Machine Learning - Artificial Intelligence - Lecture Slides, Slides of Artificial Intelligence

Download Machine Learning - Artificial Intelligence - Lecture Slides and more Slides Artificial Intelligence in PDF only on Docsity!

Lecture 34 of 41

Introduction to Machine Learning

Lecture Outline

• Next Week: Sections 18.3-18.4, 18.6-18.7, Russell and Norvig
• Previously: Representation and Reasoning (Inference)
  • Logical
  • Probabilistic (“Soft Computing”)
• Today: Introduction to Learning
  • Machine learning framework
  • Definitions
    • Taxonomies: supervised, unsupervised, reinforcement
    • Instance spaces ( X )
    • Hypotheses ( h ) and hypothesis spaces ( H )
  • Basic examples
  • Version spaces and candidate elimination algorithm
• Next Thursday: Inductive Bias and Learning Decision Trees

Example (Revisited):

Learning to Play Board Games

• Type of Training Experience
  • Direct or indirect?
  • Teacher or not?
  • Knowledge about the game (e.g., openings/endgames)?
• Problem: Is Training Experience Representative (of Performance Goal)?
• Software Design
  • Assumptions of the learning system: legal move generator exists
  • Software requirements: generator, evaluator(s), parametric target function
• Choosing a Target Function
  • ChooseMove: Board  Move (action selection function, or policy )
  • V: Board  R (board evaluation function)
  • Ideal target V ; approximated target
  • Goal of learning process: operational description (approximation) of V

V ˆ

Implicit Representation in Learning:

Target Evaluation Function for Checkers

• Possible Definition
  • If b is a final board state that is won, then V(b) = 100
  • If b is a final board state that is lost, then V(b) = -
  • If b is a final board state that is drawn, then V(b) = 0
  • If b is not a final board state in the game, then V(b) = V(b’) where b’ is the best final board state that can be achieved starting from b and playing optimally until the end of the game
  • Correct values, but not operational
• Choosing a Representation for the Target Function
  • Collection of rules?
  • Neural network?
  • Polynomial function (e.g., linear, quadratic combination) of board features?
  • Other?

• A Representation for Learned Function

  • bp/rp = number of black/red pieces; bk/rk = number of black/red kings; bt/rt = number of black/red pieces threatened (can be taken on next turn)

V ˆ  b   w 0  w 1 bp  b   w 2 rp  b   w 3 bk  b   w 4 rk  b   w 5 bt  b   w 6 rt  b 

Performance Element:

What to Learn?

• Classification Functions
  • Hidden functions: estimating (“fitting”) parameters
  • Concepts (e.g., chair, face, game)
  • Diagnosis, prognosis: medical, risk assessment, fraud, mechanical systems
• Models
  • Map (for navigation)
  • Distribution (query answering, aka QA)
  • Language model (e.g., automaton/grammar)
• Skills
  • Playing games
  • Planning
  • Reasoning (acquiring representation to use in reasoning)
• Cluster Definitions for Pattern Recognition
  • Shapes of objects
  • Functional or taxonomic definition
• Many Learning Problems Can Be Reduced to Classification

Representations and Algorithms:

How to Learn It?

• Supervised
  • What is learned? Classification function; other models
  • Inputs and outputs? Learning:
  • How is it learned? Presentation of examples to learner (by teacher)
• Unsupervised
  • Cluster definition, or vector quantization function ( codebook )
  • Learning:
  • Formation, segmentation, labeling of clusters based on observations, metric
• Reinforcement
  • Control policy (function from states of the world to actions)
  • Learning:
  • (Delayed) feedback of reward values to agent based on actions selected; model updated based on reward, (partially) observable state

examples x,f  x  approximation f ˆ x 

observations x distancemetric d  x 1 ,x 2  discretecodebook f   x

state/rew ard sequence si ,r i : 1  i  n  policy p:s  a

Example:

Supervised Inductive Learning Problem

Unknown Function

x 1 x 2 x 3 x 4

y = f (x 1 , x 2 , x 3 , x 4 )

• xi: ti, y: t, f : (t 1  t 2  t 3  t 4 )  t
• Our learning function: Vector (t 1  t 2  t 3  t 4  t)  (t 1  t 2  t 3  t 4 )  t

Example x 1 x 2 x 3 x 4 y 0 0 1 1 0 0 1 0 0 0 0 0 2 0 0 1 1 1 3 1 0 0 1 1 4 0 1 1 0 0 5 1 1 0 0 0 6 0 1 0 1 0

