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As we have seen, the term machine learning is used in a very general way, and refers to the general techniques used to extrapolate patterns from large sets, or it is the ability to make predictions on new data based on what is learned by analyzing available known data. Machine learning techniques can roughly be divided in two large classes, while one more class is often added. Here are the classes:
Supervised learning algorithms are a class of machine learning algorithms that use previously-labeled data to learn its features, so they can classify similar but unlabeled data. Let's use an example to understand this concept better.
Let's assume that a user receives a large amount of emails every day, some of which are important business emails and some of which are unsolicited junk emails, also known as spam. A supervised machine algorithm will be presented with a large body of emails that have already been labeled by a teacher as spam or not spam (this is called training data). For each sample, the machine will try to predict whether the email is spam or not, and it will compare the prediction with the original target label. If the prediction differs from the target, the machine will adjust its internal parameters in such a way that the next time it encounters this sample it will classify it correctly. Conversely, if the prediction was correct, the parameters will stay the same. The more training data we feed to the algorithm, the better it becomes (this rule has caveats, as we'll see next).
In the example we used, the emails had only two classes (spam or not spam), but the same principles apply for tasks with arbitrary numbers of classes. For example, we could train the software on a set of labeled emails where the classes are Personal, Business/Work, Social, or Spam.
In fact, Gmail, the free email service by Google, allows the user to select up to five categories, which are labeled as the following:
In some cases, the outcome may not necessarily be discrete, and we may not have a finite number of classes to classify our data into. For example, we may try to predict the life expectancy of a group of people based on their predetermined health parameters. In this case, the outcome is a continuous function, that is, the number years the person is expected to live, and we don't talk about classification but rather regression.
One way to think of supervised learning is to imagine we are building a function, f, defined over a dataset, which comprises information organized by features. In the case of email classification, the features can be specific words that may appear more frequently than others in spam emails. The use of explicit sex-related words will most likely identify a spam email rather than a business/work email. On the contrary, words such as meeting, business, or presentation are more likely to describe a work email. If we have access to metadata, we may also use the sender's information as a feature. Each email will then have an associated set of features, and each feature will have a value (in this case, how many times the specific word is present in the email body). The machine learning algorithm will then seek to map those values to a discrete range that represents the set of classes, or a real value in the case of regression. The definition of the f function is as follows:
In later chapters, we'll see several examples of either classification or regression problems. One such problem we'll discuss is the classification of handwritten digits (the famous Modified National Institute of Standards and Technology, or MNIST, database). When given a set of images representing 0 to 9, the machine learning algorithm will try to classify each image in one of the 10 classes, wherein each class corresponds to one of the 10 digits. Each image is 28x28 (= 784) pixels in size. If we think of each pixel as one feature, then the algorithm will use a 784-dimensional feature space to classify the digits.
The following screenshot depicts the handwritten digits from the MNIST dataset:
In the next sections, we'll talk about some of the most popular classical supervised algorithms. The following is by no means an exhaustive list or a thorough description of each machine learning method. We can refer to the book Python Machine Learning by Sebastian Raschka (https://www.packtpub.com/big-data-and-business-intelligence/python-machine-learning). It's a simple review meant to provide the reader with a flavor of the different techniques. Also, at the end of this chapter in the Neural networks section, we'll introduce neural networks and we'll talk about how deep learning differs from the classical machine learning techniques.
Regression algorithms are a type of supervised algorithm that uses features of the input data to predict a value, such as the cost of a house, given certain features, such as size, age, number of bathrooms, number of floors, and location. Regression analysis tries to find the value of the parameters for the function that best fits an input dataset.
In a linear-regression algorithm, the goal is to minimize a cost function by finding appropriate parameters for the function, over the input data that best approximates the target values. A cost function is a function of the error, that is, how far we are from getting a correct result. A popular cost function is the mean square error (MSE), where we take the square of the difference between the expected value and the predicted result. The sum over all the input examples gives us the error of the algorithm and represents the cost function.
