Machine Learning

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Machine Learning

• Foundations of Artificial Intelligence

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Learning

• What is Learning?
• Learning in AI is also called machine learning or
  pattern recognition.
• The basic objective is to allow an intelligent
  agent to discover autonomously knowledge from
  experience.
• Lets examine the definition more closely
• an intelligent agent The ability to learn
  requires a prior level of intelligence and
  knowledge. Learning has to start from an
  existing level of capability.
• to discover autonomously Learning is
  fundamentally about an agent recognizing new
  facts for its own use and acquiring new abilities
  that reinforce its own existing abilities.
  Literal programming, i.e. rote learning from
  instruction, is not useful.
• knowledge Whatever is learned has to be
  represented in some way that the agent can use.
  If you can't represent it, you can't learn it
  is a corollary of the slogan Knowledge is
  power.
• from experience Experience is typically a set
  of so-called training examples examples may be
  categorized or not. They may be random or
  selected by a teacher. They may include
  explanations or not.

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Learning Agent
Critic
Percepts
Problem solver
Learning element
KB
Actions
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Learning element

• Design of a learning element is affected by
• Which components of the performance element are
  to be learned
• What feedback is available to learn these
  components
• What representation is used for the components
• Type of feedback
• Supervised learning correct answers for each
  training example
• Unsupervised learning correct answers not given
• Reinforcement learning occasional
  rewards/feedback

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Inductive Learning

• Inductive Learning
• inductive learning involves learning generalized
  rules from specific examples (can think of this
  as the inverse of deduction)
• main task given a set of examples, each
  classified as positive or negative produce a
  concept description that matches exactly the
  positive examples
• Some Notes
• The examples are coded in some representation
  language, e.g. they are coded by a finite set of
  real-valued features.
• The concept description is in a certain language
  that is presumably a superset of the language of
  possible example encodings.
• A correct concept description is one that
  classifies correctly ALL possible examples, not
  just those given in the training set.
• Fundamental Difficulties with Induction
• cant generalize with perfect certainty
• examples and concepts are NOT available
  directly they are only available through
  representations which may be more or less
  adequate to capture them
• some examples may be classified as both positive
  and negative
• the features supplied may not be sufficient to
  discriminate between positive and negative
  examples

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Inductive Learning Frameworks

1. Function-learning formulation
2. Logic-inference formulation

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Inductive learning

• Simplest form learn a function from examples
• f is the target function
• An example is a pair (x, f(x))
• Problem find a hypothesis h
• such that h f
• given a training set of examples
• This is a highly simplified model of real
  learning
• Ignores prior knowledge
• Assumes examples are given

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Inductive learning

• Construct/adjust h to agree with f on training
  set
• h is consistent if it agrees with f on all
  examples
• E.g., curve fitting

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Inductive learning

• Construct/adjust h to agree with f on training
  set
• h is consistent if it agrees with f on all
  examples
• E.g., curve fitting

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Inductive learning

• Construct/adjust h to agree with f on training
  set
• h is consistent if it agrees with f on all
  examples
• E.g., curve fitting

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Inductive learning

• Construct/adjust h to agree with f on training
  set
• h is consistent if it agrees with f on all
  examples
• E.g., curve fitting

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Inductive learning

• Construct/adjust h to agree with f on training
  set
• h is consistent if it agrees with f on all
  examples
• E.g., curve fitting

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Inductive learning

• Construct/adjust h to agree with f on training
  set
• h is consistent if it agrees with f on all
  examples
• E.g., curve fitting
• Ockhams razor prefer the simplest hypothesis
  consistent with data

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Logic-Inference Formulation

• Background knowledge KB
• Training set D (observed knowledge) that is not
  logically implied by KB
• Inductive inference Find h (inductive
  hypothesis) such that KB and h imply D

h D is a trivial, but uninteresting solution
(data caching)
Usually, not a sound inference
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Rewarded Card Example

• Deck of cards, with each card designated by
  r,s, its rank and suit, and some cards
  rewarded
• Background knowledge KB
• ((r1) v v (r10)) ? NUM(r)((rJ) v (rQ) v
  (rK)) ? FACE(r)((sS) v (sC)) ?
  BLACK(s)((sD) v (sH)) ? RED(s)
• Training set DREWARD(4,C) ? REWARD(7,C) ?
  REWARD(2,S) ?
  ?REWARD(5,H) ? ?REWARD(J,S)
• Possible inductive hypothesish ? (NUM(r) ?
  BLACK(s) ? REWARD(r,s))