Hypothesis Space:

Unrestricted Case

• | A  B | = | B | |^ A^ |
• | H^4  H | = | {0,1}  {0,1}  {0,1}  {0,1}  {0,1} | = 2^24 = 65536 function values
• Complete Ignorance: Is Learning Possible?
  • Need to see every possible input/output pair
  • After 7 examples, still have 2^9 = 512 possibilities (out of 65536) for f Example x 1 x 2 x 3 x 4 y 0 0 0 0 0? 1 0 0 0 1? 2 0 0 1 0 0 3 0 0 1 1 1 4 0 1 0 0 0 5 0 1 0 1 0 6 0 1 1 0 0 7 0 1 1 1? 8 1 0 0 0? 9 1 0 0 1 1 10 1 0 1 0? 11 1 0 1 1? 12 1 1 0 0 0 13 1 1 0 1? 14 1 1 1 0? 15 1 1 1 1?

Representing Hypotheses

• Many Possible Representations
• Hypothesis h : Conjunction of Constraints on Attributes
• Constraint Values
  • Specific value (e.g., Water = Warm )
  • Don’t care (e.g., “Water = ?” )
  • No value allowed (e.g., “Water = Ø ”)
• Example Hypothesis for EnjoySport
  • Sky AirTemp Humidity Wind Water Forecast <Sunny?? Strong? Same>
  • Is this consistent with the training examples?
  • What are some hypotheses that are consistent with the examples?

Typical Concept Learning Tasks

• Given
  • Instances X: possible days, each described by attributes Sky, AirTemp, Humidity, Wind, Water, Forecast
  • Target function c  EnjoySport: X  H  {{Rainy, Sunny}  {Warm, Cold}  {Normal, High}  {None, Mild, Strong}  {Cool, Warm}  {Same, Change}}  {0, 1}
  • Hypotheses H : conjunctions of literals (e.g., )
  • Training examples D : positive and negative examples of the target function
• Determine
  • Hypothesis h  H such that h(x) = c(x) for all x  D
  • Such h are consistent with the training data
• Training Examples
  • Assumption: no missing X values
  • Noise in values of c (contradictory labels)?

x1, c  x 1  ,  , xm,c  xm 

Instances, Hypotheses, and

the Partial Ordering Less-Specific-Than

Instances X Hypotheses H

x 1 = <Sunny, Warm, High, Strong, Cool, Same> x 2 = <Sunny, Warm, High, Light, Warm, Same>

h 1 = <Sunny, ?, ?, Strong, ?, ?> h 2 = <Sunny, ?, ?, ?, ?, ?> h 3 = <Sunny, ?, ?, ?, Cool, ?>

h 2  P h 1 h 2  P h 3

x 1

x 2

Specific

General

h 1 h 3

h 2

 P  Less-Specific-Than  More-General-Than

Find-S Algorithm

1. Initialize h to the most specific hypothesis in H

H : the hypothesis space (partially ordered set under relation Less-Specific-Than )

2. For each positive training instance x

For each attribute constraint ai in h IF the constraint ai in h is satisfied by x THEN do nothing ELSE replace ai in h by the next more general constraint that is satisfied by x

3. Output hypothesis h

Version Spaces

• Definition: Consistent Hypotheses
  • A hypothesis h is consistent with a set of training examples D of target concept c if and only if h(x) = c(x) for each training example < x, c(x) > in D.
  • Consistent ( h , D )   < x , c(x) >  D. h(x) = c(x)
• Definition: Version Space
  • The version space VSH,D , with respect to hypothesis space H and training examples D , is the subset of hypotheses from H consistent with all training examples in D.
  • VSH,D  { h  H | Consistent (h, D) }

1. Initialization

G  (singleton) set containing most general hypothesis in H , denoted {} S  set of most specific hypotheses in H , denoted {<Ø, … , Ø>}

2. For each training example d

If d is a positive example ( Update-S ) Remove from G any hypotheses inconsistent with d For each hypothesis s in S that is not consistent with d Remove s from S Add to S all minimal generalizations h of s such that

1. h is consistent with d
2. Some member of G is more general than h (These are the greatest lower bounds, or meets , s  d , in VSH,D ) Remove from S any hypothesis that is more general than another hypothesis in S (remove any dominated elements)

Candidate Elimination Algorithm [1]