbofQ9SG43pLp9YAIH+NDev9RNhyASGRLYRCIorYWHjLqVEzEGgJVfGbHlrfgw4bWeAsYmwQ3eYwF39AePwZwPrlD5KBriXVErlt4Mue+B6XRgpgxgwBqcjmRMpwAngkhQSGATmGijbmNjeUvAoA1s4ryAyFYO9DR6hFmFQKbYVtSS7/Tjm+s4CZn394CZg6Ol1Y8MJwhCLUhgExz1o25VhjEIQwpaSBBDfjxia3QkFbVClleUCSRqOgb++euyLm+dihZ5NDAmHy1N1itBJC4ksIlEIqQEySBXEpFLkkfcuOQvVJyDqVyS0fOBCHJQQ0aA53miiAPe4xKH1N0Ab5rMkHfAIEGIUS1iWWIc0U4QhDqQwCYCKt9AQ1mJZz8gPwa5esOAbElESeRAXzt44zFIQ1rCcS6BOwfkG6jHqL7zcGum3rH4XY/bDanuC7C0HLAh1ZJ4AkTqxnINmCAI9SCBTQDUvIEO29QcCE65gbIFyQCwnBKgeIF/WovbDd5wADClB9fHHegOLUgaV0QCwliHDrxOb8AYg58rljOVXd5REs81YIIgooMENkFQ7QYaykq0toKDB3e5GaZtH285Bg6dn2BwUQS4CPR1gAUUP0CqWZUAJ/+BhF8EA0BMLLtEb2lIEER8IYFNViLMAVWEc8AxAJZd7Oc6ZaIEnjEe7MJbodMZh3xcArd2QFAQWEkSAdEZFA0LScFSjKYIBkYicDzAvR3CEk/wloYEQcQXElgiPAJcp2CSJ4JY0EMQAtZgFcRVFEVIX7wOOO0IUiRjCsQlN0EfsG80RTCiEjjGPDmlA9ZgSR0u1zQGLm+CIEYfJLBEmChYdgq9XWXrF4tuwDEImNKDD+/ol3f1YrgiGNxThQmBAhdZUBITBAgzLgTv6wx+LyNPMU3K2wzdf5skH+RFEMSYggQ2WYkgB3S4OsVey26oyDEugadmgtva/QrQAwDSczzlGgNct263y9Mc3ZQBDO1ryuFvgQZeikIgkSRJntzVoCbpnlShSIrgM8agj7ACFvfWY245GXR+8BDNEAiCGBOQwCYbw6X8IDgH1PeeQk1fVjgHLHO8fxQxB5htFvRLblIsjh/oumUuO7jkBgwmYEhxCnARGBSV3cAKgURSaiaktirAmOY3ds65J1VIkoAIclcjDjTjHHD2A9lF/pHU3mpWZMUScYI8KOoTTcAiCWySEU0OqPc9pe43QmYeeF9H0FtCRl5Ea5N+YusniMqHAOeQbJ1BAg8OSD3NgNsBZIwD/KocScOnCqkBY2dbBlqDLWhTWmRiHWPiXd+Z0AaXy4WGhgY4HI54DyXpMJlMKCkpgcFgCHsfEtgkJNIc0OGOJdsSjnOIx7Z52rgF7pOeE9o9ygHOQ+eXDj2PohtWdAGCAXANBK/B6oyefQPXdVUUEMYYhMIyIDO4RjBsiVsjmNKLkpeGhgZkZmZi8uTJ9B2qCOccnZ2daGhowNSpU8PejwSWGBZZwZYkoL9bMd9WfmFX53EPD3T5H49zICVT3p3rdcPmFHn29yECnQ2AOR/IK/V3OUtuoG4fpP1vBUU0k4CA0ouSFM45HA4HJk+erJgmR0QHYwx5eXno6OjwGA9h/n2QwBIjI1SKSkAwlU7QwV26GELZajCd4Pc59HdCF3K9NDCQiXn2s7YCzn7/NVBJAvo6gYxxYPohv+IqCwjnHFLzMfBmAYFKxTAKgpwovSgpGdMPjxpCa7BEYsAAlh4caMU5h5BdADbYHaRvLHOYmsscfs0GfAYyY/CkEAV82DsOrQWEy7mcGcDpJkcQYx0SWEIDGIQ5VwRZb5xzuI9tAwa6w89S9QUS9QZFCrOUdCBlGsD8yzhKkgS47ADT1k1GfVqJ0YzWgW779+/H4sWL8c477+C6664Lev/jjz/Gpk2bsGPHjpDH0ev1cLvdAIDFixdj3759IT+fSJDAEiNDJqeWcw5+fDukwBKGnAPNx8FmrvIruxjKdesLJMoIjiLm1naAcTDzBD+BY5Ib3NUXsRc4mhsOY572dixQzEeDuCZoe0RCe2IR6Pbyyy9j5cqVePnll2UFNhpGk7gCGgvs5Zdfjra2NnDOMXPmTLzwwgs4cOAA1q5di2nTpgEApk+fji1btmg5DEILQubb5oD3d4Fl5vuJIpckoG6fRxSHBCUN39tVIU0oMxeSTOWlIQcOv8rU2ahodesaJyjUX5bQONDN7Xbjrbfewq5du7Bs2TJ0dXUhNzcXr7zyCn72s58hOzsbK1eu9H1ekiT85Cc/wfbt2zE4OIi1a9fiscceCzruUGv2448/xiOPPILBwUHk5ubihRdeQElJSdRj1gJNBXbLli3IysoCANx///349a9/jVWrVmHZsmXDugWIxCacGsFBa6As8jXQUOeRJAn8vZ9CajmJoXcJziWgvwvM2u5fMQohGgRwDqn5OIQIrGu/z4wiS5D6yxI+NIpT2LZtG+bOnYvJkydj3bp1ePPNN3HttdfiwQcfxP79+1FQUIAbbrjB9/mXXnoJnHN8/vnnEEUR11xzDf7xj39gzZo1ssfv6urCj370I3zwwQfIysrCG2+8gQceeABvvBGcNhhPNBVYr7hKkoSBgQHfz0RyELpGsPbnYZzLBhkxJoBnl0C35AYIAZHJSlWmoreuR6clSP1lCS15+eWXcfPNNwMAbr75Zjz88MMoLCzERRddhMLCQgDALbfcgt/+9rcAgL///e/48ssv8fe//x0A0N/fj9OnTysK7GeffYZTp05h1apVADwak5mZqfVlRYzma7Dr1q3D7t27UVZWhv/3//4f9u3bh/3796OiogJmsxkPP/wwVq9erfUwiERCwXUbKcMFGQk6XXCRfq/4a2xdkyVIjFVsNhvef/997Nq1Cz/96U8BAE1NTThz5oziPpxzPPnkk7j22mvDOgfnHCtWrMDWrVtVGLF2aJ6N/O6776KlpQXnn38+nnnmGSxcuBB1dXU4dOgQfvOb3+COO+5AXV1d0H6bN29GWVmZ79XdHbw2RiQ4Z4XU+wI/GxFsawO3DnnZ2kJafN6KTEGvswnf3iAj/1dsxI0xBiYIwa8ozx/qWglCdYL+Rkd+yC1btuDKK69EfX09amtrUVtbi/vvvx99fX3YuXMnmpubwTnHK6+84ttnzZo1ePbZZ2G32wEAzc3NaGlpUTzHBRdcgM8//xxHjx4F4FnzPXLkyMgHrzIxiSLW6XT45je/iQ0bNuDBBx/0ba+oqMDy5ctx6NAhTJo0yW+fjRs3YuPGjb6fy8rKYjFUQg1CuE6F6RdBmH1ZsAApiFLIaMfhSjJGg0rWdVSnphKGRKzQcHnj5Zdfxj333OO37Wtf+xpuvPFGPPHEE1i1ahXy8/OxcuVK7N27FwBw5513wmKxYPHixWCMIT09HS+99BIKCgpkzzFu3Dj8+c9/xl133YXBwUG43W585zvfwbx586IetxZoJrBWqxX9/f0+f/vbb7+N8vJyNDc3o6CgAIwxWCwW7N27F7/85S+1GgahApGmrwxXv1ja/1bwPhm5YHICEira0VuSMZogo6B9zlnXgfmzMVtPpRKGRIzQcnnjX//6V9C2RYsW+VzEt9xyi+x4Hn30UTz66KNB73mjhgP/vWrVKuzZsyfqccYCzQS2t7cX69evh91uB2MMs2fPxm9/+1u89dZbePbZZ30dCR5//HHMmDFDq2EQIyRaqyri+sXDCYhctKNCxSjv2GSPFeLJXTf9IghlVwRfT6zXU6mEIREDKNBNezQT2JKSEnzxxRdB2++77z7cd999Wp2WUBstrCrVBIRBV6bgNo3Qug61D0EQRDRQJSciPBLUqvIGGUW6j9xDgWx7O88OJLwEQUQMCSwRNTEVJI2LOSRUgNEoK1xBEIQ8JLBEVHgboXsqNgUUehhOkCIRkFgVc0iEAKNRXLiCIIhgSGCJ8AgSxbON0DPH+7toQwlSFAIS8zXTOLrCaX2YIJILElgiNAqiyLkEmNLO3vjDE6RoBWQsRTuOpWslEgNJ4nC7Rej1OgiCer97/f39+NGPfoT33nsPGRkZMBgMuP/++7Fjxw5cdtllsuk6I2lH9/TTT+Ob3/wmzGbzSIeuGiSwREgUc1olCeK+NyK2qkhACCIx4JyjpckKS10PXC4RBoMOxZOyUTDRrIq35O677wYAHDt2DKmpqejq6hq2GP9