机器学习入门：基本概念与实践应用

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"《An Introduction to Machine Learning》是Miroslav Kubat撰写的一本关于机器学习的入门书籍，旨在以易于理解的方式介绍机器学习的基本概念，通过实践经验、简单示例和有趣应用的讨论来激发学生的学习兴趣。本书涵盖了多种机器学习方法，如贝叶斯分类器、最近邻分类器、线性和多项式分类器、决策树、神经网络、支持向量机，以及组合工具的提升方法、更复杂领域的应用和实际问题的处理。书中还专门有一章讨论了流行的遗传算法，并涉及强化学习的内容。" 本书的内容结构包括： 1. 第一章介绍了机器学习的基础任务，让读者对机器学习有初步认识。 2. 第二章讲解概率理论，特别是贝叶斯分类器，这是机器学习中的基础概念。 3. 第三章通过相似性分析，阐述最近邻分类器的工作原理和应用。 4. 第四章讨论了线性分类器和多项式分类器，这些是构建分类边界的重要工具。 5. 第五章深入探讨人工神经网络，这是模拟人脑学习模式的一种重要模型。 6. 第六章介绍了决策树，一种直观且易于理解的预测模型。 7. 第七章探讨了计算学习理论，解释了学习算法的理论基础和性能界限。 8. 第八章通过一些具有启发性的应用实例，展示了机器学习在实际问题中的应用。 9. 第九章介绍了投票组装的归纳，这是一种将多个分类器组合起来的方法。 10. 第十章关注机器学习的一些实际方面，如数据预处理和模型选择等。 11. 第十一章详细讲述了性能评估，这是评估模型效果的关键步骤。 12. 第十二章讨论了统计显著性，解释如何判断结果是否具有统计学意义。 13. 第十三章专门讨论了遗传算法，这是一种基于自然选择和遗传的优化技术。 14. 最后，第十四章涉足强化学习，这是机器学习的一个重要分支，特别是在智能体的学习和决策制定中。这本书适合机器学习初学者，它不仅提供了理论基础，还强调了实践应用和问题解决策略，帮助读者建立起坚实的机器学习知识体系。通过阅读本书，读者可以掌握多种机器学习算法，并了解如何在实际项目中应用这些知识。

2 1 A Simple Machine-Learning Task

Johnny likes:

Johnny does NOT like:

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-

1.1 Training Sets and Classiﬁers 3

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

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 1.1 speciﬁes the values of these

attributes for the twelve examples in Fig. 1.1. 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)

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

4 1 A Simple Machine-Learning Task

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 D 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 D 18. Extending this

line of reasoning to all attributes, we realize that the size of the instance space is

3  2  3  2  3 D 108 different examples.

Each subset of these examples—and there are 2

108

subsets!—may constitute the

list of positive examples of someone’s 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.

Manual approach and search. Uncertain about how to invent a classiﬁer-inducing

algorithm, we may try to glean some inspiration from an attempt to create a classiﬁer

“manually,” by the good old-fashioned pencil-and-paper method. When doing so,

we begin with some tentative initial version, say, shape=circular.Having

checked it against the training set, we ﬁnd it to be true for four positive examples, but

also for two negative ones. Apparently, the classiﬁer needs to be “narrowed” (spe-

cialized) so as to exclude the two negative examples. One way to go about the spe-

cialization is to add a conjunction, such as when turning shape=circular into

[(shape=circular) AND (filling-shade=dark)]. This new expres-

sion, while false for all negative examples, is still imperfect because it cov-

ers only four (ex1, ex2, ex4, and ex6) of the six positive examples. The

next step should therefore attempt some generalization, perhaps by adding a

disjunction: {[(shape=circular) AND (filling-shade=dark)] OR

(crust-size=thick)}. We continue in this way until we ﬁnd a hundred-

percent accurate classiﬁer (if it exists).

The lesson from this little introspection is that the classiﬁer can be created by

means of a sequence of specialization and generalization steps which gradually

modify a given version of the classiﬁer until it satisﬁes certain predeﬁned require-

ments. This is encouraging. Readers with background in Artiﬁcial Intelligence will

recognize this procedure as a search through the space of boolean expressions. And

Artiﬁcial Intelligence is known to have developed and explored quite a few search

algorithms. It may be an idea to take a look at least at one of them.

1.2 Minor Digression: Hill-Climbing Search 5

What Have You Learned?

To make sure you understand the topic, try to answer the following questions. If

needed, return to the appropriate place in the text.

• What is the input and output of the learning problem we have just described?

• How do we describe the training examples? What is instance space?Canwe

calculate its size?

• In the “pies” domain, ﬁnd a boolean expression that correctly classiﬁes all the

training examples from Table 1.1.

1.2 Minor Digression: Hill-Climbing Search

Let us now formalize what we mean by search, and then introduce one popular algo-

rithm, the so-called hill climbing. Artiﬁcial Intelligence deﬁnes search something

like this: starting from an initial state, ﬁnd a sequence of steps which, proceeding

through a set of interim search states, lead to a pre-deﬁned ﬁnal state. The individual

steps—transitions from one search state to another—are carried out by search

operators which, too, have been pre-speciﬁed by the programmer. The order in

which the search operators are applied follows a speciﬁc search strategy. The whole

principle is depicted by Fig. 1.2.

Hill climbing—an illustration. One popular search strategy is hill climbing.Let

us illustrate its essence on a well-known brain-teaser, the sliding-tiles puzzle. The

board of a trivial version of this game consists of nine squares arranged in three

rows, eight covered by numbered tiles (integers from 1 to 8), the last left empty. We

convert one search state into another by sliding to the empty square a tile from one

of its neighbors. The goal is to achieve a pre-speciﬁed arrangement of the tiles.

The ﬂowchart in Fig. 1.3 starts with a concrete initial state, in which we can

choose between two operators: “move tile-6 up” and “move tile-2 to the

left.” The choice is guided by an evaluation function that estimates for each state

its distance from the goal. A simple possibility is to count the squares that the tiles

have to traverse before reaching their ﬁnal destinations. In the initial state, tiles 2,

4 and 5 are already in the right locations; tile 3 has to be moved by four squares;

and each of the tiles 1, 6, 7, and 8 has to be moved by two squares. This sums-up to

distance d D 4 C 4  2 D 12.

In Fig. 1.3, each of the two operators applicable to the initial state leads to a

state whose distance from the ﬁnal state is d D 13. In the absence of any other

guidance, we choose randomly and go to the left, reaching the situation where the

empty square is in the middle of the top row. Here, three moves are possible. One of

them would only get us back to the initial state, and can thus be ignored; as for the

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