{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# In Depth: Naive Bayes Classification" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\n", "\n", "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", "\n", "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\n", "< [Feature Engineering](05.04-Feature-Engineering.ipynb) | [Contents](Index.ipynb) | [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) >" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "``Naive Bayes models`` are a group of **extremely fast and simple** classification algorithms that are often suitable for **very high-dimensional** datasets.\n", "\n", "A quick-and-dirty baseline for a classification problem.\n", "- so fast\n", "- so few tunable parameters\n", "- very useful \n", "\n", "\n", "This section will focus on \n", "- an intuitive explanation of how naive Bayes classifiers work\n", "- followed by a couple examples of them in action on some datasets.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Bayesian Classification\n", "\n", "Naive Bayes classifiers are built on Bayesian classification methods. \n", "\n", "Bayes's theorem is an equation describing the relationship of conditional probabilities of statistical quantities.\n", "\n", "- We are intrested in finding the probability of a label given some observed features\n", " - which we can write as $P(L~|~{\\rm features})$.\n", "\n", "Bayes's theorem:\n", "\n", "$$\n", "P(L~|~{\\rm features}) = \\frac{P({\\rm features}~|~L)P(L)}{P({\\rm features})}\n", "$$\n", "\n", "$$\n", "\\mbox{posterior} = \\frac{\\mbox{likelihood}\\times \\mbox{prior}}{\\mbox{evidence}} \\\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "https://en.wikipedia.org/wiki/Naive_Bayes_classifier\n", "\n", "In practice, there is interest only in the numerator of that fraction, \n", "- because the denominator does not depend on $L$ and the values of the features $x_i$ are given\n", "- so that the denominator is effectively constant.\n", "\n", "The numerator is equivalent to the ``joint probability`` model\n", "\n", "$$p(x_1, \\dots, x_n|L_k) p(L_k) = p(L_k, x_1, \\dots, x_n)$$\n", "\n", "\n", "$$\n", "p(L_k \\mid x_1, \\dots, x_n) \\varpropto p(L_k, x_1, \\dots, x_n)\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "\\begin{align}\n", "p(L_k, x_1, \\dots, x_n) & = p(x_1, \\dots, x_n, L_k) \\\\\n", " & = p(x_1 \\mid x_2, \\dots, x_n, L_k) p(x_2, \\dots, x_n, L_k) \\\\\n", " & = p(x_1 \\mid x_2, \\dots, x_n, L_k) p(x_2 \\mid x_3, \\dots, x_n, L_k) p(x_3, \\dots, x_n, L_k) \\\\\n", " & = \\dots \\\\\n", " & = p(x_1 \\mid x_2, \\dots, x_n, L_k) p(x_2 \\mid x_3, \\dots, x_n, L_k) \\dots p(x_{n-1} \\mid x_n, L_k) p(x_n \\mid L_k) p(L_k) \\\\\n", "\\end{align}\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now the \"naive\" conditional independenLe assumptions come into play: assume that each feature $x_i$ is conditionally statistical independence of every other feature $x_j$ for $j\\neq i$, given the category $L_k$. This means that\n", "\n", "$$p(x_i \\mid x_{i+1}, \\dots ,x_{n}, L_k ) = p(x_i \\mid L_k)$$\n", "\n", "Thus, the joint model can be expressed as\n", "\n", "\n", "\\begin{align}\n", "p(L_k \\mid x_1, \\dots, x_n) & \\varpropto p(L_k, x_1, \\dots, x_n) = \\\\\n", " & = p(L_k) \\ p(x_1 \\mid L_k) \\ p(x_2\\mid L_k) \\ p(x_3\\mid L_k) \\ \\cdots \\\\\n", " & = p(L_k) \\prod_{i=1}^n p(x_i \\mid L_k)\\,.\n", "\\end{align}\n", "\n", "\n", "The maximum a posteriori (MAP) decision rule\n", "\n", "$$\\hat{y} = \\underset{k \\in \\{1, \\dots, K\\}}{\\operatorname{argmax}} \\ p(C_k) \\displaystyle\\prod_{i=1}^n p(x_i \\mid C_k)$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Bayesian Classification\n", "\n", "If we are trying to decide between two labels $L_1$ and $L_2$\n", "- to compute the ratio of the posterior probabilities for each label:\n", "\n", "$$\n", "\\frac{P(L_1~|~{\\rm features})}{P(L_2~|~{\\rm features})} = \\frac{P({\\rm features}~|~L_1)}{P({\\rm features}~|~L_2)}\\frac{P(L_1)}{P(L_2)}\n", "$$\n", "\n", "We can compute $P({\\rm features}~|~L_i)$ for each label.\n", "- Such a model is called a *generative model* \n", " - because it specifies the hypothetical random process that generates the data." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Bayesian Classification\n", "\n", "``Specifying this generative model`` for each label is the main piece of the training of such a Bayesian classifier.