More Symbolic Learning CPSC 386 Artificial Intelligence Ellen Walker Hiram College

Ensemble Learning Instead of learning exactly one hypothesis, learn several and combine them Example –Learn 5 hypotheses (classification rules) from the same training set –For each element in the test set, let all hypotheses vote on classification –Result: for an item to be mis-classified, it has to be mis- classified (in the same way) by 3 different hypotheses! Assumption: errors made by each hypothesis are independent (or at least, different)

Multiple Simple Hypotheses Simple hypotheses –Require less time to compute –Require less space to represent –Limit the “expressiveness” of what can be learned Multiple simple hypotheses (fixed number) –Don’t significantly increase time or space needs –Can significantly increase expressiveness Example (next slide): Multiple linear thresholds

Multiple Linear Threshold Hypotheses A point must be on the correct side of all lines to be classified + (blue)

Boosting Generate M hypotheses sequentially, from “weighted training sets” First set has equal weights. Second set has misclassified examples from first set weighted higher, correctly classified weighted lower. Third set revises weights based on classified/misclassified examples from second set, etc. Result is weighted majority classification of all hypotheses, weighted according to how they did on the training set.

Boosting Training Data 1.Foreign, small, red + 2.Domestic, large green – 3.Foreign, small, blue – 4.Domestic, small, red + 5.Foreign, large, green – 6.Foreign, large, red –

Boosting Example example123456Error, Z Weight 1/6 H1:small ++–+++ 1/6 log 5 weight 1/10 1/21/10 H2: red +++++– 1/10 log 9 Weight 1/18 5/181/18 1/2 H3: dom ––++++ 1/9 log 8

Test Classifications Rules: small (log 5), red (log 9), dom (log 8) Domestic, large, blue –NO (log 5 + log 9), YES (log 8) --> NO Domestic, large, red –NO(log 5), YES (log 9 + log 8) --> YES Foreign, small, green –NO(log 8 + log 9), YES (log 5) --> NO

Knowledge in Learning What you learn depends on what you know –Attributes for classification –Organizational structure Relationships in structural learning (e.g. above, next to, touching) –Relevance Copper wire {conducts electricity / is 2m long}

Explanation Based Learning “Learning” from one example Extract a general rule from an example –A penny conducts electricity –(Pennies are made of copper) –Therefore, copper conducts electricity Generalization of optimization technique called memoization –Build table of results from prior computations

Steps in EBL 1.Build an explanation of the observation. For example, prove that the instance is a member of a query class (goal predicate) 2.In parallel, construct a generalized proof tree, using the same inference steps (rules) 3.Transform the generalized proof tree into a new rule. This generalizes the new explanation.

Operationality Define an “easy” subgoal as operational Use operationality to know when to stop the proof Examples: –Operational concept is a structural constraint that can be easily observed –Operational concept is a LISP primitive that can be easily applied

EBL Example: Learn “cup” Goal: A cup is stable, liftable, and holds liquid Operationality: only structural criteria (geometry, topology) may be used Example: a coffee-cup

Explain the Observation Prove why the object is a cup: –Goal: stable(x) & liftable(x) & holds-liquid(x) -> cup(x) –Facts: flatbottom(cup1) & red(cup1) & attach(cup1,handle) & weight(cup1,2oz) & concave(cup1) & ceramic(cup1) –Proof: Cup is stable because it has a flat bottom; liftable because it has a handle and weighs 2oz (which is less than 16oz), and holds-liquid because it is concave.

Generalize Replace all constants in the proof (e.g. cup1) with variables cup(x) <- flatbottom(x) & attach(x,y) & weight(x,z) & concave(x) Re-prove to find any variables that should really be constants! cup(x) <- flatbottom(x) & attach(x,handle) & weight(x,z) & (< z 16oz) A cup is an object that has a flat bottom, a handle, and weighs < 1lb and is concave

Relevance Based Learning Find simplest determination consistent with the observations –Determination is a set of features P,Q so that if examples match on P, they will also match on Q –In this case, Q is the target predicate (classification to be learned) –Simplest has the fewest attributes Combine with Decision Tree for great improvement –RBL to select a subset of attributes, then DTL

Inductive Logic Programming Combines inductive learning (from examples) with first-order logical representations Allows relational concepts (like grandparent) to be learned, unlike attribute-based methods Is a rigorous approach

Top-Down ILP Start with a very general rule –Analogy: empty decision tree –Actual: empty left side – (empty) => grandfather(X,Y) Gradually specialize the rule until it fits the data –Analogy: growing the decision tree –Actual: adding predicates to left side until all examples are correctly classified father(X,Z) => grandfather(X,Y) father(X,Z) and parent(Z,Y) => grandfather(X,Y)

Inverse Resolution We know that resolution takes two clauses c1 and c2 and generates a result c Inverse resolution starts with c (and possibly c1) and determines c2 Working “backwards” through a proof, generate the necessary rules –This can be done for discovery = unsupervised symbolic learning!

Some Final Comments Learning requires prior knowledge –E.g. which attributes are available? –E.g. current rules for EBL Prior knowledge can bias a learning system –This can be good or bad Existing learning systems are focused; we are a long way from creating a system that learns like an infant.