Say we have a 100-square-meter house that was built 25 years ago with 3 bathrooms and 2 floors. Let's also assume that the city is divided into 10 different neighborhoods, which we'll denote with integers from 1 to 10, and say this house is located in the area denoted by 7. We can parameterize this house with a five-dimensional vector, x = (100, 25, 3, 2, 7). Say that we also know that this house has an estimated value of €100,000. What we want is to create a function, f, such that f(x) = 100000.
In linear regression, this means finding a vector of weights, w= (w1, w2, w3, w4, w5), such that the dot product of the vectors, x • w = 10000, would be 100*w1 + 25*w2 + 3*w3 + 2*w4 + 7*w5 = 100000 or 
. If we had 1,000 houses, we could repeat the same process for every house, and ideally we would like to find a single vector, w, that can predict the correct value that is close enough for every house. The most common way to train a linear regression model can be seen in the following pseudocode block:
Initialize the vector w with some random values
repeat:
E = 0 # initialize the cost function E with 0
for every sample/target pair (xi, ti) of the training set:
E +=# here ti is the real cost of the house
MSE = E / total_number_of_samples # Mean Square Error
use gradient descent to update the weights w based on MSE
until MSE falls below threshold
First, we iterate over the training data to compute the cost function, MSE. Once we know the value of MSE, we'll use the gradient-descent algorithm to update w. To do this, we'll calculate the derivatives of the cost function with respect to each weight, wi . In this way, we'll know how the cost function changes (increase or decrease) with respect to wi . Then we'll update its value accordingly. In Chapter 2, Neural Networks, we will see that training neural networks and linear/logistic regressions have a lot in common.
We demonstrated how to solve a regression problem with linear regression. Let's take another task: trying to determine whether a house is overvalued or undervalued. In this case, the target data would be categorical [1, 0] - 1 for overvalued, 0 for undervalued, if the price of the house will be an input parameter instead of target value as before. To solve the task, we'll use logistic regression. This is similar to linear regression but with one difference: in linear regression, the output is 
. However, here the output will be a special logistic function (https://en.wikipedia.org/wiki/Logistic_function), 
. This will squash the value of 
in the (0:1) interval. You can think of the logistic function as a probability, and the closer the result is to 1, the more chance there is that the house is overvalued, and vice versa. Training is the same as with linear regression, but the output of the function is in the (0:1) interval and the labels is either 0 or 1.
Logistic regression is not a classification algorithm, but we can turn it into one. We just have to introduce a rule that determines the class based on the logistic function output. For example, we can say that a house is overvalued if the value of 
and undervalued otherwise.
A support vector machine (SVM) is a supervised machine learning algorithm that is mainly used for classification. It is the most popular member of the kernel method class of algorithms. An SVM tries to find a hyperplane, which separates the samples in the dataset.
In the following diagram, on the top and bottom, you can see two classes of points (red and blue) that are in a two-dimensional feature space (the x and y axes). If both the x and y values of a point are below five, then the point is blue. In all other cases, the point is red. In this case, the classes are linearly-separable, meaning we can separate them with a hyperplane. Conversely, the classes in the image at the bottom are linearly-inseparable:
The SVM tries to find a hyperplane that maximizes the distance between itself and the points. In other words, from all possible hyperplanes that can separate the samples, the SVM finds the one that has the maximum distance from all points. In addition, SVMs can also deal with data that is not linearly-separable. There are two methods for this: introducing soft margins or using the kernel trick.
Soft margins work by allowing a few misclassified elements while retaining the most predictive ability of the algorithm. In practice, it's better not to overfit the machine learning model, and we could do so by relaxing some of the support-vector-machine hypotheses.
