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Ch 9. Machine Learning: Symbol-based

9.0 Introduction

9.1 A Framework for Symbol-Based Learning

9.2 Version Space Search The Candidate Elimination Algorithm

9.3 ID3 Decision Tree Induction Algorithm

9.5 Knowledge and Learning Explanation-Based Learning

9.6 Unsupervised Learning Conceptual clustering

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9.0 Introduction

Learning through the course of their interactions with the world through the experience of their own internal states and

processes Is important for practical applications of AI

Knowledge engineering bottleneck major obstacle to the widespread use of intelligent systems the cost and difficulty of building expert systems using

traditional knowledge acquisition techniques one solution

For program to begin with a minimal amount of knowledge And learn from examples, high-level advice, own

explorations of the domain

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9.0 Introduction

Definition of learning

Views of Learning Generalization from experience

Induction: must generalize correctly to unseen instances of domain

Inductive biases: selection criteria (must select the most effective aspects of their experience)

Changes in the learner acquisition of explicitly represented domain knowledge,

based on its experience, the learner constructs or modifies expressions in a formal language (e.g. logic).

Any change in a system that allow it to perform better the second time on repetition of the same task or on another task drawn form the same population (Simon, 1983)

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9.0 Introduction

Learning Algorithms vary in goals, available training data, learning strategies and

knowledge representation languages

All algorithms learn by searching through a space of possible concepts to find an acceptable generalization (concept space Fig. 9.5)

Inductive learning learning a generalization from a set of examples concept learning is a typical inductive learning

infer a definition from given examples of some concept (e.g. cat, soybean disease)

allow to correctly recognize future instances of that concept Two algorithms: version space search and ID3

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9.0 Introduction

Similarity-based vs. Explanation-based

Similarity-based (data-driven) using no prior knowledge of the domain rely on large numbers of examples generalization on the basis of patterns in training data

Explanation-based Learning(prior knowledge-driven) using prior knowledge of the domain to guide generalization learning by analogy and other technology that utilize prior knowledge

to learn from a limited amount of training data

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9.0 Introduction

Supervised vs. Unsupervisedsupervised learning

learning from training instances of known classification

unsupervised learning learning from unclassified training data conceptual clustering or category formation

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9.1 Framework for Symbol-based Learning

Learning Algorithms are characterized by a general

model (Fig. 9.1, p 354, sp 8)

Data and goals of the learning task

Representation Language

A set of operations

Concept space

Heuristic Search

Acquired knowledge

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A general model of the learning process (Fig. 9.1)

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9.1 Framework for Symbol-based Learning

Data and Goals Type of data

positive or negative examples Single positive example and domain specific knowledge high-level advice (e.g. condition of loop termination) analogies(e.g. electricity vs. water)

Goal of Learning algorithms: acquisition of concept, general description of a class of objects plans problem-solving heuristics other forms of procedural knowledge

Properties and quality of data come from the outside environment (e.g. teacher) or generated by the program itself reliable or contain noise well-structured or unorganized positive and negative or only positive

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9.1 Framework for Symbol-based Learning

Concept learning

Explanation-based

Clustering

Data Positive/negative examples of a target class

A training example + prior knowledge

A set of unclassified instances

Goal To infer a general definition

To infer a general concept

To discover categorizations

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9.1 Framework for Symbol-based Learning

Representation of learned knowledge concept expressions in predicate calculus

A simple formulation of the concept learning problem as

conjunctive sentences containing variables

structured representation such as frames

description of plans as a sequence of operations or triangle table

representation of heuristics as problem-solving rules

size(obj1, small) ^ color(obj1, red) ^ shape(obj1, round) size(obj2, large) ^ color(obj2, red) ^ shape(obj2, round)=> size(X, Y) ^ color(X, red) ^ shape(X, round)

size(obj1, small) ^ color(obj1, red) ^ shape(obj1, round) size(obj2, large) ^ color(obj2, red) ^ shape(obj2, round)=> size(X, Y) ^ color(X, red) ^ shape(X, round)

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9.1 Framework for Symbol-based Learning

A Set of operations Given a set of training instances, the leaner must construct a

generalization, heuristic rule, or plan that satisfies its goal Requires ability to manipulate representations Typical operations include

generalizing or specializing symbolic expressions adjusting the weights in a neural network modifying the program’s representations

Concept space defines a space of potential concept definitions complexity of potential concept space is a measure of difficulty of

learning algorithms

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9.1 Framework for Symbol-based Learning

Heuristic Search Use available training data and heuristics to search efficiently Patrick Winston’s work on learning concepts from positive and

negative examples along with near misses (Fig. 9.2). The program learns by refining candidate description of the target

concept through generalization and specialization. Generalization changes the candidate description to let it

accommodate new positive examples (Fig. 9.3) Specialization changes the candidate description to exclude near

misses (Fig. 9.4) Performance of learning algorithm is highly sensitive to the quality

and order of the training examples

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Examples and Near Misses for the concept “Arch” (Fig. 9.2)

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Generalization of descriptions (Figure 9.3)

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Generalizations of descriptions (Fig 9.3 continued)

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Specialization of description (Figure 9.4)