Note There are several possible inductive
hypotheses
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Learning a Predicate

• Set E of objects (e.g., cards)
• Goal predicate CONCEPT(x), where x is an object
  in E,
• takes the value True or False (e.g., REWARD)
• Observable predicates A(x), B(X),
• e.g., NUM, RED
• Training set
• values of CONCEPT for some combinations of values
  of the observable predicates

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A Possible Training Set
Ex. A B C D E CONCEPT
1 True True False True False False
2 True False False False False True
3 False False True True True False
4 True True True False True True
5 False True True False False False
6 True True False True True False
7 False False True False True False
8 True False True False True True
9 False False False True True False
10 True True True True False True
Note that the training set does not say whether
an observable predicate A, , E is pertinent or
not
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Learning a Predicate

• Set E of objects (e.g., cards)
• Goal predicate CONCEPT(x), where x is an object
  in E,
• takes the value True or False (e.g., REWARD)
• Observable predicates A(x), B(X),
• e.g., NUM, RED
• Training set
• values of CONCEPT for some combinations of values
  of the observable predicates
• Find a representation of CONCEPT in the form
• CONCEPT(x) ? S(A,B, )
• where S(A,B,) is a sentence built with the
  observable predicates, e.g.
• CONCEPT(x) ? A(x) ? (?B(x) v C(x))

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Example set

• An example consists of the values of CONCEPT and
  the observable predicates for some object x
• A example is positive if CONCEPT is True, else it
  is negative
• The set X of all examples is the example set
• The training set is a subset of X

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Hypothesis Space

• An hypothesis is any sentence h of the form
• CONCEPT(x) ? S(A,B, )
• where S(A,B,) is a sentence built with the
  observable predicates
• The set of all hypotheses is called the
  hypothesis space H
• An hypothesis h agrees with an example if it
  gives the correct value of CONCEPT

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Inductive Learning Scheme
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Size of Hypothesis Space

• n observable predicates
• 2n entries in truth table
• In the absence of any restriction (bias), there
  are 22n hypotheses to choose from
• n 6 ? 2x1019 hypotheses!

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Multiple Inductive Hypotheses
Rewarded Card Example (Continued)
h1 ? NUM(x) ? BLACK(x) ? REWARD(x) h2 ?
BLACK(r,s) ? ?(rJ) ? REWARD(r,s) h3 ?
(r,s4,C) ? (r,s7,C) ? r,s2,S) ?
REWARD(r,s) h4 ? ?(r,s5,H) ?
?(r,sJ,S) ? REWARD(r,s) agree with all the
examples in the training set
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Inductive Bias

• Need for a system of preferences called a bias
  to compare possible hypotheses
• Keep-It-Simple (KIS) Bias
• If an hypothesis is too complex it may not be
  worth learning it
• There are much fewer simple hypotheses than
  complex ones, hence the hypothesis space is
  smaller
• Examples
• Use much fewer observable predicates than
  suggested by the training set
• Constrain the learnt predicate, e.g., to use only
  high-level observable predicates such as NUM,
  FACE, BLACK, and RED and/or to have simple syntax
  (e.g., conjunction of literals)

If the bias allows only sentences S that are
conjunctions of k ltlt n predicates picked from the
n observable predicates, then the size of H is
O(nk)
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Version Spaces

• Idea assume you are looking for a CONJUNCTIVE
  CONCEPT
• e.g., spade A, club 7, club 9 yes
• club 8, heart 5 no
• concept odd and black
• now notice that the set of conjunctive concepts
  is partially ordered by specificity

any card

• at any point, keep most specific and least
  specific
• conjuncts consistent with data
• most specific
• anything more specific misses some positive
  instances
• always exists -- conjoin all OK conjunctions
• least specific
• anything less specific admits some negative
  instances
• may not be unique -- imagine all you know is
  club
• 4 not ok, odd black ok, spade ok, black not ok
• Idea is to gradually merge least and most
  specific as data comes in.

black
odd black
spade
odd spade
3 of spade
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Version Spaces Example

• Step 0 most specific concept (msc) is the empty
  set least specific concept (lsc) is the set of
  all cards.
• Step 1 A-spade is found to be in target set
• msc A-spade
• lsc set of all cards
• Step 2 7-club is found to be in target set
• msc odd black cards
• lsc set of all cards
• Step 3 8-heart is not in target set
• msc odd black cards
• lsc all odd cards OR all black cards
• . . .

The training examples (obtained) incrementally
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Predicate as a Decision Tree
The predicate CONCEPT(x) ? A(x) ? (?B(x) v C(x))
can be represented by the following decision
tree

• ExampleA mushroom is poisonous iffit is yellow
  and small, or yellow,
• big and spotted
• x is a mushroom
• CONCEPT POISONOUS
• A YELLOW
• B BIG
• C SPOTTED

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Decision Trees

• What is a Decision Tree
• it takes as input the description of a situation
  as a set of attributes (features) and outputs a
  yes/no decision (so it represents a Boolean
  function)
• each leaf is labeled "positive or "negative",
  each node is labeled with an attribute (or
  feature), and each edge is labeled with a value
  for the feature of its parent node
• Attribute-value language for examples
• in many inductive tasks, especially learning
  decision trees, we need a representation language
  for examples
• each example is a finite feature vector
• a concept is a decision tree where nodes are
  features

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Decision Trees

• Example is it a good day to play golf?
• a set of attributes and their possible values
• outlook sunny, overcast, rain
• temperature cool, mild, hot
• humidity high, normal
• windy true, false

A particular instance in the training set might
be ltovercast, hot, normal, falsegt play
In this case, the target class is a binary
attribute, so each instance represents a
positive or a negative example.
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Using Decision Trees for Classification

• Examples can be classified as follows
• 1. look at the example's value for the feature
  specified
• 2. move along the edge labeled with this value
• 3. if you reach a leaf, return the label of the
  leaf
• 4. otherwise, repeat from step 1
• Example (a decision tree to decide whether to go
  play golf)

outlook
sunny
overcast
rain
humidity
windy
high
normal
true
false
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Classification 3 Step Process

• 1. Model construction (Learning)
• Each record (instance) is assumed to belong to a
  predefined class, as determined by one of the
  attributes, called the class label
• The set of records used for construction of the
  model is called training set
• The model is usually represented in the form of
  classification rules, (IF-THEN statements) or
  decision trees
• 2. Model Evaluation (Accuracy)
• Estimate accuracy rate of the model based on a
  test set
• The known label of test sample is compared to
  classified result from model
• Accuracy rate percentage of test set samples
  correctly classified by the model
• Test set is independent of training set otherwise
  over-fitting will occur
• 3. Model Use (Classification)
• The model is used to classify unseen instances
  (assigning class labels)
• Predict the value of an actual attribute

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Memory-Based Reasoning

• Basic Idea classify new instances based on their
  similarity to instances we have seen before
• also called instance-based learning
• Simplest form of MBR Rote Learning
• learning by memorization
• save all previously encountered instance given a
  new instance, find one from the memorized set
  that most closely resembles the new one assign
  new instance to the same class as the nearest
  neighbor
• more general methods try to find k nearest
  neighbors rather than just one
• but, how do we define resembles?
• MBR is lazy
• defers all of the real work until new instance is
  obtained no attempts are made to learn a
  generalized model from the training set
• less data preprocessing and model evaluation, but
  more work has to be done at classification time

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MBR Collaborative Filtering

• Collaborative Filtering or Social Learning
• idea is to give recommendations to a user based
  on the ratings of objects by other users
• usually assumes that features in the data are
  similar objects (e.g., Web pages, music, movies,
  etc.)
• usually requires explicit ratings of objects by
  users based on a rating scale
• there have been some attempts to obtain ratings
  implicitly based on user behavior (mixed results
  problem is that implicit ratings are often
  binary)
• Nearest Neighbors Strategy
• Find similar users and predicted (weighted)
  average of user ratings
• We can use any distance or similarity measure to
  compute similarity among users (user ratings on
  items viewed as a vector)
• In case of ratings, often the Pearson r algorithm
  is used to compute correlations

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MBR Collaborative Filtering

• Collaborative Filtering Example
• A movie rating system
• Ratings scale 1 detest 7 love it
• Historical DB of users includes ratings of movies
  by Sally, Bob, Chris, and Lynn
• Karen is a new user who has rated 3 movies, but
  has not yet seen Independence Day should we
  recommend it to her?

Will Karen like Independence Day?
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Clustering
Clustering is a process of partitioning a set of
data (or objects) in a set of meaningful
sub-classes, called clusters
Helps users understand the natural grouping or
structure in a data set

• Cluster
• a collection of data objects that are similar
  to one another and thus can be treated
  collectively as one group
• but as a collection, they are sufficiently
  different from other groups
• Clustering
• unsupervised classification
• no predefined classes

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Distance or Similarity Measures

• Measuring Distance
• In order to group similar items, we need a way to
  measure the distance between objects (e.g.,
  records)
• Note distance inverse of similarity
• Often based on the representation of objects as
  feature vectors

Term Frequencies for Documents
An Employee DB
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Distance or Similarity Measures

• Common Distance Measures
• Manhattan distance
• Euclidean distance
• Cosine similarity

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What Is Good Clustering?

• A good clustering will produce high quality
  clusters in which
• the intra-class (that is, intra-cluster)
  similarity is high
• the inter-class similarity is low
• The quality of a clustering result also depends
  on both the similarity measure used by the method
  and its implementation
• The quality of a clustering method is also
  measured by its ability to discover some or all
  of the hidden patterns
• The quality of a clustering result also depends
  on the definition and representation of cluster
  chosen

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Applications of Clustering

• Clustering has wide applications in Pattern
  Recognition
• Spatial Data Analysis
• create thematic maps in GIS by clustering feature
  spaces
• detect spatial clusters and explain them in
  spatial data mining
• Image Processing
• Market Research
• Information Retrieval
• Document or term categorization
• Information visualization and IR interfaces
• Web Mining
• Cluster Web usage data to discover groups of
  similar access patterns
• Web Personalization

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Learning by Discovery

• One example AM by Doug Lenat at Stanford
• a mathematical system
• inputs set theory (union, intersection, etc)
  how to do mathematics (based on a book by
  Polya), e.g., if f is an interesting function of
  two arguments, then f(x,x) is an interesting
  function on one, etc.
• speculated about what was interesting an made
  conjectures, etc.
• What AM discovered
• integers (as equivalence relation on cardinality
  of sets)
• addition (using disjoint union of sets)
• multiplication
• primes 1 was interesting, the function returning
  the cardinality of set of divisors was
  interesting, etc.
• Glodbachs conjecture all even numbers are the
  sum of two prime numbers (note that AM did not
  prove it, just discovered that it was
  interesting)
• Why was AM so successful?
• Connection between LISP and mathematics
  (mutations of small bits of LISP code are likely
  to be interesting)
• Doesnt extend to other domains
• Lessons from EURISKO (fleet game)

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Explanation-Based Learning

• Explanation- based learning (EBL) systems try to
  explain why each training instance belongs to the
  target concept.
• The resulting proof is then generalized and
  saved.
• If a new instance can be explained in the same
  manner as a previous instance, then it is also
  assumed to be a member of the target concept.
• Like macro- operators, EBL systems never learn to
  solve a problem that they couldnt solve before
  (in principle).
• However, they can become much more efficient at
  problem-solving by reorganizing the search space.
• One of the strengths of EBL is that the resulting
  explanations are typically easy to understand.
• One of the weaknesses of EBL is that they rely on
  a domain theory to generate the explanations.

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Case-Based Learning

• Case-based reasoning (CBR) systems keep track of
  previously seen instances and apply them directly
  to new ones.
• In general, a CBR system simply stores each
  case that it experiences in a case base which
  represents its memory of previous episodes.
• To reason about a new instance, the system
  consults its case base and finds the most similar
  case that its seen before. The old case is then
  adapted and applied to the new situation.
• CBR is similar to reasoning by analogy. Many
  people believe that much of human learning is
  case- based in nature.

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Connectionist Algorithms

• Connectionist models (also called neural
  networks) are inspired by the interconnectivity
  of the brain.
• Connectionist networks typically consist of many
  nodes that are highly interconnected. When a node
  is activated, it sends signals to other nodes so
  that they are activated in turn.
• Using layers of nodes allows connectionist models
  to learn fairly complex functions.
• Neural networks are loosely modeled after the
  biological processes involved in cognition
• 1. Information processing involves many simple
  elements called neurons.
• 2. Signals are transmitted between neurons using
  connecting links.
• 3. Each link has a weight that controls the
  strength of its signal.
• 4. Each neuron applies an activation function to
  the input that it receives from other neurons.
  This function determines its output.