Miroslav Kubat - An Introduction to Machine Learning

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Springer International Publishing AG 2017

Miroslav Kubat An Introduction to Machine Learning

1. A Simple Machine-Learning Task

Miroslav Kubat 1

(1)

Department of Electrical and Computer Engineering, University of Miami, Coral Gables, FL, USA

You will find it difficult to describe your mothers face accurately enough for your friend to recognize her in a supermarket. But if you show him a few of her photos, he will immediately spot the tell-tale traits he needs. As they say, a picturean exampleis worth a thousand words.

This is what we want our technology to emulate. Unable to define certain objects or concepts with adequate accuracy, we want to convey them to the machine by way of examples. For this to work, however, the computer has to be able to convert the examples into knowledge. Hence our interest in algorithms and techniques for machine learning , the topic of this textbook.

The first chapter formulates the task as a search problem, introducing hill-climbing search not only as our preliminary attempt to address the machine-learning task, but also as a tool that will come handy in a few auxiliary problems to be encountered in later chapters. Having thus established the foundation, we will proceed to such issues as performance criteria, experimental methodology, and certain aspects that make the learning process difficultand interesting.

1.1 Training Sets and Classifiers

Let us introduce the problem, and certain fundamental concepts that will accompany us throughout the rest of the book.

The Set of Pre-Classified Training Examples Figure shows six pies that Johnny likes, and six that he does not. These positive and negative examples of the underlying concept constitute a training set from which the machine is to induce a classifier an algorithm capable of categorizing any future pie into one of the two classes : positive and negative.

Fig. 1.1

A simple machine-learning task: induce a classifier capable of labeling future pies as positive and negative instances of a pie that Johnny likes

The number of classes can of course be greater. Thus a classifier that decides whether a landscape snapshot was taken in spring, summer, fall , or winter distinguishes four. Software that identifies characters scribbled on an iPad needs at least 36 classes: 26 for letters and 10 for digits. And document-categorization systems are capable of identifying hundreds, even thousands of different topics. Our only motivation for choosing a two-class domain is its simplicity.

Attribute Vectors To be able to communicate the training examples to the machine, we have to describe them in an appropriate way. The most common mechanism relies on so-called attributes . In the pies domain, five may be suggested: shape (circle, triangle, and square), crust-size (thin or thick), crust-shade (white, gray, or dark), filling-size (thin or thick), and filling-shade (white, gray, or dark). Table . For instance, the pie in the upper-left corner of the picture (the table calls it ex1 ) is described by the following conjunction:

(shape=circle) AND (crust-size=thick) AND (crust-shade=gray)

AND (filling-size=thick) AND (filling-shade=dark)

Table 1.1

The twelve training examples expressed in a matrix form

		Crust	Filling
Example	Shape	Size	Shade	Size	Shade	Class
ex1	Circle	Thick	Gray	Thick	Dark	pos
ex2	Circle	Thick	White	Thick	Dark	pos
ex3	Triangle	Thick	Dark	Thick	Gray	pos
ex4	Circle	Thin	White	Thin	Dark	pos
ex5	Square	Thick	Dark	Thin	White	pos
ex6	Circle	Thick	White	Thin	Dark	pos
ex7	Circle	Thick	Gray	Thick	White	neg
ex8	Square	Thick	White	Thick	Gray	neg
ex9	Triangle	Thin	Gray	Thin	Dark	neg
ex10	Circle	Thick	Dark	Thick	White	neg
ex11	Square	Thick	White	Thick	Dark	neg
ex12	Triangle	Thick	White	Thick	Gray	neg

A Classifier to Be Induced The training set constitutes the input from which we are to induce the classifier. But what classifier?

Suppose we want it in the form of a boolean function that is true for positive examples and false for negative ones. Checking the expression [(shape=circle) AND (filling-shade=dark)] against the training set, we can see that its value is false for all negative examples: while it is possible to find negative examples that are circular, none of these has a dark filling. As for the positive examples, however, the expression is true for four of them and false for the remaining two. This means that the classifier makes two errors, a transgression we might refuse to tolerate, suspecting there is a better solution. Indeed, the reader will easily verify that the following expression never goes wrong on the entire training set:

[ (shape=circle) AND (filling-shade=dark) ] OR

[ NOT(shape=circle) AND (crust-shade=dark) ]

Problems with a Brute-Force Approach How does a machine find a classifier of this kind? Brute force (something that computers are so good at) will not do here. Just consider how many different examples can be distinguished by the given set of attributes in the pies domain. For each of the three different shapes , there are two alternative crust-sizes , the number of combinations being 3 2 = 6. For each of these, the next attribute, crust-shade , can acquire three different values, which brings the number of combinations to 3 2 3 = 18. Extending this line of reasoning to all attributes, we realize that the size of the instance space is 3 2 3 2 3 = 108 different examples.

Each subset of these examplesand there are 2108 subsets!may constitute the list of positive examples of someones notion of a good pie. And each such subset can be characterized by at least one boolean expression. Running each of these classifiers through the training set is clearly out of the question.

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