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9.2 Version Space Search

Implementation of inductive learning as search through a concept space

Generalization operations impose an ordering on the concepts in a space, and uses this ordering to guide the search

9.2.1 Generalization Operators and Concept Space 9.2.2 Candidate Elimination Algorithm

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9.2.1 Generalization Operators and the Concept Spaces

Primary generalization operations used in ML Replacing constants with variables

color(ball, red) -> color(X, red) Dropping conditions from a conjunctive expression

shape(X, round) ^ size(X, small) ^ color(X, red) -> shape(X, round) ^ color(X, red)

Adding a disjunct to an expression shape(X, round) ^ size(X, small) ^ color(X, red)

-> shape(X, round) ^ size(X, small) ^ (color(X, red) color(X, blue))

Replacing a property with its parent in a class hierarchy color(X, red)

-> color(X, primary_color) if primary_color is superclass of red

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9.2.1 Generalization Operators and the Concept Spaces

Notion of covering If concept P is If concept P is more generalmore general than concept Q, we say that than concept Q, we say that “ “P P coverscovers Q” Q” Color(X,Y) Color(X,Y) coverscovers color(ball,Y), which in turn color(ball,Y), which in turn covers covers color(ball,red color(ball,red

)) Concept spaceConcept space

Defines a Defines a space of potential concept definitionsspace of potential concept definitions The example concept space representing the The example concept space representing the predicate obj(Sizes, Color, Shapes) with properties and valuespredicate obj(Sizes, Color, Shapes) with properties and values

Sizes = {large, small}Sizes = {large, small} Colors = {red, white, blue}Colors = {red, white, blue} Shapes = {ball, brick, cube}Shapes = {ball, brick, cube}

is presented in Figure 9.5 (p 362, sp21)is presented in Figure 9.5 (p 362, sp21)

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A Concept Space (Fig. 9.5)

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9.2.2 The candidate elimination algorithm

Version space: the set of all concept descriptions

consistent with the training examples.

Toward reducing the size of the version space as

more examples become available (Fig. 9.10) Specific to general search from positive examples General to specific search from negative examples Candidate elimination algorithm combines these into a bi-

directional search

Generalize based on regularities found in the

training data

Supervised learning

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9.2.2 The candidate elimination algorithm

The learned concept must be general enough to cover

all positive examples, also must be specific enough

to exclude all negative examples maximally specific generalization

Maximally general specialization

A concept c, is maximally specific if it covers all positive examples, none of the negative examples, and for any concept c’, that covers the positive examples, c c’

A concept c, is maximally specific if it covers all positive examples, none of the negative examples, and for any concept c’, that covers the positive examples, c c’

A concept c, is maximally general if it covers none of the negative training instances, and for any other concept c’, that covers no negative training instance, c c’.

A concept c, is maximally general if it covers none of the negative training instances, and for any other concept c’, that covers no negative training instance, c c’.

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Specific to General Search

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Specific to General Search (Fig 9.7)

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General to Specific Search

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General to Specific Search (Fig 9.8)

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9.2.2 The candidate elimination algorithm

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9.2.2 The candidate elimination algorithm

Begin

Initialize G to the most general concept in the space;

Initialize S to the first positive training instance;

For each new positive instance p

Begin

Delete all members of G that fail to match p;

For every s in S, if s does not match p, replace s with its most specific generalizations that match p and are more specific than some members of G;

Delete from S any hypothesis more general than some other hypothesis in S;

End;

For each new negative instance n

Begin

Delete all members of S that match n;

For each g in G that matches n, replace g with its most general specializations that do not match n and are more general than some members of S;

Delete from G any hypothesis more specific than some other hypothesis in G;

End

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9.2.2 The candidate elimination algorithm (Fig. 9.9)

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9.2.2 The candidate elimination algorithm

Combining the two directions of search into a

single algorithm has several benefits. G and S sets summarizes the information in the negative

and positive training instances.

Fig. 9.10 gives an abstract description of the

candidate elimination algorithm. “+” signs represent positive instances “-” signs indicate negative instances The search “shrinks” the outermost concept to exclude

negative instances The search “expands” the innermost concept to include new

positive instances

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9.2.2 The candidate elimination algorithm

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9.2.2 The candidate elimination algorithm

An incremental nature of learning algorithm Accepts training instances one at a time, forming a usable,

although possibly incomplete, generalization after each example (unlike the batch algorithm such as ID3).

Even before the algorithm converges on a single

concept, the G and S sets provide usable

constraints on that concept If c is the goal concept, then for all g∈G and s∈S, s≤c≤g. Any concept that is more general than some concept in G

will cover negative instance; any concept that is more specific than some concept in S will fail to cover some positive instances

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9.2.4 Evaluating Candidate Elimination

Problems combinatorics of problem space: excessive growth of search spac

e Useful to develop heuristics for pruning states from G and S (be

am search) Uses an inductive bias to reduce the size of concept space trade off between expressiveness and efficiency

The algorithm may fail to converge because of noise or inconsistency in training data

One solution to this problem is to maintain multiple G and S sets

Contribution explication of the relationship between knowledge representation,

generalization, and search in inductive learning