\n", "- The general version of such a training step is a very difficult task, \n", "- but we can make it simpler through the use of some simplifying assumptions about the form of this model.\n", "\n", "This is where the \"naive\" in \"naive Bayes\" comes in: \n", "- if we make very naive assumptions about the generative model for each label, \n", " - we can find a rough approximation of the generative model for each class, and then proceed with the Bayesian classification.\n", " \n", "Different types of naive Bayes classifiers rest on different naive assumptions about the data, and we will examine a few of these in the following sections.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Gaussian Naive Bayes\n", "\n", "Perhaps the easiest naive Bayes classifier to understand is Gaussian naive Bayes.\n", "- In this classifier, the assumption is that *data from each label is drawn from a simple Gaussian distribution*.\n", "\n", "Imagine that you have the following data:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "When dealing with continuous data, a typical assumption is that the continuous values associated with each class are distributed according to a Normal distribution (Gaussian) distribution. \n", "\n", "The probability density of the normal distribution is\n", "\n", "$$\n", "f(x \\mid \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2} } e^{ -\\frac{(x-\\mu)^2}{2\\sigma^2} }\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "For example, suppose the training data contains a continuous attribute, $x$. \n", "\n", "We first segment the data by the class, and then compute the mean and variance of $x$ in each class. \n", "- Let $\\mu_k$ be the mean of the values in $x$ associated with class $C_k$\n", "- Let $\\sigma^2_k$ be the variance of the values in $x$ associated with class $C_k$. \n", "\n", "Suppose we have collected some observation value $v$. \n", "Then, the probability distribution of $v$ given a class $C_k$, \n", "\n", "$p(x=v \\mid C_k)$, can be computed by plugging $v$ into the equation for a Normal distribution parameterized by $\\mu_k$ and $\\sigma^2_k$. That is,\n", "\n", "\n", "\n", "\\begin{align}\n", "p(x=v \\mid C_k)=\\frac{1}{\\sqrt{2\\pi\\sigma^2_k}}\\,e^{ -\\frac{(v-\\mu_k)^2}{2\\sigma^2_k} }\n", "\\end{align}\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2018-05-22T07:56:56.792419Z", "start_time": "2018-05-22T07:56:56.699660Z" }, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2018-05-22T07:57:34.230534Z", "start_time": "2018-05-22T07:57:33.610601Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_blobs\n", "X, y = make_blobs(100, 2, centers=2, random_state=2, cluster_std=1.5)\n", "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='RdBu');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "One extremely fast way to create a simple model is to assume that \n", "- the data is described by a Gaussian distribution with no covariance between dimensions.\n", "\n", "This model can be fit by \n", "- simply finding the mean and standard deviation of the points within each label\n", "\n", "The result of this naive Gaussian assumption is shown in the following figure:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "![(run code in Appendix to generate image)](img/figures/05.05-gaussian-NB.png)\n", "[figure source in Appendix](06.00-Figure-Code.ipynb#Gaussian-Naive-Bayes)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "slideshow": { "slide_type": "subslide" } }, "source": [ "The ellipses here represent the Gaussian generative model for each label\n", "- with larger probability toward the center of the ellipses.\n", "\n", "With this generative model in place for each class, we have a simple recipe to compute the likelihood $P({\\rm features}~|~L_1)$ for any data point\n", "- and thus we can quickly compute the posterior ratio and determine which label is the most probable for a given point.