The kernel trick solves the same problem in a different way. Imagine that we have a two-dimensional feature space, but the classes are linearly-inseparable. The kernel trick uses a kernel function that transforms the data by adding more dimensions to it. In our case, after the transformation, the data will be three-dimensional. The linearly-inseparable classes in the two-dimensional space will become linearly-separable in the three dimensions and our problem is solved:
Another popular supervised algorithm is the decision tree. A decision tree creates a classifier in the form of a tree. This is composed of decision nodes, where tests on specific attributes are performed; and leaf nodes, which indicate the value of the target attribute. To classify a new sample, we start at the root of the tree and navigate down the nodes until we reach a leaf.
A classic application of this algorithm is the Iris flower dataset (http://archive.ics.uci.edu/ml/datasets/Iris), which contains data from 50 samples of three types of Irises (Iris Setosa, Iris Virginica, and Iris Versicolor). Ronald Fisher, who created the dataset, measured four different features of these flowers:
Based on the different combinations of these features, it's possible to create a decision tree to decide which species each flower belongs to. In the following diagram, we have defined a decision tree that will correctly classify almost all the flowers using only two of these features, the petal length and width:
To classify a new sample, we start at the root note of the tree (petal length). If the sample satisfies the condition, we go left to the leaf, representing the Iris Setosa class. If not, we go right to a new node (petal width). This process continues until we reach a leaf. There are different ways to build decision trees, and we will discuss them later, in the chapter.
In recent years, decision trees have seen two major improvements. The first is Random Forests, which is an ensemble method that combines the predictions of multiple trees. The second is Gradient-Boosting Machines, which creates multiple sequential decision trees, where each tree tries to improve the errors made by the previous tree. Thanks to these improvements, decision trees have become very popular when working with certain types of data. For example, they are one of the most popular algorithms used in Kaggle competitions.
Naive Bayes is different from many other machine learning algorithms. Most machine learning techniques try to evaluate the probability of a certain event, Y , and given conditions, X, which we denote with 
. For example, when we are given a picture that represents digits (that is, a picture with a certain distribution of pixels), what is the probability that the number is five? If the pixel's distribution is close to the pixel distribution of other examples that were labeled as five, the probability of that event will be high. If not, the probability will be low.
Sometimes we have the opposite information, given the fact that we know that we have an event, Y. We also know the probability, that our sample is X. The Bayes theorem states that 
, where 
means the probability of event, X, given Y, which is also why naive Bayes is called a generative approach. For example, we may calculate the probability that a certain pixel configuration represents the number five, knowing what the probability is. Given that we have a five, that a random pixel configuration may match the given one.
This is best understood in the realm of medical testing. Let's say we conduct a test for a specific disease or cancer. Here, we want to know the probability of a patient having a particular disease, given that our test result was positive. Most tests have a reliability value, which is the percentage chance of the test being positive when administered on people with a particular disease. By reversing the 
expression, we get the following:
p(cancer | test=positive) = p(test=positive | cancer) * p(cancer) / p(test=positive)
Let's assume that the test is 98% reliable. This means that if the test is positive, it will also be positive in 98% of cases. Conversely, if the person does not have cancer, the test result will be negative. Let's make some assumptions on this kind of cancer:
We can ask the following question: if a test is 98% accurate for cancer and if a 45-year-old person took the test, which turned out to be positive, what is the probability that they may have cancer? Using the preceding formula, we can calculate the following:
p(cancer | test=positive) = 0.98 * 0.02 / 0.039 = 0.50
We call this classifier naive because it assumes the independence of different events to calculate their probability. For example, if the person had two tests instead of one, the classifier will assume that the outcome of test 2 did not know about the outcome of test 1, and the two tests were independent from one another. This means that taking test 1 could not change the outcome of test 2, and therefore its result was not biased by the first test.
The second class of machine learning algorithms is unsupervised learning. Here, we don't label the data beforehand, but instead we let the algorithm come to its conclusion. One of the most common, and perhaps simplest, examples of unsupervised learning is clustering. This is a technique that attempts to separate the data into subsets.
