Introduction to ILP

ILP = Inductive Logic Programming

= machine learning logic programming

= learning with logic

Introduced by Muggleton in 1992

(Machine) Learning

• The process by which relatively permanent changes occur in behavioral potential as a result of experience. (Anderson)

• Learning is constructing or modifying representations of what is being experienced. (Michalski)

• A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E. (Mitchell)

Machine Learning Techniques

• Decision tree learning

• Conceptual clustering

• Case-based learning

• Reinforcement learning

• Neural networks

• Genetic algorithms

• and… Inductive Logic Programming

Why ILP ? - Structured data

Seed example of East-West trains (Michalski)

What makes a train to go eastward ?

Why ILP ? – Structured data

Mutagenicity of chemical molecules(King, Srinivasan, Muggleton, Sternberg, 1994)

What makes a molecule to be mutagenic ?

Why ILP ? – multiple relations

This is related to structured data

Train Car

t1 c11

t1 c12

t1 c13

t1 c14

t2 c21

… …

Car Length Shape Axes Roof …

c11 short rectangle 2 none …

c12 long rectangle 3 none …

c13 short rectangle 2 peaked …

c14 long rectangle 2 none …

c21 short rectangle 2 flat …

… … … … … …

has_car car_properties

Why ILP ? – multiple relations

Genealogy example:• Given known relations…

– father(Old,Young) and mother(Old,Young)– male(Somebody) and female(Somebody)

• …learn new relations– parent(X,Y) :- father(X,Y).– parent(X,Y) :- mother(X,Y).– brother(X,Y) :-

male(X),father(Z,X),father(Z,Y).

Most ML techniques can’t use more than 1 relatione.g.: decision trees, neural networks, …

Why ILP ? – logical foundation

• Prolog = Programming with Logicis used to represent:– Background knowledge (of the domain): facts– Examples (of the relation to be learned): facts– Theories (as a result of learning): rules

• Supports 2 forms of logical reasoning– Deduction– Induction

Prolog - definitions

• Variables: X, Y, Something, Somebody• Terms: arthur, 1, [1,2,3]• Predicates: father/2, female/1

• Facts:– father(christopher,victoria).– female(victoria).

• Rules:– parent(X,Y) :- father(X,Y).

Logical reasoning: deduction

From rules to facts…

B T |- E

mother(penelope,victoria).

mother(penelope,arthur).

father(christopher,victoria).

father(christopher,arthur).

parent(X,Y) :- father(X,Y).

parent(X,Y) :- mother(X,Y).

parent(penelope,victoria).

parent(penelope,arthur).

parent(christopher,victoria).

parent(christopher,arthur).

Logical reasoning: induction

From facts to rules…

B E |- T

mother(penelope,victoria).

mother(penelope,arthur).

father(christopher,victoria).

father(christopher,arthur).

parent(X,Y) :- father(X,Y).

parent(X,Y) :- mother(X,Y).

parent(penelope,victoria).

parent(penelope,arthur).

parent(christopher,victoria).

parent(christopher,arthur).

Induction of a classifieror Concept Learning

Most studied task in Machine Learning

Given:– background knowledge B– a set of training examples E– a classification c C for each example e

Find: a theory T (or hypothesis) such that

B T |- c(e), for all e E

Induction of a classifier: example

Example of East-West trains• B: relations has_car and car_properties

(length, roof, shape, etc.)

ex.: has_car(t1,c11), shape(c11,bucket)• E: the trains t1 to t10• C: east, west

Why ILP ? - Structured data

Seed example of East-West trains (Michalski)

What makes a train to go eastward ?

Induction of a classifier: example

Example of East-West trains• B: relations has_car and car_properties

(length, roof, shape, etc.)

ex.: has_car(t1,c11)• E: the trains t1 to t10• C: east, west

• Possible T: east(T) :-

has_car(T,C), length(C,short), roof(C,_).

Induction of a classifier: example

Example of mutagenicity• B: relations atom and bond

ex.: atom(mol23,atom1,c,195). bond(mol23,atom1,atom3,7).

