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Machine Learning
Foundations of Artificial Intelligence
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.
 Let’s 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
sensors
?
environment
agent
actuators
Critic
Learning
element
Percepts
KB
Problem
solver
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
 can’t 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:
 Ockham’s 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:
((r=1) v … v (r=10))  NUM(r)
((r=J) v (r=Q) v (r=K))  FACE(r)
((s=S) v (s=C))  BLACK(s)
((s=D) v (s=H))  RED(s)
 Training set D:
REWARD([4,C])  REWARD([7,C])  REWARD([2,S]) 
REWARD([5,H])  REWARD([J,S])
 Possible inductive hypothesis:
h  (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
Training set D
-
+
+
+
-
-
+
+
+
- -
+
-+
+
+
-
+
-
+
Example set X
{[A, B, …, CONCEPT]}
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Inductive
hypothesis h
Hypothesis space H
{[CONCEPT(x)  S(A,B, …)]}
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Size of Hypothesis Space
n observable predicates
2n entries in truth table
n
2
In the absence of any restriction (bias), there are 2
hypotheses to choose from
n = 6  2x1019 hypotheses!
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Rewarded
Card Example
Multiple
Inductive
Hypotheses
Rewarded
Card Example
(Continued)
Background knowledge KB:
((r=1) v … v (r=10))  NUM([r,s])
((r=J) v (r=Q) v (r=K))  FACE([r,s])
((s=S) v (s=C))  BLACK([r,s])
((s=D) v (s=H))  RED([r,s])
Training set D:
REWARD([4,C])  REWARD([7,C])  REWARD([2,S])

REWARD([5,H]) 
REWARD([J,S])
Possible inductive hypothesis:
h  (NUM(x)  BLACK(x)  REWARD(x))
h1  NUM(x)  BLACK(x)  REWARD(x)
h2  BLACK([r,s])  (r=J)  REWARD([r,s])
h3  ([r,s]=[4,C])  ([r,s]=[7,C])  [r,s]=[2,S])  REWARD([r,s])
h4  ([r,s]=[5,H])  ([r,s]=[J,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 << 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
club 8, heart 5
 concept: odd and black
yes
no
 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:
black
most specific:
• anything more specific misses some positive instances
• always exists -- conjoin all OK conjunctions
odd black
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.
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spade
odd spade
3 of spade
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Version Spaces: Example
The training examples
(obtained) incrementally:
Card
In Target Set?
A-ª
yes
7-§
yes
8-©
no
9-§
yes
5-©
no
K-¨
no
6-¨
no
7-ª
yes
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 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
 ...
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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:
Example:
A?
A mushroom is poisonous iff
True
it is yellow and small, or yellow,
big and spotted
B?
• x is a mushroom
False
True
• CONCEPT = POISONOUS
• A = YELLOW
True
• B = BIG
C?
• C = SPOTTED
True
False
True
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False
False
False
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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:
<overcast, hot, normal, false>: 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
no
Foundations of Artificial Intelligence
rain
yes
humidity
high
overcast
windy
normal
yes
true
no
false
yes
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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, (IFTHEN 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?
Star Wars
Jurassic Park
Terminator II
Independence Day
Sally
7
6
3
7
Bob
7
4
4
6
Chris
3
7
7
2
Lynn
4
4
6
2
Karen
7
4
3
?
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”
An Employee DB
ID
1
2
3
4
5
Gender
F
M
M
F
M
Age
27
51
52
33
45
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Salary
19,000
64,000
100,000
55,000
45,000
Term Frequencies for Documents
Doc1
Doc2
Doc3
Doc4
Doc5
T1
0
3
3
0
2
T2
4
1
0
1
2
T3
0
4
0
0
2
T4
0
3
0
3
3
T5
0
1
3
0
1
T6
2
2
0
0
4
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Distance or Similarity Measures
 Common Distance Measures:
 Manhattan distance:
 Euclidean distance:
 Cosine similarity:
dist ( X , Y )  1  sim( X , Y )
sim( X , Y ) 
 ( xi  yi )
i
 xi   yi
2
i
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2
i
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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.
 Glodbach’s 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)
 Doesn’t 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 couldn’t 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 it’s 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.
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