To illustrate this, let's view the spam-or-not-spam email classification as an unsupervised learning problem. In the supervised case, for each email, we had a set of features and a label (spam or not spam). Here, we'll use the same set of features, but the emails will not be labeled. Instead, we'll ask the algorithm, when given the set of features, to put each sample in one of two separate groups (or clusters). Then the algorithm will try to combine the samples in such a way that the intraclass similarity (which is the similarity between samples in the same cluster) is high and the similarity between different clusters is low. Different clustering algorithms use different metrics to measure similarity. For some more advanced algorithms, you don't have to specify the number of clusters.
In the following graph, we show how a set of points can be classified to form three subsets:
Deep learning also uses unsupervised techniques, albeit different than clustering. In natural language processing (NLP), we use unsupervised (or semi-supervised, depending on who you ask) algorithms for vector representations of words. The most popular way to do this is called word2vec. For each word, we use its surrounding words (or its context) in the text and feed them to a simple neural network. The network produces a numerical vector, which contains a lot of information for the word (derived by the context). We then use these vectors instead of the words for various NLP tasks, such as sentiment analysis or machine translation. We’ll describe word2vec in Chapter 7, Recurrent Neural Networks and Language Models.
Another interesting application of unsupervised learning is in generative models, as opposed to discriminative models. We will train a generative model with a large amount of data of a certain domain, such as images or text, and the model will try to generate new data similar to the one we used for training. For example, a generative model can colorize black and white images, change facial expressions in images, or even synthesize images based on a text description. In Chapter 6, Generating Images with GANs and Variational Autoencoders, we'll look at two of the most popular generative techniques, Variational Autoencoders and Generative Adversarial Networks (GANs).
The following depicts the techniques:
In the preceding image, you can see how the authors of StackGAN: Text to Photo-realistic Image Synthesis with Stacked Generative Adversarial Networks, Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang, Xiaogang Wang, Xiaolei Huang, and Dimitris Metaxas, use a combination of supervised learning and unsupervised GANs to produce photo-realistic images based on text descriptions.
K-means is a clustering algorithm that groups the elements of a dataset into k distinct clusters (hence the k in the name). Here is how it works:
The preceding method is sensitive to the initial choice of random centroids and it may be a good idea to repeat it with different initial choices. It's also possible for some centroids to not be close to any of the points in the dataset, reducing the number of clusters down from k. Finally, it's worth mentioning that if we used k-means with k=3 on the Iris dataset, we may get different distributions of the samples compared to the distribution of the decision tree that we'd introduced. Once more, this highlights how important it is to carefully choose and use the correct machine learning method for each problem.
Now let's discuss a practical example that uses k-means clustering. Let's say a pizza-delivery place wants to open four new franchises in a city, and they need to choose the locations for the sites. We can solve this problem with k-means:
The third class of machine learning techniques is called reinforcement learning (RL). We will illustrate this with one of the most popular applications of reinforcement learning: teaching machines how to play games. The machine (or agent) interacts with the game (or environment). The goal of the agent is to win the game. To do this, the agent takes actions that can change the environment’s state. The environment provides the agent with reward signals that help the agent to decide its next action. Winning the game would provide the biggest reward. In formal terms, the goal of the agent is to maximize the total rewards it receives throughout the game:
In reinforcement learning, the agent takes an action, which changes the state of the environment. The agent uses the new state and the reward to determine its next action.
Let’s imagine a game of chess as an RL problem. The environment here would include the chess board along with the locations of the pieces. The goal of our agent is to beat the opponent. The agent will then receive a reward when they capture the opponent’s piece, and they will win the biggest reward if they checkmate the opponent. Conversely, if the opponent captures a piece or checkmates the agent, the reward will be negative. However, as part of their larger strategies, the players will have to make moves that neither capture a piece, nor checkmate the other’s king. The agent won’t receive any reward then. If this was a supervised learning problem, we would have to provide a label or a reward for each move. This is not the case with reinforcement learning. In this book, we’ll demonstrate how to use RL to allow the agent to use its previous experience in order to take new actions and learn from them in situations such as this.
Let’s take another example, in which sometimes we have to sacrifice a pawn to achieve a more important goal (such as a better position on the chessboard). In such situations, our humble agent has to be smart enough to take a short-term loss as a long-term gain. In an even more extreme case, imagine we had the bad luck of playing against Magnus Carlsen, the current world chess champion. Surely, the agent will lose in this case. However, how would we know which moves were wrong and led to the agent's loss? Chess belongs to a class of problems where the game should be considered in its entirety in order to reach a successful solution, rather than just looking at the immediate consequences of each action. Reinforcement learning will give us the framework that will help the agent to navigate and learn in this complex environment.
An interesting problem arises from this newfound freedom to take actions. Imagine that the agent has learned one successful chess-playing strategy (or policy, in RL terms). After some games, the opponent might guess what that policy is and manage to beat us. The agent will now face a dilemma with the following decisions: either to follow the current policy and risk becoming predictable, or to experiment with new moves that will surprise the opponent, but also carry the risk of turning out even worse. In general terms, the agent uses a policy that gives them a certain reward, but their ultimate goal is to maximize the total reward. A modified policy might be more rewarding and the agent will be ineffective if they don’t try to find such a policy. One of the challenges of reinforcement learning is the tradeoff between exploitation (following the current policy) and exploration (trying new moves). In this book, we’ll learn the strategies to find the right balance between the two. We’ll also learn how to combine deep neural networks with reinforcement learning, which made the field so popular in recent years.
So far, we’ve used only games as examples; however, many problems can fall into the RL domain. For example, you can think of an autonomous vehicle driving as an RL problem. The vehicle can get positive rewards if it stays within its lane and observes the traffic rules. It will gain negative rewards if it crashes. Another interesting recent application of RL is in managing stock portfolios. The goal of the agent would be to maximize the portfolio value. The reward is directly derived from the value of the stocks in the portfolio.
Q-learning is an off-policy temporal-difference reinforcement learning algorithm. What a mouthful! But fear not, let’s not worry about what all this means, and instead just see how the algorithm works. To do this, we’ll use the game of chess we introduced in the previous section. As a reminder, the board configuration (the locations of the pieces) is the current state of the environment. Here, the agents can take actions, a, by moving pieces, thus changing the state into a new one. We'll represent a game of chess as a graph where the different board configurations are the graph’s vertices, and the possible moves from each configuration are the edges. To make a move, the agent follows the edge from the current state, s, to a new state, s'. The basic Q-learning algorithm uses Q-table to help the agent decide which moves to make. The Q-table contains one row for each board configuration, while the columns of the table are all possible actions that the agent can take (the moves). A table cell, q(s, a), contains the cumulative expected reward, called Q-value. This is the potential total reward that the agent will receive for the remainder of the game if they take an action, a, from their current state, s. At the beginning, the Q-table is initialized with an arbitrary value. With that knowledge, let’s see how Q-learning works:
Initialize the Q table with some arbitrary value
for each episode:
Observe the initial state s
for each step of the episode:
Select new action a using a policy based on the Q-table
Observe reward r and go to the new state s’
Update q(s, a) in the Q table using the Bellman Equation
until we reach a terminal state for the episode
An episode starts with a random initial state and finishes when we reach the terminal state. In our case, one episode would be one full game of chess.
The question that arises is this: how does the agent's policy determine what will be the next action? To do so, the policy has to take into account the Q-values of all the possible actions from the current state. The higher the Q-value, the more attractive the action is. However, the policy will sometimes ignore the Q-table (exploitation of the existing knowledge) and choose another random action to find higher potential rewards (exploration). In the beginning, the agent will take random actions because the Q-table doesn’t contain much information. As time progresses and the Q-table is gradually filled, the agent will become more informed in interacting with the environment.
We update q(s, a) after each new action, by using Bellman equation. The Bellman equation is beyond the scope of this introduction, but we’ll discuss it in detail in the later chapters. For now, it's enough to know that the updated value, q(s, a), is based on the newly-received reward, r , as well as the maximum possible Q-value, q*(s’, a’), of the new state, s'.
This example was intended to help you understand the basic workings of Q-learning, but you might have noticed an issue with this. We store the combination of all possible board configurations and moves in the Q-table. This would make the table huge and impossible to fit in today’s computer memory. Fortunately, there is a solution for this: we can replace the Q-table with a neural network, which will tell the agent what the optimal action is in each state. In recent years, this development has allowed reinforcement learning algorithms to achieve superhuman performance on tasks such as the game of Go, Dota 2, and Doom. In this book, we’ll discuss how to apply Q-learning and other RL algorithms to some of these tasks.
So far, we've discussed three major classes of machine learning algorithms. However, to solve an ML problem, we'll need a system in which the ML algorithm is only part of it. The most important aspects of such a system are as follows:
It can never be emphasized enough: any machine learning algorithm can only achieve an approximation of the target and not a perfect numerical description. Machine learning algorithms are not exact mathematical solutions to problems, they are just approximations. In the previous paragraph, we defined learning as a function from the space of features (the input) into a range of classes. We'll later see how certain machine learning algorithms, such as neural networks, can approximate any function to any degree, in theory. This theorem is called the Universal Approximation Theorem, but it does not imply that we can get a precise solution to our problem. In addition, solutions to the problem can be better achieved by better understanding the training data.
Typically, a problem that is solvable with classic machine learning techniques may require a thorough understanding and processing of the training data before deployment. The steps to solve an ML problem are as follows:
There are many valid reasons to create testing and validation datasets. As mentioned, machine learning techniques can only produce an approximation of the desired result. Often, we can only include a finite and limited number of variables, and there may be many variables that are outside of our control. If we only used a single dataset, our model may end up memorizing the data, and producing an extremely high accuracy value on the data it has memorized. However, this result may not be reproducible on other similar but unknown datasets. One of the key goals of machine learning algorithms is their ability to generalize. This is why we create both, a validation set used for tuning our model selection during training, and a final test set only used at the end of the process to confirm the validity of the selected algorithm.
To understand the importance of selecting valid features and to avoid memorizing the data, which is also referred to as overfitting in the literature-and we'll use that term from now on-let's use a joke taken from an xkcd comic as an example (http://xkcd.com/1122):
It's apparent that such a rule is meaningless, but it underscores the importance of selecting valid features and the question, "how much is a name worth in Scrabble," can bear any relevance while selecting a US president? Also, this example doesn't have any predictive power over unknown data. We'll call this overfitting, which refers to making predictions that fit the data at hand perfectly, but don't generalize to larger datasets. Overfitting is the process of trying to make sense of what we'll call noise (information that does not have any real meaning) and trying to fit the model to small perturbations.
To further explain this, let's try to use machine learning to predict the trajectory of a ball thrown from the ground up into the air (not perpendicularly) until it reaches the ground again. Physics teaches us that the trajectory is shaped as a parabola. We also expect that a good machine learning algorithm observing thousands of such throws would come up with a parabola as a solution. However, if we were to zoom into the ball and observe the smallest fluctuations in the air due to turbulence, we might notice that the ball does not hold a steady trajectory but may be subject to small perturbations, which in this case is the noise. A machine learning algorithm that tries to model these small perturbations would fail to see the big picture and produce a result that is not satisfactory. In other words, overfitting is the process that makes the machine learning algorithm see the trees, but forgets about the forest:
This is why we separate the training data from the validation and test data; if the accuracy on the test data was not similar to the training data accuracy, that would be a good indication that the model overfits. We need to make sure that we don't make the opposite error either, that is, underfitting the model. In practice though, if we aim to make our prediction model as accurate as possible on our training data, underfitting is much less of a risk, and care is taken to avoid overfitting.
The following image depicts underfitting:
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