\n", "\n", "This procedure is implemented in Scikit-Learn's ``sklearn.naive_bayes.GaussianNB`` estimator:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2018-05-22T08:00:43.749425Z", "start_time": "2018-05-22T08:00:43.744632Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "from sklearn.naive_bayes import GaussianNB\n", "model = GaussianNB()\n", "model.fit(X, y);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now let's generate some new data and predict the label:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2018-05-22T08:00:52.349506Z", "start_time": "2018-05-22T08:00:52.344249Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "rng = np.random.RandomState(0)\n", "Xnew = [-6, -14] + [14, 18] * rng.rand(2000, 2)\n", "ynew = model.predict(Xnew)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now we can plot this new data to get an idea of where the decision boundary is:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2018-05-22T08:00:57.841948Z", "start_time": "2018-05-22T08:00:57.584185Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='RdBu')\n", "lim = plt.axis()\n", "plt.scatter(Xnew[:, 0], Xnew[:, 1], c=ynew, s=20, cmap='RdBu', alpha=0.1)\n", "plt.axis(lim);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We see a slightly curved boundary in the classifications—in general, the boundary in Gaussian naive Bayes is quadratic.\n", "\n", "A nice piece of this Bayesian formalism is that it naturally allows for probabilistic classification, which we can compute using the ``predict_proba`` method:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.89, 0.11],\n", " [ 1. , 0. ],\n", " [ 1. , 0. ],\n", " [ 1. , 0. ],\n", " [ 1. , 0. ],\n", " [ 1. , 0. ],\n", " [ 0. , 1. ],\n", " [ 0.15, 0.85]])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "yprob = model.predict_proba(Xnew)\n", "yprob[-8:].round(2)\n", "# The columns give the posterior probabilities of the first and second label, respectively." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "If you are looking for estimates of uncertainty in your classification, Bayesian approaches like this can be a useful approach.\n", "\n", "The final classification will only be as good as the model assumptions that lead to it\n", "- This is why Gaussian naive Bayes often does not produce very good results." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Multinomial Naive Bayes\n", "\n", "- The Gaussian assumption is only one simple assumption that could be used to specify the generative distribution for each label.\n", "- Multinomial naive Bayes assumes that the features are generated from a simple multinomial distribution.\n", "\n", "$$\n", "p(\\mathbf{x} \\mid L_k) = \\frac{(\\sum_i x_i)!}{\\prod_i x_i !} \\prod_i {p_{ki}}^{x_i}\n", "$$\n", "\n", "The multinomial distribution describes the probability of observing counts among a number of categories, \n", "- multinomial naive Bayes is most appropriate for features that represent counts or count rates.\n", "- The idea is precisely the same as before, but we model the data distribuiton with a best-fit multinomial distribution." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Example: Classifying Text\n", "\n", "One place where multinomial naive Bayes is often used is in ``text classification``\n", "- the features are related to word counts or frequencies within the documents to be classified.\n", " - the extraction of such features from text in [Feature Engineering](05.04-Feature-Engineering.ipynb)\n", "\n", "Using the sparse word count features from the 20 Newsgroups corpus to classify these documents.\n", "- Let's download the data and take a look at the target names:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T00:54:05.725947Z", "start_time": "2018-05-18T00:52:02.457586Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Downloading dataset from http://people.csail.mit.edu/jrennie/20Newsgroups/20news-bydate.tar.gz (14 MB)\n" ] }, { "data": { "text/plain": [ "['alt.atheism',\n", " 'comp.graphics',\n", " 'comp.os.ms-windows.misc',\n", " 'comp.sys.ibm.pc.hardware',\n", " 'comp.sys.mac.hardware',\n", " 'comp.windows.x',\n", " 'misc.forsale',\n", " 'rec.autos',\n", " 'rec.motorcycles',\n", " 'rec.sport.baseball',\n", " 'rec.sport.hockey',\n", " 'sci.crypt',\n", " 'sci.electronics',\n", " 'sci.med',\n", " 'sci.space',\n", " 'soc.religion.christian',\n", " 'talk.politics.guns',\n", " 'talk.politics.mideast',\n", " 'talk.politics.misc',\n", " 'talk.religion.misc']" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.datasets import fetch_20newsgroups\n", "\n", "data = fetch_20newsgroups()\n", "data.target_names" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "For simplicity here, we will select just a few of these categories, and download the training and testing set:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T00:55:05.164406Z", "start_time": "2018-05-18T00:55:04.697003Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "categories = ['talk.religion.misc', 'soc.religion.christian',\n", " 'sci.space', 'comp.graphics']\n", "train = fetch_20newsgroups(subset='train', categories=categories)\n", "test = fetch_20newsgroups(subset='test', categories=categories)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Here is a representative entry from the data:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T00:55:08.217458Z", "start_time": "2018-05-18T00:55:08.213480Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From: dmcgee@uluhe.soest.hawaii.edu (Don McGee)\n", "Subject: Federal Hearing\n", "Originator: dmcgee@uluhe\n", "Organization: School of Ocean and Earth Science and Technology\n", "Distribution: usa\n", "Lines: 10\n", "\n", "\n", "Fact or rumor....? Madalyn Murray O'Hare an atheist who eliminated the\n", "use of the bible reading and prayer in public schools 15 years ago is now\n", "going to appear before the FCC with a petition to stop the reading of the\n", "Gospel on the airways of America. And she is also campaigning to remove\n", "Christmas programs, songs, etc from the public schools. If it is true\n", "then mail to Federal Communications Commission 1919 H Street Washington DC\n", "20054 expressing your opposition to her request. Reference Petition number\n", "\n", "2493.\n", "\n" ] } ], "source": [ "print(train.data[5])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "To convert the content of each string into a vector of numbers.\n", "- Use TF-IDF vectorizer (discussed in [Feature Engineering](05.04-Feature-Engineering.ipynb))\n", "- Create a pipeline that attaches it to a multinomial naive Bayes classifier:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T00:56:32.515878Z", "start_time": "2018-05-18T00:56:32.507211Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "from sklearn.feature_extraction.text import TfidfVectorizer\n", "from sklearn.naive_bayes import MultinomialNB\n", "from sklearn.pipeline import make_pipeline\n", "\n", "model = make_pipeline(TfidfVectorizer(), MultinomialNB())" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "With this pipeline, we can apply the model to the training data, and predict labels for the test data:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T00:57:05.983324Z", "start_time": "2018-05-18T00:57:04.960188Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/datalab/Applications/anaconda/lib/python3.5/site-packages/sklearn/feature_extraction/text.py:1015: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " if hasattr(X, 'dtype') and np.issubdtype(X.dtype, np.float):\n" ] } ], "source": [ "model.fit(train.data, train.target)\n", "labels = model.predict(test.data)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Evaluate the performance of the estimator.\n", "- the confusion matrix between the true and predicted labels for the test data" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T00:57:46.473482Z", "start_time": "2018-05-18T00:57:46.310422Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import confusion_matrix\n", "sns.set_context(\"notebook\", font_scale=1.7)\n", "\n", "mat = confusion_matrix(test.target, labels)\n", "sns.heatmap(mat.T, square=True, annot=True, fmt='d', cbar=False,\n", " xticklabels=train.target_names, yticklabels=train.target_names)\n", "plt.xlabel('true label')\n", "plt.ylabel('predicted label');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Evidently, even this very simple classifier can successfully separate space talk from computer talk, \n", "- but it gets confused between talk about religion and talk about Christianity.\n", "- This is perhaps an expected area of confusion!\n", "\n", "### The very cool thing here\n", "we now have the tools to determine the category for *any* string\n", "- using the ``predict()`` method of this pipeline.