I2tE9/fTTuP7662UFVhRF6ALqkscCzUslEqMfpXKAULeGUlSoXlpQg9JxBJGItDRZUXWyA0aTDtk5qTCadKg62YGWJuuIj11dXY2//vWveOaZZ5CamgoAyM3Nxb333gsA2Lt3L1auXIkpU6Zg8+bNvv30er3fvzdt2oQFCxbgvPPOw6lTpwAAu3btwqJFi1BRUYHy8nLs3bsXTz75JJqamrB69WpUVFTA6XTi4osvxsMPP4yLL74YDzzwAPbv348LL7wQCxcuxIIFC7Bt2za/c/3kJz/Beeedh4ULF6pWdpEsWGJkxDHiVdXIXwowIsYQksRhqetBZpYJBoPHsjMYdMjMMqGxvgf5heYRuYsrKysxffp0xQ5qNTU1+Oijj9DS0oK5c+fi7rvv9hUf8iKKIqZPn46DBw/iySefxJNPPonf//73eOKJJ/D0009jxYoVcLvdsNvtWLZsGTZv3owPP/wQxcXFvmNYLBZ89NFHYIzBarXi448/hsFgQGNjI1asWIHq6mrfuYqKinD48GG8//77uOOOO1Rp7k4CS0RHIgiSipG/FGBEjCXcbhEul4j0DKPfdoNBh/4+J9xuEUZj9PLgbcShxHXXXQedToeioiLk5OSgtbXVTxgBz9/khg0bAABLly7Fhx9+CABYuXIlfvjDH+Kmm27CVVddhVmzZime5z/+4z984+jr68Ndd92FY8eOQa/Xw2KxoKOjA+PGjQMA3HrrrQCAq6++Grfddhv6+/uRnp4e9RwAJLBElCSUIKkU+Uvrw8RYQa/XwWDQ+dZevbhcIoxGHfT6ka1XlpeX48yZM7BarbJroiaTyfdvnU7nV2PYiyAIPqt26Gd++MMf4uqrr8aHH36Ia665Bj/72c9w4403yo4jIyPD9++HH34YCxcuxBtveGJH8vLyfN17tILWYBOE0dimTO1WbQRBxAZBYCielA1brwMulwjAI662XgeKSrNHHE08depUrFu3Dhs3bvSJWG9vL55//vkRj/306dOYNWsWvvvd7+K2227zuXLNZjNsNpviflarFUVFRWCMYcuWLejq8l9aevnllwEA77//PqZOnTpi6xUgCzYhSKgqQgRBjAkKJnosy8b6HvT3OWE06jBt1jjf9pHyu9/9Dg899BDmzJmDjIwMGI1G/PCHPxzxcZ9++ml8/PHHMBqNyMnJwZ/+9CcAwHe+8x2sX78e6enp+Oyzz4L2e+ihh3DbbbfhmWeewfnnn4/S0lLfezqdDl1dXVi6dCncbjdeeumlEY8TABhPZBNpCGVlZTh27Fi8h6EJXJLg/vx1xbVE/dKbIq63OxageSOIc3DOceLECcyePTuiB3Kt8mBHE3q9XtZNPRSl+Q2lTWTBJhIJWlA/YUmEQCuCGOUIAhtRQBOhDM0qMWpJqEArgiBGLcNZr9FCAkuMaijylyCIRIUENpGgNmUEQRBJAwlsIkBriQRBEEkHCWwCQGuJBEEQyQflMCQIVLSBIIhkYmBgAN/73vcwdepUzJ8/HxUVFXjwwQchimJUx3v66adhtY68EUEsIYElEobRWM2KIEY7gw47PjqyG4MOdcsGfutb30JnZyeOHj2KL7/8Env27EFmZiYcDkdUxxuNAksuYiIhoGpWBBEfjlvOYPfJA8hKy8TCaeWqHLO6uhrvvvsuGhsbkZaWBgBISUnBT37yEwDA4cOH8f3vfx+9vb1ISUnBc889h3nz5uHRRx9FbW0tLBYLampqcOONN+Kxxx7za0dnMBjw+eef4/Tp07jnnnvQ29uL7Oxs/P73v8esWbPgdDrxve99D59++ikA4Pvf/z7uuusuVa4rUkhgicRAxc44BEGEx6DDjv1VRzB5QjH2Vx3BnOLpSDWljPi4lZWVmDZtmmyhf5fLhbvvvhtvv/02ioqKsHfvXtx1113Yu3cvAI/47tq1C5IkYdq0afjOd76D//qv/wpqR3frrbfi0Ucfxbp16/D222/jG9/4Bvbs2YPnnnsO7e3tOHz4MHp6erB48WJccMEFmDt37oivK1LIRUwkFmerWXlfCdDTnSCSluOWM3CLIjJT0+EWRRy3nFHt2EM9Tm+88QYqKipQWlqK3bt3o7KyEldddRUqKirw7W9/G83Nzb7PXnXVVUhNTUV6ejrmzJmD2traoGNbrVY0NDRg3bp1AIANGzbg1KlTGBgYwMcff4w77rgDgiAgNzcX69atwyeffKLadUUCWbAEQRBjEK/1Oj4rFwAwPitXNSt27ty5OHPmDGw2GzIzM3HjjTfixhtvxMUXXwzGGKZNm4ZDhw7J7htOKzu5uAzvNrn34rW8RBYsQRDEGMRrvRr0ekhcgkGvh8vtVsWKnTp1Kq655hrcd999GBwcBABIkuRrXWez2bBjxw4AHkFUEtuhDG1Hl5WVhZKSEvz1r38FALz99tuYNWsW0tLScMkll+DFF1+EJEno6urCu+++i5UrV474mqKBLFgisaBqVgQRE9p6OwAGNHWdK3DDBIZ2a6cqx3/++efx4x//GGVlZcjKykJaWhouvfRSVFRUYOvWrfjud7+LH/7wh3C5XFi/fj0qKipCHi+wHd3LL7+Me+65Bz/5yU+QnZ3ta1t3zz334Pjx4zjvvPMAAD/+8Y/jsv4KULs6IkGgKGKCGBmRtqvjnCu6U+lvLRhqV0eMWqiaFUHEFhJS7SGBJRIG6oxDEEQyQUFOBEEQBKEBJLAEQRBJxCgJqxl1RDOv5CImCIJIAhhjMJlM6OzsRF5eHq2vqgjnHJ2dnTCZTBHNKwksQRBEklBSUoKGhgZ0dHTEeyhJh8lkQklJSUT7kMASBEEkCQaDAVOnTiU3sQZE4xEggSUIgkgyyD2cGFCQE0EQBEFoAAksQRAEQWjAqCmVaDabfX0Ah9Ld3Y2cnJw4jCixoHmgOQBoDgCaA4DmAIjdHFgsFlitVtn3Ro3AKkE1ij3QPNAcADQHAM0BQHMAJMYckIuYIAiCIDSABJYgCIIgNGDUC+zGjRvjPYSEgOaB5gCgOQBoDgCaAyAx5mDUr8ESBEEQRCIy6i1YgiAIgkhESGAJgiAIQgMSXmD/8z//E8XFxdDrz1V1fO6551BRUeF7GY1G/PWvfwUANDQ0YMWKFZg5cyZWrVqFpqameA1dNeTmgHOO73//+5g7dy7Kyspw7733QhRFAGNnDqxWK2666SbMmzcP8+bNw9atW33vJeMcNDQ04Ctf+QrmzJmD8vJyPPLII773HnzwQUyfPh0zZ87Eli1b/PZJpnlQmoPa2lqsXLkS6enpuOuuu4L2GQtz8Oqrr2L+/Pk477zzsGTJEnz88cd++4yFOdi9e7dPF8rLy/HMM8/47RPzOeAJzqeffspbWlq4TqeTfb++vp5nZ2fzwcFBzjnn//Ef/8Gff/55zjnnmzdv5rfddlvMxqoVcnPwz3/+ky9fvpy73W7udrv5RRddxN9//33O+diZgwcffJDff//9nHPOu7u7eXl5ObdarZzz5JyDpqYm/sUXX3DOOXc4HHzlypX8r3/9K//www/5ihUruMvl4haLhRcXFyftPCjNQWdnJ9+1axd/9tln+Z133um3z1iZg127dvHOzk7OOedHjx7l+fn5XBRFzvnYmYP+/n7ucrk455zbbDZeWlrKa2pqOOfxmYOEF1gvSgL7y1/+kn/zm9/knHMuSRLPysryiW1fXx/Pzs6O2Ri1Zugc/Otf/+ILFy7kAwMDfGBggC9ZsoR/8cUXY2oOvvrVr/Jt27b5fv7a177G33zzzaSfAy/33Xcf/81vfsO//e1v8z/+8Y++7TfddBPfsmXLmJgH7xx4efHFF/0EdizOAefnrru3t3fMzkFbWxsvKiri1dXVcZuDhHcRD8crr7yCW2+9FQDQ2dmJ9PR0pKSkAADS09NhNBrR29sbzyFqwiWXXIJLLrkEhYWFKCwsxIoVK7B48eIxNQeLFi3Cm2++CUmS0NjYiJ07d6KhoWFMzEFnZye2bt2Kyy67DBaLxa9PZWlpKSwWS9LPw9A5CPWZsTgHr732GubOnQuz2Tzm5uDQoUOYN28eSktL8cADD2DKlClxm4NRLbAHDx6E1WrFqlWrfNsC2zTxJM1C2rdvH+rr69Hc3Izm5mZUVlbirbfeAjB25uChhx6CXq/HwoULcc8992DVqlW+NdpkngOHw4Hrr78e999/P+bMmQPA/3qHXmuyzoPcHCgx1ubgwIEDeOSRR/DSSy/5to2lOaioqMCRI0dQU1ODLVu24OTJkwDiMwejWmBfeeUV3Hzzzb6Jy8vLQ19fH+x2OwBgYGAALpcLWVlZ8RymJrz00ku4/PLLkZqaitTUVKxfvx4fffTRmJqDtLQ0PPvsszh06BDee+89DAwMYNasWUk9B6Io4uabb8bixYvxgx/8AABQUlKC+vp632csFguKi4uTdh7k5kCJsTYHp06dwte+9jW8/vrrmDFjBoCxNwdeCgoKsGLFCrz33ntxm4NRK7CiKOLPf/6zzz0MeJ5QrrrqKrz88ssAgD/96U9Yt25dvIaoKZMmTcKOHTsgSRJEUcT27dtRVlY2puagt7cXDocDALBz507U1NTg8ssvT+o5uPvuu2E2m/HEE0/4tq1fvx5/+tOfIIoimpqasHPnTlxxxRVJOw9yc6DEWJoDi8WCq666Cs899xyWLVvm2z6W5qCqqgoulwsAYLPZsG3bNpSXl8dvDjRf5R0hd999Ny8qKuIAeFFREb/77rs555x/+OGHfMGCBUGfr6+v5xdddBGfMWMGX7FiBbdYLLEesurIzUF/fz//+te/zufMmcPLysr4nXfeyZ1OJ+d87MzB3r17+fTp0/ns2bP5qlWr+IkTJ3yfT8Y52LlzJwfAy8vL+fz58/n8+fP5//f//X+cc87/67/+i0+bNo1Pnz6dv/nmm759km0elOagv7+fFxUV8ZycHJ6WlsaLior4jh07OOdjZw7uuusubjabfdvmz5/vi6AdK3Pwhz/8gZeVlfHzzjuPz5s3jz/55JO+feIxB1QqkSAIgiA0YNS6iAmCIAgikSGBJQiCIAgNIIElCIIgCA0ggSUIgiAIDSCBJQiCIAgNIIEliGFgjPl1b9qxYwdqa2sxffp0AEBTU1Pc8gonT54Mi8Wi6Tm2bt2Kw4cP+35+9NFHsWnTprD2/clPfuLX3UdNXnvtNfyf//N/NDk2QagBCSxBDINOp8OhQ4d8r8C6rxMnTsS7776r+Ti87QhjTaDAhovVasXWrVuxYcMGDUYF3HTTTfjzn/+Mvr4+TY5PECOFBJYgRshQa7a2thZTp07F3XffjfLycqxYsQINDQ0APJbfrbfeipUrV2LmzJl44IEHfMc4fPgwLr30UixatAgXXnghjhw54tvnzjvvxJo1a/CVr3wl7DH99re/xdKlSzF//nzcddddvuo2kydPxk9/+lMsWbIEM2fOxGeffQbAU5f1e9/7HmbNmoVVq1bh5ptvxqZNm/DRRx/h3XffxcMPP4yKigrf58+cOYPLLrsM06ZNw49//GPZMWzZsgVXXnmlr5Tp7bffjnvvvReXXXYZJk2ahNdffx2bNm3CggULsGTJErS0tPjN05o1azB58mT86le/wu9//3ssWbIEZWVlOH78OABAEAR85StfwTvvvBP2vBBELCGBJYhhEEXRz0U8HDU1NVi/fj2OHj2KG2+80a9O6t69e/H+++/j6NGj+Oyzz/D+++/D5XLh7rvvxssvv4z9+/fjV7/6lV/T8D179uDNN9/0a6Adin/961/Yu3cv9uzZgy+//BJGoxF/+MMffO+npaXhiy++wC9+8Qv89Kc/BQD85S9/wZdffomjR4/i3XffxZ49ewB4ujatW7cOv/jFL3Do0CEsX74cgOeB4L333sPhw4fxwgsvyLqpP/30UyxevNhvW2NjI7Zt24b33nsPd955J6ZPn46DBw/ikksuwfPPP+/73PHjx/GXv/wFX3zxBR599FH09vbiiy++wH333edXGm/p0qX49NNPw5oXgog1+ngPgCASHa+LOFzGjRuHK6+8EgBw66234mc/+5nvvWuvvRZmsxkAcOONN+KTTz7B5MmTUVlZiauuusr3ua6uLt+/165di8zMzLDP//e//x2ffvopFi5cCACw2+1IT0/3vX/99dcD8IjTj370IwDAv//9b9xwww0wGAzIysoadk35qquuQmpqKgBgzpw5qK2tRXFxsd9nmpqaMGHCBL9t11xzDQRBwLx582C323HdddcB8HRA2bZtm+9za9asQUpKClJSUjBu3DisXbvW97k333zT97mCggI0NTWFPTcEEUtIYAlCZYa2xWKMBbXJCvws5xzTpk1TFPGMjIyIzs85xw9+8AN8//vfl33fZDIB8Dw4uN1u2XEPh/cYcsfxkpqa6mvGELifd168PwuC4HeMoccXBEHxc4ODgz6hJ4hEg1zEBKEy7e3t+OCDDwAA//u//4uVK1f63tu6dSusViucTifeeOMNrFy5ErNnz4bNZsOOHTsAeAQyEos5kDVr1uDFF19Ed3c3AKCnpwc1NTUh91mxYgXeeOMNuFwu9Pb2+gVtmc1m2Gy2iMcxd+5cnD59OuL9IuHkyZMoLy/X9BwEES0ksAShMlOnTsU//vEPLFy4EG+88QZ+/etf+95buXIlNmzYgHnz5mH58uW4+uqrYTAYsHXrVvziF7/A/PnzMXfu3IhSW5YsWYLi4mIUFxdj9erVuOyyy3wN6M877zxceumlw6byXHfddSgvL0d5eTluuOEGnH/++T5X9s0334xnnnkGS5Yswe7du8Me17p163wPDVqxY8cOn/uYIBIN6qZDECpSW1uLyy67DGfOnAl679FHH4Ver8cjjzwSh5ENT19fHzIyMtDf348VK1Zg8+bNuOCCC0Z0zJUrV+LPf/4zioqKVBrlOerq6nD77bfjo48+Uv3YBKEGtAZLEAQAjxXb2toKp9OJW2+9dcTiCnjSherq6jQR2IaGBvzmN79R/bgEoRZkwRIEQRCEBtAaLEEQBEFoAAksQRAEQWgACSxBEARBaAAJLEEQBEFoAAksQRAEQWgACSxBEARBaMD/D2Ytu93TLDTBAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "var1 = 'Flipper Length (mm)'\n", "var2 = 'Culmen Length (mm)'\n", "scatterplot(df, var1, var2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Within each species, the joint distribution of these measurements forms an oval shape, at least roughly. The orientation of the ovals is along a diagonal, which indicates that there is a correlation between culmen length and flipper length.\n", "\n", "If we ignore these correlations, we are assuming that the features are independent. To see what that looks like, I'll make a joint distribution for each species assuming independence.\n", "\n", "The following function makes a discrete `Pmf` that approximates a normal distribution." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "def make_pmf_norm(dist, sigmas=3, n=101):\n", " \"\"\"Make a Pmf approximation to a normal distribution.\"\"\"\n", " mean, std = dist.mean(), dist.std()\n", " low = mean - sigmas * std\n", " high = mean + sigmas * std\n", " qs = np.linspace(low, high, n)\n", " ps = dist.pdf(qs)\n", " pmf = Pmf(ps, qs)\n", " pmf.normalize()\n", " return pmf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use it, along with `make_joint`, to make a joint distribution of culmen length and flipper length for each species." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "from utils import make_joint\n", "\n", "joint_map = {}\n", "for species in hypos:\n", " pmf1 = make_pmf_norm(flipper_map[species])\n", " pmf2 = make_pmf_norm(culmen_map[species])\n", " joint_map[species] = make_joint(pmf1, pmf2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following figure compares a scatter plot of the data to the contours of the joint distributions, assuming independence." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from utils import plot_contour\n", "\n", "scatterplot(df, var1, var2)\n", "for species in hypos:\n", " plot_contour(joint_map[species], alpha=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The contours of a joint normal distribution form ellipses.\n", "In this example, because the features are uncorrelated, the ellipses are aligned with the axes.\n", "But they are not well aligned with the data.\n", "\n", "We can make a better model of the data, and use it to compute better likelihoods, with a multivariate normal distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate Normal Distribution\n", "\n", "As we have seen, a univariate normal distribution is characterized by its mean and standard deviation.\n", "\n", "A multivariate normal distribution is characterized by the means of the features and the **covariance matrix**, which contains **variances**, which quantify the spread of the features, and the **covariances**, which quantify the relationships among them.\n", "\n", "We can use the data to estimate the means and covariance matrix for the population of penguins.\n", "First I'll select the columns we want." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "features = df[[var1, var2]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And compute the means." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Flipper Length (mm) 200.915205\n", "Culmen Length (mm) 43.921930\n", "dtype: float64" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean = features.mean()\n", "mean" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also compute the covariance matrix:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Flipper Length (mm)Culmen Length (mm)
Flipper Length (mm)197.73179250.375765
Culmen Length (mm)50.37576529.807054
\n", "
" ], "text/plain": [ " Flipper Length (mm) Culmen Length (mm)\n", "Flipper Length (mm) 197.731792 50.375765\n", "Culmen Length (mm) 50.375765 29.807054" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cov = features.cov()\n", "cov" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a `DataFrame` with one row and one column for each feature. The elements on the diagonal are the variances; the elements off the diagonal are covariances.\n", "\n", "By themselves, variances and covariances are hard to interpret. We can use them to compute standard deviations and correlation coefficients, which are easier to interpret, but the details of that calculation are not important right now.\n", "\n", "Instead, we'll pass the covariance matrix to `multivariate_normal`, which is a SciPy function that creates an object that represents a multivariate normal distribution.\n", "\n", "As arguments it takes a sequence of means and a covariance matrix: " ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "from scipy.stats import multivariate_normal\n", "\n", "multinorm = multivariate_normal(mean, cov)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following function makes a `multivariate_normal` object for each species." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "def make_multinorm_map(df, colnames):\n", " \"\"\"Make a map from each species to a multivariate normal.\"\"\"\n", " multinorm_map = {}\n", " grouped = df.groupby('Species2')\n", " for species, group in grouped:\n", " features = group[colnames]\n", " mean = features.mean()\n", " cov = features.cov()\n", " multinorm_map[species] = multivariate_normal(mean, cov)\n", " return multinorm_map" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's how we make this map for the first two features, flipper length and culmen length." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "multinorm_map = make_multinorm_map(df, [var1, var2])" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "## Visualizing a Multivariate Normal Distribution\n", "\n", "This section uses some NumPy magic to generate contour plots for multivariate normal distributions. If that's interesting for you, great! Otherwise, feel free to skip to the results. In the next section we'll do the actual classification, which turns out to be easier than the visualization.\n", "\n", "I'll start by making a contour map for the distribution of features among Adélie penguins. \n", "Here are the univariate distributions for the two features we'll use and the multivariate distribution we just computed." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [], "source": [ "norm1 = flipper_map['Adelie']\n", "norm2 = culmen_map['Adelie']\n", "multinorm = multinorm_map['Adelie']" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "I'll make a discrete `Pmf` approximation for each of the univariate distributions." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [], "source": [ "pmf1 = make_pmf_norm(norm1)\n", "pmf2 = make_pmf_norm(norm2)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "And use them to make a mesh grid that contains all pairs of values." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "(101, 101)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X, Y = np.meshgrid(pmf1.qs, pmf2.qs)\n", "X.shape" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "The mesh is represented by two arrays: the first contains the quantities from `pmf1` along the `x` axis; the second contains the quantities from `pmf2` along the `y` axis.\n", "\n", "In order to evaluate the multivariate distribution for each pair of values, we have to \"stack\" the arrays." ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "(101, 101, 2)" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pos = np.dstack((X, Y))\n", "pos.shape" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "The result is a 3-D array that you can think of as a 2-D array of pairs. When we pass this array to `multinorm.pdf`, it evaluates the probability density function of the distribution for each pair of values." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "(101, 101)" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "densities = multinorm.pdf(pos)\n", "densities.shape" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "The result is an array of probability densities. If we put them in a `DataFrame` and normalize them, the result is a discrete approximation of the joint distribution of the two features." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "15.87134363991382" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from utils import normalize\n", "\n", "joint = pd.DataFrame(densities, columns=pmf1.qs, index=pmf2.qs)\n", "normalize(joint)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "Here's what the result looks like." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_contour(joint)\n", "decorate(xlabel=var1,\n", " ylabel=var2)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "The contours of a multivariate normal distribution are still ellipses, but now that we have taken into account the correlation between the features, the ellipses are no longer aligned with the axes.\n", "\n", "The following function encapsulate the steps we just did." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [], "source": [ "def make_joint(norm1, norm2, multinorm):\n", " \"\"\"Make a joint distribution.\n", " \n", " norm1: `norm` object representing the distribution of the first feature\n", " norm2: `norm` object representing the distribution of the second feature\n", " multinorm: `multivariate_normal` object representing the joint distribution\n", " \"\"\"\n", " pmf1 = make_pmf_norm(norm1)\n", " pmf2 = make_pmf_norm(norm2)\n", " X, Y = np.meshgrid(pmf1.qs, pmf2.qs)\n", " pos = np.dstack((X, Y))\n", " densities = multinorm.pdf(pos)\n", " joint = pd.DataFrame(densities, columns=pmf1.qs, index=pmf2.qs)\n", " return joint" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following figure shows a scatter plot of the data along with the contours of the multivariate normal distribution for each species." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scatterplot(df, var1, var2)\n", "\n", "for species in hypos:\n", " norm1 = flipper_map[species]\n", " norm2 = culmen_map[species]\n", " multinorm = multinorm_map[species]\n", " joint = make_joint(norm1, norm2, multinorm)\n", " plot_contour(joint, alpha=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because the multivariate normal distribution takes into account the correlations between features, it is a better model for the data. And there is less overlap in the contours of the three distributions, which suggests that they should yield better classifications." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Less Naive Classifier\n", "\n", "In a previous section we used `update_penguin` to update a prior `Pmf` based on observed data and a collection of `norm` objects that model the distribution of observations under each hypothesis. Here it is again:" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "def update_penguin(prior, data, norm_map):\n", " \"\"\"Update hypothetical species.\"\"\"\n", " hypos = prior.qs\n", " likelihood = [norm_map[hypo].pdf(data) for hypo in hypos]\n", " posterior = prior * likelihood\n", " posterior.normalize()\n", " return posterior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Last time we used this function, the values in `norm_map` were `norm` objects, but it also works if they are `multivariate_normal` objects.\n", "\n", "We can use it to classify a penguin with flipper length 193 and culmen length 48:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "Adelie 0.002740\n", "Chinstrap 0.997257\n", "Gentoo 0.000003\n", "dtype: float64" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data = 193, 48\n", "update_penguin(prior, data, multinorm_map)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A penguin with those measurements is almost certainly a Chinstrap.\n", "\n", "Now let's see if this classifier does any better than the naive Bayesian classifier.\n", "I'll apply it to each penguin in the dataset:" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "df['Classification'] = \"None\"\n", "\n", "for i, row in df.iterrows():\n", " data = row[colnames]\n", " posterior = update_penguin(prior, data, multinorm_map)\n", " df.loc[i, 'Classification'] = posterior.idxmax()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And compute the accuracy:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9532163742690059" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "accuracy(df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It turns out to be only a little better: the accuracy is 95.3%, compared to 94.7% for the naive Bayesian classifier." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "In this chapter, we implemented a naive Bayesian classifier, which is \"naive\" in the sense that it assumes that the features it uses for classification are independent.\n", "\n", "To see how bad that assumption is, we also implemented a classifier that uses a multivariate normal distribution to model the joint distribution of the features, which includes their dependencies.\n", "\n", "In this example, the non-naive classifier is only marginally better.\n", "In one way, that's disappointing. After all that work, it would have been nice to see a bigger improvement.\n", "But in another way, it's good news. In general, a naive Bayesian classifier is easier to implement and requires less computation. If it works nearly as well as a more complex algorithm, it might be a good choice for practical purposes.\n", "\n", "Speaking of practical purposes, you might have noticed that this example isn't very useful. If we want to identify the species of a penguin, there are easier ways than measuring its flippers and beak.\n", "\n", "But there *are* scientific uses for this type of classification. One of them is the subject of the research paper we started with: [sexual dimorphism](https://en.wikipedia.org/wiki/Sexual_dimorphism), that is, differences in shape between male and female animals.\n", "\n", "In some species, like angler fish, males and females look very different. In other species, like mockingbirds, they are difficult to tell apart.\n", "And dimorphism is worth studying because it provides insight into social behavior, sexual selection, and evolution. \n", "\n", "One way to quantify the degree of sexual dimorphism in a species is to use a classification algorithm like the one in this chapter. If you can find a set of features that makes it possible to classify individuals by sex with high accuracy, that's evidence of high dimorphism.\n", "\n", "As an exercise, you can use the dataset from this chapter to classify penguins by sex and see which of the three species is the most dimorphic." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** In my example I used culmen length and flipper length because they seemed to provide the most power to distinguish the three species. But maybe we can do better by using more features.\n", "\n", "Make a naive Bayesian classifier that uses all four measurements in the dataset: culmen length and depth, flipper length, and body mass.\n", "Is it more accurate than the model with two features?" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# Here are the norm maps for the other two features\n", "\n", "depth_map = make_norm_map(df, 'Culmen Depth (mm)')\n", "mass_map = make_norm_map(df, 'Body Mass (g)')" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# And here are sequences for the features and the norm maps\n", "\n", "colnames4 = ['Culmen Length (mm)', 'Flipper Length (mm)', \n", " 'Culmen Depth (mm)', 'Body Mass (g)']\n", "norm_maps4 = [culmen_map, flipper_map, \n", " depth_map, mass_map]" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9678362573099415" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "# Now let's classify and compute accuracy.\n", "\n", "# We can do a little better with all four features,\n", "# almost 97% accuracy\n", "\n", "df['Classification'] = \"None\"\n", "\n", "for i, row in df.iterrows():\n", " data_seq = row[colnames4]\n", " posterior = update_naive(prior, data_seq, norm_maps4)\n", " df.loc[i, 'Classification'] = posterior.max_prob()\n", "\n", "accuracy(df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** One of the reasons the penguin dataset was collected was to quantify sexual dimorphism in different penguin species, that is, physical differences between male and female penguins. One way to quantify dimorphism is to use measurements to classify penguins by sex. If a species is more dimorphic, we expect to be able to classify them more accurately.\n", "\n", "As an exercise, pick a species and use a Bayesian classifier (naive or not) to classify the penguins by sex. Which features are most useful? What accuracy can you achieve?" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "Note: One Gentoo penguin has an invalid value for `Sex`. I used the following code to select one species and filter out invalid data." ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [], "source": [ "gentoo = (df['Species2'] == 'Gentoo')\n", "subset = df[gentoo].copy()" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "Sex\n", "MALE 61\n", "FEMALE 58\n", "Name: count, dtype: int64" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "subset['Sex'].value_counts()" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "342" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "valid = df['Sex'] != '.'\n", "valid.sum()" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "tags": [ "hide-cell" ] }, "outputs": [], "source": [ "subset = df[valid & gentoo].copy()" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "hide-cell" ] }, "source": [ "OK, you can finish it off from here." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "# Here are the feature distributions grouped by sex\n", "\n", "plot_cdfs(subset, 'Culmen Length (mm)', by='Sex')" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "plot_cdfs(subset, 'Culmen Depth (mm)', by='Sex')" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "plot_cdfs(subset, 'Flipper Length (mm)', by='Sex')" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "plot_cdfs(subset, 'Body Mass (g)', by='Sex')" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# Here are the norm maps for the features, grouped by sex\n", "\n", "culmen_map = make_norm_map(subset, 'Culmen Length (mm)', by='Sex')\n", "flipper_map = make_norm_map(subset, 'Flipper Length (mm)', by='Sex')\n", "depth_map = make_norm_map(subset, 'Culmen Depth (mm)', by='Sex')\n", "mass_map = make_norm_map(subset, 'Body Mass (g)', by='Sex')" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# And here are the sequences we need for `update_naive`\n", "\n", "norm_maps4 = [culmen_map, flipper_map, depth_map, mass_map]\n", "colnames4 = ['Culmen Length (mm)', 'Flipper Length (mm)', \n", " 'Culmen Depth (mm)', 'Body Mass (g)']" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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probs
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" ], "text/plain": [ "FEMALE 0.5\n", "MALE 0.5\n", "dtype: float64" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "# Here's the prior\n", "\n", "hypos = culmen_map.keys()\n", "prior = Pmf(1/2, hypos)\n", "prior" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# And the update\n", "\n", "subset['Classification'] = \"None\"\n", "\n", "for i, row in subset.iterrows():\n", " data_seq = row[colnames4]\n", " posterior = update_naive(prior, data_seq, norm_maps4)\n", " subset.loc[i, 'Classification'] = posterior.max_prob()" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# This function computes accuracy\n", "\n", "def accuracy_sex(df):\n", " \"\"\"Compute the accuracy of classification.\n", " \n", " Compares columns Classification and Sex\n", " \n", " df: DataFrame\n", " \"\"\"\n", " valid = df['Classification'].notna()\n", " same = df['Sex'] == df['Classification']\n", " return same.sum() / valid.sum()" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9186991869918699" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "# Using these features we can classify Gentoo penguins by\n", "# sex with almost 92% accuracy\n", "\n", "accuracy_sex(subset)" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# Here's the whole process in a function so we can\n", "# classify the other species\n", "\n", "def classify_by_sex(subset):\n", " \"\"\"Run the whole classification process.\n", " \n", " subset: DataFrame\n", " \"\"\"\n", " culmen_map = make_norm_map(subset, 'Culmen Length (mm)', by='Sex')\n", " flipper_map = make_norm_map(subset, 'Flipper Length (mm)', by='Sex')\n", " depth_map = make_norm_map(subset, 'Culmen Depth (mm)', by='Sex')\n", " mass_map = make_norm_map(subset, 'Body Mass (g)', by='Sex')\n", "\n", " norm_maps4 = [culmen_map, flipper_map, depth_map, mass_map]\n", "\n", " hypos = culmen_map.keys()\n", " prior = Pmf(1/2, hypos)\n", "\n", " subset['Classification'] = \"None\"\n", "\n", " for i, row in subset.iterrows():\n", " data_seq = row[colnames4]\n", " posterior = update_naive(prior, data_seq, norm_maps4)\n", " subset.loc[i, 'Classification'] = posterior.max_prob()\n", " \n", " return accuracy_sex(subset)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.8807947019867549" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "# Here's the subset of Adelie penguins\n", "\n", "# The accuracy is about 88%\n", "\n", "adelie = df['Species2']=='Adelie'\n", "subset = df[adelie].copy()\n", "classify_by_sex(subset)" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9264705882352942" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "# And for Chinstrap, accuracy is about 92%\n", "\n", "chinstrap = df['Species2']=='Chinstrap'\n", "subset = df[chinstrap].copy()\n", "classify_by_sex(subset)" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "# It looks like Gentoo and Chinstrap penguins are about equally\n", "# dimorphic, Adelie penguins a little less so.\n", "\n", "# All of these results are consistent with what's in the paper." ] }, { "cell_type": "markdown", "metadata": { "tags": [ "remove-print" ] }, "source": [ "*Think Bayes*, Second Edition\n", "\n", "Copyright 2020 Allen B. Downey\n", "\n", "License: [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/)" ] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.11" } }, "nbformat": 4, "nbformat_minor": 4 }