Knowledge is the information about a domain that can be used to solve problems in that domain. To solve many problems requires much knowledge, and this knowledge must be represented in the computer. As part of designing a program to solve problems, we must define how the knowledge will be represented.
1. DEPARTMENT OF CS &IT
KNOWLEDGE IN LEARNING
PRESENTED BY:
S.SABTHAMI
I.MSC(IT)
Nadar saraswathi college of arts and science
2. A logical formulation of learning
What’re Goal and Hypotheses
Goal predicate Q - WillWait
Learning is to find an equivalent logical
expression we can classify examples
Each hypothesis proposes such an
expression - a candidate definition of Q
r WillWait(r) Pat(r,Some)
Pat(r,Full) Hungry(r)Type(r,French)
3. A logical formulation of learning
Hypothesis space is the set of all hypotheses
the learning algorithm is designed to
entertain.
One of the hypotheses is correct:
H1 V H2 V…V Hn
Each Hi predicts a certain set of examples -
the extension of the goal predicate.
Two hypotheses with different extensions
are logically inconsistent with each other,
otherwise, they are logically equivalent.
4. Examples
An example is an object of some logical
description to which the goal concept may
or may not apply.
Alt(X1)^!Bar(X1)^!Fri/Sat(X1)^…
Ideally, we want to find a hypothesis that
agrees with all the examples.
The relation between f and h are: ++, --, +-
(false negative), -+ (false positive). If the
last two occur, example I and h are logically
inconsistent.
5. Current-best hypothesis search
Maintain a single hypothesis
Adjust it as new examples arrive to maintain
consistency
Generalization
Specialization
6. Example of WillWait
Problems: nondeterministic, no
guarantee for simplest and
correct h, need backtrack
7. Least-commitment search
Keeping only one h as its best guess is the
problem -> Can we keep as many as
possible?
Version space (candidate elimination)
Algorithm
incremental
least-commitment
8. Least-commitment search
From intervals to boundary sets
G-set and S-set
S0 – the most specific set contains nothing <0,0,…,0>
G0 – the most general set covers everything <?,?,…,?>
Everything between is guaranteed to be
consistent with examples.
VS tries to generalize S0 and specialize G0
incrementally
9. Version space
Generalization and specialization
find d-sets that contain only true/+, and true/-;
Sj can only be generalized and Gj can only be specialized
False positive for Si, too general, discard it
False negative for Si, too specific, generalize it minimally
False positive for Gi, too general, specialize it minimally
False negative for Gi, too specific, discard it
10. Version space
When to stop
One concept left (Si = Gi)
The version space collapses (G is more special than S, or..)
Run out of examples
An example with 4 instances from Tom Mitchell’s
book
One major problem: can’t handle noise
11. Using prior knowledge
For DT and logical description learning, we
assume no prior knowledge
We do have some prior knowledge, so how
can we use it?
We need a logical formulation as opposed to
the function learning.
12. Inductive learning in the logical setting
The objective is to find a hypothesis that
explains the classifications of the examples,
given their descriptions.
Hypothesis ^ Description |= Classifications
Hypothesis is unknown, explains the
observations
Descriptions - the conjunction of all the example
descriptions
Classifications - the conjunction of all the
example classifications
Knowledge free learning
Decision trees
Description = Classifications
13. A procecumulative learning ss
Observations, K-based learning,
Hypotheses, and prior knowledge
The new approach is to design agents that
already know something and are trying to
learn some more.
Intuitively, this should be faster and better
than without using knowledge, assuming
what’s known is always correct.
14. Some examples of using knowledge
One can leap to general conclusions after
only one observation.
Your such experience?
Traveling to Brazil: Language and name
A pharmacologically ignorant but
diagnostically sophisticated medical
student …
15. Some general schemes
Explanation-based learning (EBL)
Hypothesis^Description |= Classifications
Background |= Hypothesis
doesn’t learn anything factually new from instance
Relevance-based learning (RBL)
Hypothesis^Descriptions |= Classifications
Background^Descrip’s^Class |= Hypothesis
deductive in nature
Knowledge-based inductive learning (KBIL)
Background^Hypothesis^Descrip’s |=
Classifications
16. Inductive logical programming (ILP)
ILP can formulate hypotheses in general
first-order logic
Others like DT are more restricted languages
Prior knowledge is used to reduce the
complexity of learning:
prior knowledge further reduces the H space
prior knowledge helps find the shorter H
Again, assuming prior knowledge is correct
17. Explanation-based learning
A method to extract general rules from individual
observations
The goal is to solve a similar problem faster next
time.
Memoization - speed up by saving results and
avoiding solving a problem from scratch
EBL does it one step further - from observations to
rules
18. Basic EBL
Given an example, construct a proof tree using the
background knowledge
In parallel, construct a generalized proof tree for
the variabilized goal
Construct a new rule (leaves => the root)
Drop any conditions that are true regardless of the
variables in the goal
19. Efficiency of EBL
Choosing a general rule
too many rules -> slow inference
aim for gain - significant increase in speed
as general as possible
Operationality - A subgoal is operational means it is
easy to solve
Trade-off between Operationality and Generality
Empirical analysis of efficiency in EBL
20. Learning using relevant information
Prior knowledge: People in a country
usually speak the same language
Nat(x,n) ^Nat(y,n)^Lang(x,l)=>Lang(y,l)
Observation: Given nationality, language is
fully determined
Given Fernando is Brazilian & speaks Portuguese
Nat(Fernando,B) ^ Lang(Fernando,P)
We can logically conclude
Nat(y,B) => Lang(y,P)
21. Functional dependencies
We have seen a form of relevance:
determination - language (Portuguese) is a
function of nationality (Brazil)
Determination is really a relationship
between the predicates
The corresponding generalization follows
logically from the determinations and
descriptions.
22. Functional dependencies
Determinations specify a sufficient basis
vocabulary from which to construct hypotheses
concerning the target predicate.
A reduction in the H space size should make it
easier to learn the target predicate