\n", "\n", "Here's a quick utility function that will return the prediction for a single string:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T01:00:14.856206Z", "start_time": "2018-05-18T01:00:14.852395Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "def predict_category(s, train=train, model=model):\n", " pred = model.predict([s])\n", " return train.target_names[pred[0]]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's try it out:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T01:00:19.062296Z", "start_time": "2018-05-18T01:00:19.055232Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/datalab/Applications/anaconda/lib/python3.5/site-packages/sklearn/feature_extraction/text.py:1015: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " if hasattr(X, 'dtype') and np.issubdtype(X.dtype, np.float):\n" ] }, { "data": { "text/plain": [ "'sci.space'" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "predict_category('sending a payload to the ISS')" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T01:00:33.991007Z", "start_time": "2018-05-18T01:00:33.984095Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/datalab/Applications/anaconda/lib/python3.5/site-packages/sklearn/feature_extraction/text.py:1015: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " if hasattr(X, 'dtype') and np.issubdtype(X.dtype, np.float):\n" ] }, { "data": { "text/plain": [ "'soc.religion.christian'" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "predict_category('discussing islam vs atheism')" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2018-05-18T01:00:40.945263Z", "start_time": "2018-05-18T01:00:40.938345Z" }, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/datalab/Applications/anaconda/lib/python3.5/site-packages/sklearn/feature_extraction/text.py:1015: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " if hasattr(X, 'dtype') and np.issubdtype(X.dtype, np.float):\n" ] }, { "data": { "text/plain": [ "'comp.graphics'" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "predict_category('determining the screen resolution')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Remember that this is nothing more sophisticated than a simple probability model for the (weighted) frequency of each word in the string; \n", "- nevertheless, the result is striking.\n", "\n", "> ## Even a very naive algorithm, when used carefully and trained on a large set of high-dimensional data, can be surprisingly effective." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## When to Use Naive Bayes\n", "\n", "Because naive Bayesian classifiers make such stringent assumptions about data, they will generally not perform as well as a more complicated model.\n", "\n", "Advantages:\n", "\n", "- They are extremely fast for both training and prediction\n", "- They provide straightforward probabilistic prediction\n", "- They are often very easily interpretable\n", "- They have very few (if any) tunable parameters" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## When to Use Naive Bayes\n", "\n", "\n", "A good choice as an initial baseline classification.\n", "- If it performs suitably, then congratulations: you have a very fast, very interpretable classifier for your problem.\n", "- If it does not perform well, then you can begin exploring more sophisticated models, with some baseline knowledge of how well they should perform.\n", "\n", "Naive Bayes classifiers tend to perform especially well in one of the following situations:\n", "\n", "- When the naive assumptions actually match the data (very rare in practice)\n", "- For very well-separated categories, when model complexity is less important\n", "- For very high-dimensional data, when model complexity is less important\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## When to Use Naive Bayes\n", "\n", "The last two points seem distinct, but they actually are related: \n", "- as the dimension of a dataset grows, it is much less likely for any two points to be found close together (after all, they must be close in *every single dimension* to be close overall).\n", "- clusters in high dimensions tend to be more separated, on average, than clusters in low dimensions, assuming the new dimensions actually add information.\n", "\n", "> ## simplistic classifiers like naive Bayes tend to work as well or better than more complicated classifiers as the dimensionality grows: once you have enough data, even a simple model can be very powerful." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "\n", "< [Feature Engineering](05.04-Feature-Engineering.ipynb) | [Contents](Index.ipynb) | [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) >" ] } ], "metadata": { "anaconda-cloud": {}, "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python [default]", "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": "3.5.4" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }