Introduction.ipynb

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    "\n",
    "# What is Machine Learning?\n",
    "___\n",
    "\n",
    "As a scientific endeavour, machine learning is a sub-field that grew out of the quest for artificial intelligence. In the early days of AI as an academic discipline, some researchers wanted to make inroads in the field by having machines learn from data. This is simplistically, how machine learning can be described; the study and construction of algorithms that can learn from and make predictions on data. Such algorithms operate by building a model from example inputs in order to make data-driven predictions or decisions expressed as outputs. \n",
    "\n",
    "Arthur Samuel, a computer scientist who pioneered the study of artificial intelligence, said that machine learning is \"the study that gives computers the ability to learn without being explicitly programmed.\" Throughout the 1950s and 1960s, Samuel developed programs that played checkers. While the rules of checkers are simple, complex strategies are required to defeat skilled opponents. Samuel never explicitly programmed these strategies, but through the experience of playing thousands of games, the program learned complex behaviors that allowed it to beat many human opponents.\n",
    "\n",
    "Tom M. Mitchell provided a widely quoted, a more formal definition of Machine Learning as: \"A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E\". \n",
    "Any machine learning problem can be represented with these three concepts:\n",
    "\n",
    "* We will have to learn to solve a task T. For example, build a spam filter that learns to classify e-mails as spam or ham.\n",
    "* We will need some experience E to learn to perform the task. Usually, experience is represented through a dataset. For the spam filter, experience comes as a set of e-mails, manually classified by a human as spam or ham.\n",
    "* We will need a measure of performance P to know how well we are solving the task and also to know whether after doing some modifications, our results are improving or getting worse. The percentage of e-mails that our spam filtering is correctly classifying as spam or ham could be P for our spam-filtering task.\n",
    "\n",
    "Another example would be: \n",
    "Assume that you have a collection of pictures. Each picture depicts either a dog or cat. A task could be sorting the pictures into separate collections of dog and cat photos. A program could learn to perform this task by observing pictures that have already been sorted, and it could evaluate its performance by calculating the percentage of correctly classified pictures.\n",
    "\n",
    "In this age of modern technology, there is one resource that we have in abundance: a large amount of structured and unstructured data. In the second half of the twentieth century, machine learning evolved as a subfield of artificial intelligence that involved the development of self-learning algorithms to gain knowledge from that data in order to make predictions. Instead of requiring humans to manually derive rules and build models from analyzing large amounts of data, machine learning offers a more efficient alternative for capturing the knowledge in data to gradually improve the performance of predictive models, and make data-driven decisions. Not only is machine learning becoming increasingly important in computer science research but it also plays an ever greater role in our everyday life. Thanks to machine learning, we enjoy robust e-mail spam filters, personal assistants, reliable Web search engines, challenging chess players, and, hopefully soon, safe and efficient self-driving cars.\n",
    "In my opinion, machine learning, the application and science of algorithms that makes sense of data, is the most exciting field of all the computer sciences! We are living in an age where data comes in abundance; using the self-learning algorithms from the field of machine learning, we can turn this data into knowledge. Thanks to the many powerful open source libraries that have been developed in recent years, there has probably never been a better time to break into the machine learning field and learn how to utilize powerful algorithms to spot patterns in data and make predictions about future events.\n",
    "\n",
    "___\n",
    "# So how this website can help you?\n",
    "Maybe you are in general interested in machine learning and for some time you have been reading blogs and articles about it. Everything seems great as you discover an exciting field ,that can help you to solve many different problems.  However, given the ocean of resources regarding machine learning on the internet, you start thinking- Which of the myriad of algorithms should you actually choose? What to do when you have different sizes of data? How can you get optimal results? etc. Maybe the availability of so many resources out there has put you in a spot of bother. Don't worry, most of the beginners in the machine learning field have been there. If the depth of the field seems too overwhelming and you wish to understand all the main techniques by actually implementing them on different datasets and see the amazing results on your own, then you've come to the right place. As the name suggests, this section and most parts of the website would help you to get hands-on knowledge so that you \"learn by experience\" just like the machine learning algorithms ;).  Along with the codes to tackle different sets of problems, mathematical or statistical theory would be introduced wherever essential. \n",
    "\n",
    "As you will see that doing the fun stuff, that is, using and tweaking machine learning algorithms such as support vector machines, nearest neighbor search, or ensembles thereof, will\n",
    "only consume a tiny fraction of the overall time of a good machine learning expert.\n",
    "Looking at the following typical workflow, we see that most of the time will be spent in rather mundane but important tasks:\n",
    "                                  \n",
    "1. Reading in the data and cleaning it\n",
    "2. Exploring and understanding the input data\n",
    "3. Analyzing how best to present the data to the learning algorithm\n",
    "4. Choosing the right model and learning algorithm\n",
    "5. Measuring the performance correctly\n",
    "                                  \n",
    "When talking about exploring and understanding the input data, we will need a bit of statistics and basic math. However, while doing that, you will see that those topics that seemed to be so dry in your math class can actually be really exciting when you use them to look at interesting data.\n",
    "                                  \n",
    "1) The journey starts when you read in the data. When you have to answer questions such as how to handle invalid or missing values, you will see that this is more an art than a precise science. And a very rewarding one, as doing this part right will open your data to more machine learning algorithms and thus increase the likelihood of success.\n",
    "                                  \n",
    "2) With the data being ready in your program's data structures, you will want to get a real feeling of the data you are working with. Do you have enough data to answer your questions? If not, you might want to think about additional ways to get more of it. Do you even have too much data? Then you probably want to think about how best to extract a sample of it.\n",
    "                                  \n",
    "3) Often you will not feed the data directly into your machine learning algorithm. Instead you will find that you can refine parts of the data before training. Many times the machine learning algorithm will reward you with increased performance. You will even find that a simple algorithm with refined data generally outperforms a very sophisticated algorithm with raw data. This part of the machine learning workflow is called feature engineering, and is most of the time a very exciting and rewarding challenge. You will immediately see the results of being creative and intelligent.\n",
    "                                  \n",
    "4) Choosing the right learning algorithm, then, is not simply a shootout of the three or four that are in your toolbox (there will be more you will see). It is more a thoughtful process of weighing different performance and functional requirements. Do you need a fast result and are willing to sacrifice quality? Or would you rather spend more time to get the best possible result? Do you have a clear idea of the future data or should you be a bit more conservative on that side?\n",
    "\n",
    "5) Finally, measuring the performance is the part where most mistakes are waiting for the aspiring machine learner. There are easy ones, such as testing your approach with the same data on which you have trained. But there are more difficult ones, when you have imbalanced training data. Again, data is the part that determineswhether your undertaking will fail or succeed.\n",
    "\n",
    "To that end, we will not overwhelm you with the theoretical aspects of the diverse ML algorithms, as there are already excellent books in that area (you can take a look here: <a href= \"https://github.com/josephmisiti/awesome-machine-learning\">References</a>). Instead, we will try to provide an intuition of the underlying approaches in the individual chapters — just enough for you to get the idea and be able to undertake your first steps. Hence, this website is by no means the definitive guide to machine learning but more of a practical playground where you would learn to apply almost all the important algorithms to real life problems. I hope this website would be helpful to you in understanding the key concepts and would keep you eager to learn even more in this fascinating field of Machine Learning.   \n",
    "\n",
    "\n",
    "## Why Python?\n",
    "                                  \n",
    "As you will see later, the process of coming up with a decent ML approach is never a waterfall-like process. Instead, you will see yourself going back and forth in your\n",
    "analysis, trying out different versions of your input data on diverse sets of ML algorithms. It is this explorative nature that lends itself perfectly to Python. \n",
    "Python is one of the most popular programming languages for data science and therefore enjoys a large number of useful add-on libraries developed by its great community. Although the performance of interpreted languages, such as Python, for computation-intensive tasks is inferior to lower-level programming languages, extension libraries such as NumPy and SciPy have been developed that build upon lower layer Fortran and C implementations for fast and vectorized operations on multidimensional arrays. For machine learning programming tasks, we will mostly refer to the scikit-learn library, which is one of the most popular and accessible open source machine learning libraries as of today.\n",
    "__\n",
    "\n",
    "## Scikit Learn\n",
    "\n",
    "Scikit-learn is an open source Python library of popular machine learning algorithms that will allow us to build these types of systems. The project was started in 2007\n",
    "as a Google Summer of Code project by David Cournapeau. Later that year, Matthieu Brucher started working on this project as part of his thesis. In 2010, Fabian Pedregosa,\n",
    "Gael Varoquaux, Alexandre Gramfort, and Vincent Michel of INRIA took the project leadership and produced the first public release. Nowadays, the project is being developed very actively by an enthusiastic community of contributors. It is built upon NumPy (http://www.numpy.org/) and SciPy (http://scipy.org/), the standard Python libraries for scientific computation. Through this book, we will use it to show you how the incorporation of previous data as a source of experience could serve to solve several common programming tasks in an efficient and probably more effective way.\n",
    "\n",
    "In the following sections of this chapter, we will start viewing how to install scikit-learn and prepare your working environment. After that, we will have a brief introduction to machine learning in a practical way, trying to introduce key machine learning concepts while tackling real life problems.\n",
    "___"
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    "## Installing scikit-learn\n",
    "\n",
    "Installation instructions for scikit-learn are available at http://scikit-learn.org/\n",
    "stable/install.html. Several examples in this book include visualizations, so\n",
    "you should also install the matplotlib package from http://matplotlib.org/.\n",
    "We also recommend installing IPython Notebook, a very useful tool that includes a\n",
    "web-based console to edit and run code snippets, and render the results. The source\n",
    "code that comes with this book is provided through IPython notebooks.\n",
    "\n",
    "An easy way to install all packages is to download and install the Anaconda\n",
    "distribution for scientific computing from https://store.continuum.io/, which\n",
    "provides all the necessary packages for Linux, Mac, and Windows platforms. Or, if\n",
    "you prefer, the following sections gives some suggestions on how to install every\n",
    "package on each particular platform.\n",
    "\n",
    "### Linux\n",
    "\n",
    "Probably the easiest way to install our environment is through the operating system\n",
    "packages. In the case of Debian-based operating systems, such as Ubuntu, you can\n",
    "install the packages by running the following commands:\n",
    "* Firstly, to install the package we enter the following command:\n",
    ">_ sudo apt-get install build-essential python-dev python-numpy python-setuptools python-scipy libatlas-dev _\n",
    "* Then, to install matplotlib, run the following command:\n",
    ">_ sudo apt-get install python-matplotlib _\n",
    "* After that, we should be ready to install scikit-learn by issuing this command:\n",
    ">_ sudo pip install scikit-learn _\n",
    "* To install IPython Notebook, run the following command:\n",
    ">_ sudo apt-get install ipython-notebook _\n",
    "* If you want to install from source, let's say to install all the libraries within a virtual environment, you should issue the following commands:\n",
    ">_ pip install numpy _\n",
    ">_ pip install scipy _\n",
    ">_ pip install scikit-learn _\n",
    "* To install Matplotlib, you should run the following commands:\n",
    ">_ pip install libpng-dev libjpeg8-dev libfreetype6-dev _\n",
    ">_ pip install matplotlib _\n",
    "* To install IPython Notebook, you should run the following commands:\n",
    ">_ pip install ipython _\n",
    ">_ pip install tornado _\n",
    ">_ pip install pyzmq _\n",
    "\n",
    "### Mac\n",
    "\n",
    "You can similarly use tools such as MacPorts and HomeBrew that contain\n",
    "precompiled versions of these packages.\n",
    "\n",
    "### Windows\n",
    "To install scikit-learn on Windows, you can download a Windows installer from the\n",
    "downloads section of the project web page: http://sourceforge.net/projects/scikit-learn/files/\n",
    "\n",
    "### Checking your installation\n",
    "To check that everything is ready to run, just open your Python (or probably better, IPython) console and type the following:"
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   "source": [
    "import sklearn as sk\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
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    "Python will silently import the scikit-learn, NumPy, and matplotlib\n",
    "packages, which we will use through the rest of this book's examples.\n",
    "\n",
    "If you want to execute the code presented in this book, you should run\n",
    "IPython Notebook:\n",
    ">_ ipython notebook _\n",
    "\n",
    "This will allow you to open the corresponding notebooks right in your browser.\n",
    "\n",
    "### Installing pandas and matplotlib\n",
    "\n",
    "pandas is an open source library that provides data structures and analysis tools for\n",
    "Python. pandas is a powerful library, and several books describe how to use pandas\n",
    "for data analysis. We will use a few of panda's convenient tools for importing data\n",
    "and calculating summary statistics.\n",
    "\n",
    "pandas can be installed on Windows, OS X, and Linux using pip with the\n",
    "following command:\n",
    "\n",
    ">_ pip install pandas _\n",
    "\n",
    "pandas can also be installed on Debian- and Ubuntu-based Linux distributions using\n",
    "the following command:\n",
    "\n",
    ">_ apt-get install python-pandas _\n",
    "\n",
    "matplotlib is a library used to easily create plots, histograms, and other charts with\n",
    "Python. We will use it to visualize training data and models. matplotlib has several\n",
    "dependencies. Like pandas, matplotlib depends on NumPy, which should already\n",
    "be installed. On Debian- and Ubuntu-based Linux distributions, matplotlib and its\n",
    "dependencies can be installed using the following command:\n",
    "\n",
    ">_ apt-get install python-matplotlib _ \n",
    "\n",
    "Binaries for OS X and Windows can be downloaded from http://matplotlib.org/downloads.html."
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    "## Machine learning categories\n",
    "<img src=\"images/sklcheatsheet.png\">\n",
    "\n",
    "## The three different types of machine learning\n",
    "\n",
    "In this section, we will take a look at the three types of machine learning: supervised learning, unsupervised learning, and reinforcement learning. We will learn about the fundamental differences between the three different learning types and, using conceptual examples, we will develop an intuition for the practical problem domains where these can be applied:\n",
    "<img src=\"images/types.png\">\n",
    "\n",
    "## Making predictions about the future with supervised learning\n",
    "\n",
    "The main goal in supervised learning is to learn a model from labeled training data that allows us to make predictions about unseen or future data. Here, the term supervised refers to a set of samples where the desired output signals (labels) are already known.\n",
    "\n",
    "Considering the example of e-mail spam filtering, we can train a model using a supervised machine learning algorithm on a corpus of labeled e-mail, e-mail that are correctly marked as spam or not-spam, to predict whether a new e-mail belongs to either of the two categories. A supervised learning task with discrete class labels, such as in the previous e-mail spam-filtering example, is also called a classification task. Another subcategory of supervised learning is regression, where the outcome signal is a continuous value:\n",
    "\n",
    "<img src=\"images/supervised.png\">\n",
    "\n",
    "### Classification for predicting class labels\n",
    "\n",
    "In classification tasks the program must learn to predict discrete values for the response variables from one or more explanatory variables. That is, the program must predict the most probable category, class, or label for new observations. \n",
    "\n",
    "Classification is a subcategory of supervised learning where the goal is to predict the categorical class labels of new instances based on past observations. Those class labels are discrete, unordered values that can be understood as the group memberships of the instances. The previously mentioned example of e-mail-spam detection represents a typical example of a binary classification task, where the machine learning algorithm learns a set of rules in order to distinguish between two possible classes: spam and non-spam e-mail.\n",
    "\n",
    "However, the set of class labels does not have to be of a binary nature. The predictive model learned by a supervised learning algorithm can assign any class label that was presented in the training dataset to a new, unlabeled instance. A typical example of a multi-class classification task is handwritten character recognition. Here, we could collect a training dataset that consists of multiple handwritten examples of each letter in the alphabet. Now, if a user provides a new handwritten character via an input device, our predictive model will be able to predict the correct letter in the alphabet with certain accuracy. However, our machine learning system would be unable to correctly recognize any of the digits zero to nine, for example, if they were not part of our training dataset.\n",
    "\n",
    "The following figure illustrates the concept of a binary classification task given 30 training samples: 15 training samples are labeled as negative class (circles) and 15 training samples are labeled as positive class (plus signs). In this scenario, our dataset is two-dimensional, which means that each sample has two values associated with it: 1x and 2x. Now, we can use a supervised machine learning algorithm to learn a rule—the decision boundary represented as a black dashed line—that can separate those two classes and classify new data into each of those two categories given its 1x and 2x values:\n",
    "\n",
    "<img src=\"images/classification.png\">\n",
    "\n",
    "Other applications of classification include predicting whether a stock's price will rise or fall, or deciding if a news article belongs to the politics or leisure section. \n",
    "\n",
    "### Regression for predicting continuous outcomes\n",
    "We learned in the previous section that the task of classification is to assign categorical, unordered labels to instances. A second type of supervised learning is the prediction of continuous outcomes, which is also called regression analysis. In regression analysis, we are given a number of predictor (explanatory) variables and a continuous response variable (outcome), and we try to find a relationship between those variables that allows us to predict an outcome.\n",
    "\n",
    "For example, let's assume that we are interested in predicting the Math SAT scores of our students. If there is a relationship between the time spent studying for the test and the final scores, we could use it as training data to learn a model that uses the study time to predict the test scores of future students who are planning to take this test.\n",
    "\n",
    "The following figure illustrates the concept of linear regression. Given a predictor variable x and a response variable y, we fit a straight line to this data that minimizes the distance—most commonly the average squared distance—between the sample points and the fitted line. We can now use the intercept and slope learned from this data to predict the outcome variable of new data:\n",
    "\n",
    "<img src=\"images/regression.png\">\n",
    "\n",
    "In regression problems the program must predict the value of a continuous response variable. Examples of regression problems include predicting the sales for a new product, or the salary for a job based on its description. Similar to classification, regression problems require supervised learning.\n",
    "\n",
    "\n",
    "### Solving interactive problems with reinforcement learning\n",
    "Another type of machine learning is reinforcement learning. In reinforcement learning, the goal is to develop a system (agent) that improves its performance based on interactions with the environment. Since the information about the current state of the environment typically also includes a so-called reward signal, we can think of reinforcement learning as a field related to supervised learning. However, in reinforcement learning this feedback is not the correct ground truth label or value, but a measure of how well the action was measured by a reward function. Through the interaction with the environment, an agent can then use reinforcement learning to learn a series of actions that maximizes this reward via an exploratory trial-and-error approach or deliberative planning.\n",
    "\n",
    "A popular example of reinforcement learning is a chess engine. Here, the agent decides upon a series of moves depending on the state of the board (the environment), and the reward can be defined as win or lose at the end of the game:\n",
    "\n",
    "<img src=\"images/reinforcement.png\">\n",
    "\n",
    " An example of reinforcement learning would be a program that learns to play a side-scrolling video game such as Super Mario Bros. may receive a reward when it completes a level or exceeds a certain score, and a punishment when it loses a life. However, this supervised feedback is not associated with specific decisions to run, avoid Goombas, or pick up fire flowers. \n",
    " \n",
    " Some types of problems, called semi-supervised learning problems, make use of both supervised and unsupervised data; these problems are located on the spectrum between supervised and unsupervised learning. While this book will discuss semi-supervised learning, we will focus primarily on supervised and unsupervised learning, as these categories include most the common machine learning problems. In the next sections, we will review supervised and unsupervised learning in more detail.\n",
    "\n",
    "\n",
    "### Discovering hidden structures with unsupervised learning\n",
    "In supervised learning, we know the right answer beforehand when we train our model, and in reinforcement learning, we define a measure of reward for particular actions by the agent. In unsupervised learning, however, we are dealing with unlabeled data or data of unknown structure. Using unsupervised learning techniques, we are able to explore the structure of our data to extract meaningful information without the guidance of a known outcome variable or reward function.\n",
    "\n",
    "#### Finding subgroups with clustering\n",
    "Clustering is an exploratory data analysis technique that allows us to organize a pile of information into meaningful subgroups (clusters) without having any prior knowledge of their group memberships. Each cluster that may arise during the analysis defines a group of objects that share a certain degree of similarity but are more dissimilar to objects in other clusters, which is why clustering is also sometimes called \"unsupervised classification.\" Clustering is a great technique for structuring information and deriving meaningful relationships among data, For example, it allows marketers to discover customer groups based on their interests in order to develop distinct marketing programs.\n",
    "\n",
    "Clustering is often used to explore a dataset. For example, given a collection of movie reviews, a clustering algorithm might discover sets of positive and negative reviews. The system will not be able to label the clusters as \"positive\" or \"negative\"; without supervision, it will only have knowledge that the grouped observations are similar to each other by some measure. A common application of clustering is discovering segments of customers within a market for a product. By understanding what attributes are common to particular groups of customers, marketers can decide what aspects of their campaigns need to be emphasized. Clustering is also used by Internet radio services; for example, given a collection of songs, a clustering algorithm might be able to group the songs according to their genres. Using different similarity measures, the same clustering algorithm might group the songs by their keys, or by the instruments they contain.\n",
    "\n",
    "The figure below illustrates how clustering can be applied to organizing unlabeled data into three distinct groups based on the similarity of their features 1x and 2x:\n",
    "\n",
    "<img src=\"images/clustering.png\">\n",
    "\n",
    "#### Dimensionality reduction for data compression\n",
    "\n",
    "Another subfield of unsupervised learning is dimensionality reduction. Often we are working with data of high dimensionality—each observation comes with a high number of exploratory variables or measurements—that can present a challenge for limited storage space and the computational performance of machine learning algorithms. Unsupervised dimensionality reduction is a commonly used approach in feature preprocessing to remove noise from data, which can also degrade the predictive performance of certain algorithms, and compress the data onto a smaller dimensional subspace while retaining most of the relevant information. Dimensionality reduction is the process of discovering the explanatory variables that account for the greatest changes in the response variable.\n",
    "\n",
    "Sometimes, dimensionality reduction can also be useful for visualizing data—for example, a high-dimensional feature set can be projected onto one-, two-, or\n",
    "three-dimensional feature spaces in order to visualize it via 3D- or 2D-scatterplots or histograms. The figure below shows an example where non-linear dimensionality reduction was applied to compress a 3D Swiss Roll onto a\n",
    "new 2D feature subspace:\n",
    "\n",
    "<img src=\"images/dr.png\">\n",
    "\n",
    "It is easy to visualize a regression problem such as predicting the price of a home from its size; the size of the home can be plotted on the graph's x axis, and the price of the home can be plotted on the y axis. Similarly, it is easy to visualize the housing price regression problem when a second explanatory variable is added. The number of bathrooms in the house could be plotted on the z axis, for instance. A problem with thousands of explanatory variables, however, becomes impossible to visualize."
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    "___\n",
    "## A roadmap for building machine learning systems\n",
    "\n",
    "In the previous sections, we discussed the basic concepts of machine learning and the three different types of learning. In this section, we will discuss other important parts of a machine learning system accompanying the learning algorithm. The diagram below shows a typical workflow diagram for using machine learning in predictive modeling, which we will discuss in the following subsections:\n",
    "\n",
    "<img src=\"images/preprocessing.png\">\n",
    "\n",
    "### Preprocessing – getting data into shape\n",
    "\n",
    "Raw data rarely comes in the form and shape that is necessary for the optimal performance of a learning algorithm. Thus, the preprocessing of the data is one of the most crucial steps in any machine learning application. If we take the Iris flower dataset from the previous section as an example, we could think of the raw data as a series of flower images from which we want to extract meaningful features. Useful features could be the color, the hue, the intensity of the flowers, the height, and the flower lengths and widths. Many machine learning algorithms also require that the selected features are on the same scale for optimal performance, which is often achieved by transforming the features in the range [0, 1] or a standard normal distribution with zero mean and unit variance, as we will see in the later chapters.\n",
    "\n",
    "Some of the selected features may be highly correlated and therefore redundant to a certain degree. In those cases, dimensionality reduction techniques are useful for compressing the features onto a lower dimensional subspace. Reducing the dimensionality of our feature space has the advantage that less storage space is required, and the learning algorithm can run much faster.\n",
    "\n",
    "To determine whether our machine learning algorithm not only performs well on the training set but also generalizes well to new data, we also want to randomly divide the dataset into a separate training and test set. We use the training set to train and optimize our machine learning model, while we keep the test set until the very end to evaluate the final model.\n",
    "\n",
    "### Training and selecting a predictive model\n",
    "\n",
    "As we will see in later chapters, many different machine learning algorithms have been developed to solve different problem tasks. An important point that can be summarized from David Wolpert's famous No Free Lunch Theorems is that we can't get learning \"for free\" (The Lack of A Priori Distinctions Between Learning Algorithms, D.H. Wolpert 1996; No Free Lunch Theorems for Optimization, D.H. Wolpert and W.G. Macready, 1997). Intuitively, we can relate this concept to the popular saying, \"I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it\n",
    "were a nail\" (Abraham Maslow, 1966). For example, each classification algorithm has its inherent biases, and no single classification model enjoys superiority if we don't make any assumptions about the task. In practice, it is therefore essential to compare at least a handful of different algorithms in order to train and select the\n",
    "best performing model. But before we can compare different models, we first\n",
    "have to decide upon a metric to measure performance. One commonly used\n",
    "metric is classification accuracy, which is defined as the proportion of correctly classified instances.\n",
    "\n",
    "One legitimate question to ask is: how do we know which model performs well on the\n",
    "final test dataset and real-world data if we don't use this test set for the model selection but keep it for the final model evaluation? In order to address the issue embedded in this question, different cross-validation techniques can be used where the training dataset is further divided into training and validation subsets in order to estimate the generalization performance of the model. Finally, we also cannot expect that the default parameters of the different learning algorithms provided by software libraries are optimal for our specific problem task. Therefore, we will make frequent use of hyperparameter optimization techniques that help us to fine-tune the performance of our model in later chapters. Intuitively, we can think of those hyperparameters as parameters that are not learned from the data but represent the knobs of a model\n",
    "that we can turn to improve its performance, which will become much clearer in\n",
    "later chapters when we see actual examples.\n",
    "\n",
    "### Evaluating models and predicting unseen data instances\n",
    "After we have selected a model that has been fitted on the training dataset, we can use the test dataset to estimate how well it performs on this unseen data to estimate the generalization error. If we are satisfied with its performance, we can now use this model to predict new, future data. It is important to note that the parameters for the previously mentioned procedures—such as feature scaling and dimensionality reduction—are solely obtained from the training dataset, and the same parameters are later re-applied to transform the test dataset, as well as any new data samples—the performance measured on the test data may be overoptimistic otherwise.\n",
    "\n",
    "___\n",
    "\n",
    "## Important concepts related to machine learning\n",
    "The linear classifier we presented in the previous section could look too simple.\n",
    "What if we use a higher degree polynomial? What if we also take as features not\n",
    "only the sepal length and width, but also the petal length and the petal width?\n",
    "This is perfectly possible, and depending on the sample distribution, it could lead\n",
    "to a better fit to the training data, resulting in higher accuracy. The problem with\n",
    "this approach is that now we must estimate not only the three original parameters\n",
    "(the coefficients for x1, x2, and the interception point), but also the parameters for\n",
    "the new features x3 and x4 (petal length and width) and also the product\n",
    "combinations of the four features.\n",
    "\n",
    "Intuitively, we would need more training data to adequately estimate these\n",
    "parameters. The number of parameters (and consequently, the amount of training\n",
    "data needed to adequately estimate them) would rapidly grow if we add more\n",
    "features or higher order terms. This phenomenon, present in every machine learning\n",
    "method, is called the idem curse of dimensionality: when the number of parameters\n",
    "of a model grows, the data needed to learn them grows exponentially.\n",
    "\n",
    "This notion is closely related to the problem of overfitting mentioned earlier. As our\n",
    "training data is not enough, we risk producing a model that could be very good at\n",
    "predicting the target class on the training dataset but fail miserably when faced with\n",
    "new data, that is, our model does not have the generalization power. That is why it is\n",
    "so important to evaluate our methods on previously unseen data.\n",
    "The general rule is that, in order to avoid overfitting, we should prefer simple (that\n",
    "is, with less parameters) methods, something that could be seen as an instantiation\n",
    "of the philosophical principle of Occam's razor, which states that among competing\n",
    "hypotheses, the hypothesis with the fewest assumptions should be selected.\n",
    "However, we should also take into account Einstein's words:\n",
    "\n",
    "> \"Everything should be made as simple as possible, but not simpler.\"\n",
    "\n",
    "The idem curse of dimensionality may suggest that we keep our models simple,\n",
    "but on the other hand, if our model is too simple we run the risk of suffering\n",
    "from underfitting. Underfitting problems arise when our model has such a low\n",
    "representation power that it cannot model the data even if we had all the training\n",
    "data we want. We clearly have underfitting when our algorithm cannot achieve good\n",
    "performance measures even when measuring on the training set.\n",
    "\n",
    "As a result, we will have to achieve a balance between overfitting and underfitting.\n",
    "This is one of the most important problems that we will have to address when\n",
    "designing our machine learning models.\n",
    "\n",
    "Other key concepts to take into account are the idem bias and variance of a machine\n",
    "learning method. Consider an extreme method that, in a binary classification setting,\n",
    "always predicts the positive class for any new instance. Its predictions are, trivially,\n",
    "always the same, or in statistical terms, it has null variance; but it will fail to predict\n",
    "negative examples: it is very biased towards positive results. On the other hand,\n",
    "consider a method that predicts, for a new instance, the class of the nearest instance\n",
    "in the training set (in fact, this method exists, and it is called the 1-nearest neighbor).\n",
    "\n",
    "The generalization assumptions that this method uses are very small: it has a very\n",
    "low bias; but, if we change the training data, results could dramatically change,\n",
    "that is, its variance is very high. These are extreme examples of the bias-variance\n",
    "tradeoff. It can be shown that, no matter which method we are using, if we reduce\n",
    "bias, variance will increase, and vice versa.\n",
    "\n",
    "Linear classifiers have generally low-variance: no matter what subset we select for\n",
    "training, results will be similar. However, if the data distribution (as in the case of the\n",
    "versicolor and virginica species) makes target classes not separable by a hyperplane,\n",
    "these results will be consistently wrong, that is, the method is highly biased.\n",
    "\n",
    "On the other hand, kNN (a memory-based method we will not address in this book)\n",
    "has very low bias but high variance: the results are generally very good at describing\n",
    "training data but tend to vary greatly when trained on different training instances.\n",
    "There are other important concepts related to real-world applications where our\n",
    "data will not come naturally as a list of real-valued features. In these cases, we will\n",
    "need to have methods to transform non real-valued features to real-valued ones.\n",
    "\n",
    "Besides, there are other steps related to feature standardization and normalization,\n",
    "which as we saw in our Iris example, are needed to avoid undesired effects regarding\n",
    "the different value ranges. These transformations on the feature space are known as\n",
    "data preprocessing.\n",
    "\n",
    "After having a defined feature set, we will see that not all of the features that\n",
    "come in our original dataset could be useful for resolving our task. So we must also\n",
    "have methods to do feature selection, that is, methods to select the most\n",
    "promising features.\n",
    "\n",
    "In the subsequent sections, we will present several problems and in each of them we will show\n",
    "different ways to transform and find the most relevant features to use for learning\n",
    "a task, called feature engineering, which is based on our knowledge of the domain\n",
    "of the problem and/or data analysis methods. These methods, often not valued\n",
    "enough, are a fundamental step toward obtaining good results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "## Datasets\n",
    "\n",
    "As we have said, machine learning methods rely on previous experience, usually\n",
    "represented by a dataset. Every method implemented on scikit-learn assumes that\n",
    "data comes in a dataset, a certain form of input data representation that makes it\n",
    "easier for the programmer to try different methods on the same data. Scikit-learn\n",
    "includes a few well-known datasets. In this chapter, we will use one of them, the\n",
    "Iris flower dataset, introduced in 1936 by Sir Ronald Fisher to show how a statistical\n",
    "method (discriminant analysis) worked (yes, they were into data before it was big).\n",
    "You can find a description of this dataset on its own Wikipedia page, but, essentially,\n",
    "it includes information about 150 elements (or, in machine learning terminology,\n",
    "instances) from three different Iris flower species, including sepal and petal length\n",
    "and width. The natural task to solve using this dataset is to learn to guess the Iris\n",
    "species knowing the sepal and petal measures. It has been widely used on machine\n",
    "learning tasks because it is a very easy dataset in a sense that we will see later. Let's\n",
    "import the dataset and show the values for the first instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150L, 4L) (150L,)\n",
      "[ 5.1  3.5  1.4  0.2] 0\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "X_iris, y_iris = iris.data, iris.target\n",
    "print X_iris.shape, y_iris.shape\n",
    "print X_iris[0], y_iris[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the iris dataset is an object (similar to a dictionary) that has two\n",
    "main components:\n",
    "    \n",
    "* A data array, where, for each instance, we have the real values for sepal length, sepal width, petal length, and petal width, in that order (note that for efficiency reasons, scikit-learn methods work on NumPy ndarrays instead of the more descriptive but much less efficient Python dictionaries or lists). The shape of this array is (150, 4), meaning that we have 150 rows (one for each instance) and four columns (one for each feature).\n",
    "* A target array, with values in the range of 0 to 2, corresponding to each instance of Iris species (0: setosa, 1: versicolor, and 2: virginica), as you can verify by printing the iris.target.target_names value.\n",
    "\n",
    "While it's not necessary for every dataset we want to use with scikit-learn to have\n",
    "this exact structure, we will see that every method will require this data array, where\n",
    "each instance is represented as a list of features or attributes, and another target array\n",
    "representing a certain value we want our learning method to learn to predict. In\n",
    "our example, the petal and sepal measures are our real-valued attributes, while the\n",
    "flower species is the one-of-a-list class we want to predict."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training data and test data\n",
    "\n",
    "The observations in the training set comprise the experience that the algorithm uses\n",
    "to learn. In supervised learning problems, each observation consists of an observed\n",
    "response variable and one or more observed explanatory variables.\n",
    "\n",
    "The test set is a similar collection of observations that is used to evaluate the\n",
    "performance of the model using some performance metric. It is important that no\n",
    "observations from the training set are included in the test set. If the test set does contain\n",
    "examples from the training set, it will be difficult to assess whether the algorithm has\n",
    "learned to generalize from the training set or has simply memorized it. A program that\n",
    "generalizes well will be able to effectively perform a task with new data. In contrast, a\n",
    "program that memorizes the training data by learning an overly complex model could\n",
    "predict the values of the response variable for the training set accurately, but will fail\n",
    "to predict the value of the response variable for new examples.\n",
    "\n",
    "Memorizing the training set is called over-fitting. A program that memorizes its\n",
    "observations may not perform its task well, as it could memorize relations and\n",
    "structures that are noise or coincidence. Balancing memorization and generalization,\n",
    "or over-fitting and under-fitting, is a problem common to many machine learning\n",
    "algorithms. In later chapters we will discuss regularization, which can be applied to\n",
    "many models to reduce over-fitting.\n",
    "\n",
    "In addition to the training and test data, a third set of observations, called a validation\n",
    "or hold-out set, is sometimes required. The validation set is used to tune variables\n",
    "called hyperparameters, which control how the model is learned. The program is still\n",
    "evaluated on the test set to provide an estimate of its performance in the real world;\n",
    "its performance on the validation set should not be used as an estimate of the model's\n",
    "real-world performance since the program has been tuned specifically to the validation\n",
    "data. It is common to partition a single set of supervised observations into training,\n",
    "validation, and test sets. There are no requirements for the sizes of the partitions, and\n",
    "they may vary according to the amount of data available. It is common to allocate\n",
    "50 percent or more of the data to the training set, 25 percent to the test set, and the\n",
    "remainder to the validation set.\n",
    "\n",
    "Some training sets may contain only a few hundred observations; others may\n",
    "include millions. Inexpensive storage, increased network connectivity, the ubiquity\n",
    "of sensor-packed smartphones, and shifting attitudes towards privacy have\n",
    "contributed to the contemporary state of big data, or training sets with millions\n",
    "or billions of examples. While this book will not work with datasets that require\n",
    "parallel processing on tens or hundreds of machines, the predictive power of many\n",
    "machine learning algorithms improves as the amount of training data increases.\n",
    "However, machine learning algorithms also follow the maxim \"garbage in, garbage\n",
    "out.\" A student who studies for a test by reading a large, confusing textbook that\n",
    "contains many errors will likely not score better than a student who reads a short but\n",
    "well-written textbook. Similarly, an algorithm trained on a large collection of noisy,\n",
    "irrelevant, or incorrectly labeled data will not perform better than an algorithm\n",
    "trained on a smaller set of data that is more representative of problems in the\n",
    "real world.\n",
    "\n",
    "Many supervised training sets are prepared manually, or by semi-automated\n",
    "processes. Creating a large collection of supervised data can be costly in some\n",
    "domains. Fortunately, several datasets are bundled with scikit-learn, allowing\n",
    "developers to focus on experimenting with models instead. During development,\n",
    "and particularly when training data is scarce, a practice called cross-validation can\n",
    "be used to train and validate an algorithm on the same data. In cross-validation,\n",
    "the training data is partitioned. The algorithm is trained using all but one of the\n",
    "partitions, and tested on the remaining partition. The partitions are then rotated\n",
    "several times so that the algorithm is trained and evaluated on all of the data. The\n",
    "following diagram depicts cross-validation with five partitions or folds:\n",
    "\n",
    "<img src=\"images/cv.png\">\n",
    "\n",
    "The original dataset is partitioned into five subsets of equal size, labeled A through E.\n",
    "Initially, the model is trained on partitions B through E, and tested on partition A.\n",
    "In the next iteration, the model is trained on partitions A, C, D, and E, and tested on\n",
    "partition B. The partitions are rotated until models have been trained and tested on\n",
    "all of the partitions. Cross-validation provides a more accurate estimate of the model's\n",
    "performance than testing a single partition of the data.\n",
    "\n",
    "## Performance measures, bias, and variance\n",
    "\n",
    "Many metrics can be used to measure whether or not a program is learning to perform\n",
    "its task more effectively. For supervised learning problems, many performance\n",
    "metrics measure the number of prediction errors. There are two fundamental causes\n",
    "of prediction error: a model's bias and its variance. Assume that you have many\n",
    "training sets that are all unique, but equally representative of the population. A model\n",
    "with a high bias will produce similar errors for an input regardless of the training set\n",
    "it was trained with; the model biases its own assumptions about the real relationship\n",
    "over the relationship demonstrated in the training data. A model with high variance,\n",
    "conversely, will produce different errors for an input depending on the training set\n",
    "that it was trained with. A model with high bias is inflexible, but a model with high\n",
    "variance may be so flexible that it models the noise in the training set. That is, a model\n",
    "with high variance over-fits the training data, while a model with high bias under-fits\n",
    "the training data. It can be helpful to visualize bias and variance as darts thrown at a\n",
    "dartboard. Each dart is analogous to a prediction from a different dataset. A model\n",
    "with high bias but low variance will throw darts that are far from the bull's eye, but\n",
    "tightly clustered. A model with high bias and high variance will throw darts all over\n",
    "the board; the darts are far from the bull's eye and each other.\n",
    "\n",
    "A model with low bias and high variance will throw darts that are closer to the\n",
    "bull's eye, but poorly clustered. Finally, a model with low bias and low variance\n",
    "will throw darts that are tightly clustered around the bull's eye, as shown in the\n",
    "following diagram:\n",
    "\n",
    "<img src = \"images/bias-variance.png\">\n",
    "\n",
    "Ideally, a model will have both low bias and variance, but efforts to decrease one will\n",
    "frequently increase the other. This is known as the bias-variance trade-off. We will\n",
    "discuss the biases and variances of many of the models introduced in this book.\n",
    "\n",
    "Unsupervised learning problems do not have an error signal to measure; instead,\n",
    "performance metrics for unsupervised learning problems measure some attributes\n",
    "of the structure discovered in the data.\n",
    "\n",
    "Most performance measures can only be calculated for a specific type of task.\n",
    "Machine learning systems should be evaluated using performance measures that\n",
    "represent the costs associated with making errors in the real world. While this may\n",
    "seem obvious, the following example describes the use of a performance measure\n",
    "that is appropriate for the task in general but not for its specific application.\n",
    "\n",
    "Consider a classification task in which a machine learning system observes tumors\n",
    "and must predict whether these tumors are malignant or benign. Accuracy, or the\n",
    "fraction of instances that were classified correctly, is an intuitive measure of the\n",
    "program's performance. While accuracy does measure the program's performance, it\n",
    "does not differentiate between malignant tumors that were classified as being benign,\n",
    "and benign tumors that were classified as being malignant. In some applications, the\n",
    "costs associated with all types of errors may be the same. In this problem, however,\n",
    "failing to identify malignant tumors is likely to be a more severe error than mistakenly\n",
    "classifying benign tumors as being malignant.\n",
    "\n",
    "We can measure each of the possible prediction outcomes to create different views\n",
    "of the classifier's performance. When the system correctly classifies a tumor as being\n",
    "malignant, the prediction is called a true positive. When the system incorrectly\n",
    "classifies a benign tumor as being malignant, the prediction is a false positive.\n",
    "Similarly, a false negative is an incorrect prediction that the tumor is benign, and\n",
    "a true negative is a correct prediction that a tumor is benign. These four outcomes\n",
    "can be used to calculate several common measures of classification performance,\n",
    "including accuracy, precision, and recall.\n",
    "\n",
    "In this example, precision measures the fraction of tumors that were predicted\n",
    "to be malignant that are actually malignant. Recall measures the fraction of truly\n",
    "malignant tumors that were detected.\n",
    "\n",
    "The precision and recall measures could reveal that a classifier with impressive\n",
    "accuracy actually fails to detect most of the malignant tumors. If most tumors are\n",
    "benign, even a classifier that never predicts malignancy could have high accuracy.\n",
    "A different classifier with lower accuracy and higher recall might be better suited\n",
    "to the task, since it will detect more of the malignant tumors.\n",
    "\n",
    "Many other performance measures for classification can be used; we will discuss\n",
    "some, including metrics for multilabel classification problems, in later chapters.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "## Steps in developing a machine learning application\n",
    "Our approach to understanding and developing an application using machine learning\n",
    "in this book will follow a procedure similar to this:\n",
    "\n",
    "1. Collect data. You could collect the samples by scraping a website and extracting data, or you could get information from an RSS feed or an API. You could have a device collect wind speed measurements and send them to you, or blood glucose levels, or anything you can measure. The number of options is endless. To save some time and effort, you could use publicly available data.\n",
    "\n",
    "2. Prepare the input data. Once you have this data, you need to make sure it’s in a useable format. The format we’ll be using in this book is the Python list. We’ll talk about Python more in a little bit, and lists are reviewed in appendix A. The benefit of having this standard format is that you can mix and match algorithms and data sources. You may need to do some algorithm-specific formatting here. Some algorithms need features in a special format, some algorithms can deal with target variables and features as strings, and some need them to be integers. We’ll get to this later, but the algorithm-specific formatting is usually trivial compared to collecting data.\n",
    "\n",
    "3. Analyze the input data. This is looking at the data from the previous task. This could be as simple as looking at the data you’ve parsed in a text editor to make sure steps 1 and 2 are actually working and you don’t have a bunch of empty values.You can also look at the data to see if you can recognize any patterns or if  there’s anything obvious, such as a few data points that are vastly different from the rest of the set. Plotting data in one, two, or three dimensions can also help. But most of the time you’ll have more than three features, and you can’t easily plot the data across all features at one time. You could, however, use some advanced methods we’ll talk about later to distill multiple dimensions down to two or three so you can visualize the data.\n",
    "\n",
    "4. If you’re working with a production system and you know what the data should look like, or you trust its source, you can skip this step. This step takes human involvement, and for an automated system you don’t want human involvement.The value of this step is that it makes you understand you don’t have garbage  coming in.\n",
    "\n",
    "5. Train the algorithm. This is where the machine learning takes place. This step and the next step are where the “core” algorithms lie, depending on the algorithm. You feed the algorithm good clean data from the first two steps and extract knowledge or information. This knowledge you often store in a format that’s readily useable by a machine for the next two steps. In the case of unsupervised learning, there’s no training step because you don’t have a target value. Everything is used in the next step.\n",
    "\n",
    "6. Test the algorithm. This is where the information learned in the previous step isput to use. When you’re evaluating an algorithm, you’ll test it to see how well it does. In the case of supervised learning, you have some known values you can use to evaluate the algorithm. In unsupervised learning, you may have to use some other metrics to evaluate the success. In either case, if you’re not satisfied, you can go back to step 4, change some things, and try testing again. Often the collection or preparation of the data may have been the problem, and you’ll have to go back to step 1.\n",
    "\n",
    "7. Use it. Here you make a real program to do some task, and once again you see if all the previous steps worked as you expected. You might encounter some new data and have to revisit steps 1–5.\n",
    "\n",
    "Now we’ll talk about a language to implement machine learning applications. We need a language that’s understandable by a wide range of people. We also need a language that has libraries written for a number of tasks, especially matrix math operations. We also would like a language with an active developer community. Python is the best choice for these reasons.\n",
    "___"
   ]
  },
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   "source": [
    "# Next : [Getting Started](Getting-Started.ipynb)\n",
    "<hr>"
   ]
  }
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