• E: 230 molecules with known classification• C: active and nonactive w.r.t. mutagenicity

• Possible T:

active(Mol) :-

atom(Mol,A,c,22), atom(Mol,B,c,10),bond(Mol,A,B,1).

c22

c10

Learning as search

Given:– Background knowledge B

– Theory Description Language T

– Positives examples P (class +)

– Negative examples N (class -)

– A covering relation covers(B,T,e)

Find: a theory that covers– all positive examples (completeness)

– no negative examples (consistency)

Learning as search

• Covering relation in ILPcovers(B,T,e) B T |- e

• A theory is a set of rules• Each rule is searched separately (efficiency)• A rule must be consistent (cover no

negatives), but not necessary complete• Separate-and-conquer strategy

– Remove from P the examples already covered

Space exploration

Strategy?• Random walk

– Redundancy, incompleteness of the search

• Systematic according to some ordering– Better control => no redundancy, completeness

– The ordering may be used to guide the search towards better rules

What kind of ordering?

Generality ordering

• Rule 1 is more general than rule 2=> Rule 1 covers more examples than rule 2

– If a rule is consistent (covers no negatives)then every specialisation of it is consistent too

– If a rule is complete (covers all positives)then every generalisation of it is complete too

• Means to prune the search space• 2 kinds of moves: specialisation and generalisation• Common ILP ordering: θ-subsumption

Generality orderingparent(X,Y):-

parent(X,Y):- female(X) parent(X,Y) :- father(X,Y)

parent(X,Y) :- female(X), mother(X,Y)

parent(X,Y) :- female(X), father(X,Y)

consistent rulespecialisation

Search biases

“Bias refers to any criterion for choosing one generalization over another other than strict consistency with the

observed training instances.” (Mitchell)

• Restrict the search space (efficiency)• Guide the search (given domain knowledge)• Different kinds of bias

– Language bias

– Search bias

– Strategy bias

• Choice of predicates:roof(C,flat) ? roof(C) ? flat(C) ?

• Types of predicates :east(T) :- roof(T), roof(C,3)

• Modes of predicates :east(T) :- roof(C,flat)

east(T) :- has_car(T,C), roof(C,flat)

• Discretization of numerical values

Language bias

Search bias

The moves direction in the search space• Top-down

– start: the empty rule (c(X) :- .)– moves: specialisations

• Bottom-up– start: the bottom clause (~ c(X) :- B.)– moves: generalisations

• Bi-directional

Strategy bias

Heuristic search for a best rule• Hill-climbing:

– Keep only one rule– efficient but can miss global maximum

• Beam search:– also keep k rules for back-tracking– less greedy

• Best-first search:– keep all rules– more costly but complete search

A generic ILP algorithm

procedure ILP(Examples)

Initialize(Rules, Examples)

repeat

R = Select(Rules, Examples)

Rs = Refine(R, Examples)

Rules = Reduce(Rules+Rs, Examples)

until StoppingCriterion(Rules, Examples)

return(Rules)

A generic ILP algorithm

• Initialize(Rules,Examples): initialize a set of theories as the search starting points

• Select(Rules,Examples): select the most promising candidate rule R

• Refine(R,Examples): returns the neighbours of R (using specialisation or generalisation)

• Reduce(Rules,Examples): discard unpromising theories (all but one in hill-climbing, none in best-first search)

ILPnet2 – www.cs.bris.ac.uk/~ILPnet2/

Network of Excellence in ILP in Europe

• 37 universities and research institutes

• Educational materials

• Publications

• Events (conferences, summer schools, …)

• Description of ILP systems

• Applications

ILP systems

• FOIL (Quinlan and Cameron-Jones 1993): top-down hill-climbing search

• Progol (Muggleton, 1995): top-down best-first search with bottom clause

• Golem (Muggleton and Feng 1992): bottom-up hill-climbing search

• LINUS (Lavrac and Dzeroski 1994): propositionalisation

• Aleph (~Progol), Tilde (relational decision trees), …

ILP applications

• Life sciences– mutagenecity, predicting toxicology– protein structure/folding

• Natural language processing– english verb past tense– document analysis and classification

• Engineering– finite element mesh design

• Environmental sciences– biodegradability of chemical compounds

The end

A few books on ILP…• J. Lloyd. Logic for learning:

learning comprehensible theories from structured data. 2003.

• S. Dzeroski and N. Lavrac, editors. Relational Data Mining. September 2001.

• L. De Raedt, editor. Advances in Inductive Logic Programming. 1996.

• N. Lavrac and S. Dzeroski. Inductive Logic Programming: Techniques and Applications. 1994.