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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

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ch 9 machine learning symbol based
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

Machine Learning

9 0 introduction
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

Machine Learning

9 0 introduction1
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)

Machine Learning

9 0 introduction2
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

Machine Learning

9 0 introduction3
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 knowledgeto learn from a limited amount of training data

Machine Learning

9 0 introduction4
9.0 Introduction
  • Supervised vs. Unsupervised
    • supervised learning
      • learning from training instances of known classification
    • unsupervised learning
      • learning from unclassified training data
      • conceptual clustering or category formation

Machine Learning

9 1 framework for symbol based learning
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

Machine Learning

9 1 framework for symbol based learning1
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

Machine Learning

9 1 framework for symbol based learning3
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)

Machine Learning

9 1 framework for symbol based learning4
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

Machine Learning

9 1 framework for symbol based learning5
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 andnegative 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

Machine Learning

9 2 version space search
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

Machine Learning

9 2 1 generalization operators and the concept spaces
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

Machine Learning

9 2 1 generalization operators and the concept spaces1
9.2.1 Generalization Operators and the Concept Spaces
  • Notion of covering
    • If concept P is more general than concept Q, we say that

“P covers Q”

    • Color(X,Y) covers color(ball,Y), which in turn covers color(ball,red)
  • Concept space
    • Defines a space of potential concept definitions
    • The example concept space representing the

predicate obj(Sizes, Color, Shapes) with properties and values

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

is presented in Figure 9.5 (p 362, sp21)

Machine Learning

9 2 2 the candidate elimination algorithm
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

Machine Learning

9 2 2 the candidate elimination algorithm1
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 general if it covers none of the negative training instances, and for any other concept c’, that covers no negative training instance, c  c’.

Machine Learning

9 2 2 the candidate elimination algorithm3
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

Machine Learning

9 2 2 the candidate elimination algorithm4
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

Machine Learning

9 2 2 the candidate elimination algorithm6
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

Machine Learning

9 2 4 evaluating candidate elimination
9.2.4 Evaluating Candidate Elimination
  • Problems
    • combinatorics of problem space: excessive growth of search space
      • Useful to develop heuristics for pruning states from G and S (beam 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

Machine Learning