Knowledge in Learning Chapter 19 Copyright, 1996 © Dale Carnegie & Associates, Inc.

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)  … CSE 471/598 by H. Liu

One of the hypotheses is correct: 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. CSE 471/598 by H. Liu

What are 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. CSE 471/598 by H. Liu

Current-best hypothesis search Maintain a single hypothesis Adjust it as new examples arrive to maintain consistency (Fig 19.1) Generalization for positive examples Specialization for negative examples Algorithm (Fig 19.2, page 681) Need to check for consistency with all existing examples each time taking a new example CSE 471/598 by H. Liu

Example of WillWait Fig 18.3 for Current-Best-Learning Problems: nondeterministic, no guarantee for simplest and correct h, need backtrack CSE 471/598 by H. Liu

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 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 Version Space is a set of hypotheses remaining CSE 471/598 by H. Liu

Version space Generalization and specialization (Fig 19.4): find data-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 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 True/+ - true positive; true/- negative CSE 471/598 by H. Liu

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. CSE 471/598 by H. Liu

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 CSE 471/598 by H. Liu

A cumulative learning process Observations, K-based learning, Hypotheses, and prior knowledge Their relationships shown in Fig 19.6 (p 687) 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. How to implement this cumulative learning with increasing knowledge? CSE 471/598 by H. Liu

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 … Do you have any example that your background knowledge helps your learning? CSE 471/598 by H. Liu

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 CSE 471/598 by H. Liu

Inductive logical programming (ILP) ILP can formulate hypotheses in general first-order logic Others like DT are of 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 CSE 471/598 by H. Liu

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 CSE 471/598 by H. Liu

Why EBL? Explaining why something is a good idea is much easier than coming up with the idea. Once something is understood, it can be generalized and reused in other circumstances. Extracting general rules from examples EBL constructs two proof trees simultaneously by variablization of the constants in the first tree An example (Fig 19.7) CSE 471/598 by H. Liu

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 CSE 471/598 by H. Liu

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 study CSE 471/598 by H. Liu

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) CSE 471/598 by H. Liu

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. CSE 471/598 by H. Liu

We can generalize from Fernando to all Brazilians, but not to all nations. So, determinations can limit the H space to be considered. 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 For n Boolean features, if the determination contains d features, what is the saving for the required number of examples according to PAC? CSE 471/598 by H. Liu

Learning using relevant information A determination P Q says if any examples match on P, they must also match on Q Find the simplest determination consistent with the observations Search through the space of determinations from one predicate, two predicates Algorithm - Fig 19.8 (page 696) Time complexity is n choosing p Feature selection is about finding determination Feature selection is an active research area for machine learning, pattern recognition, statistics CSE 471/598 by H. Liu

Its learning performance improves (Fig 19.9). Combining relevance based learning with decision tree learning -> RBDTL Reduce the required training data Reduce the hypothesis space Its learning performance improves (Fig 19.9). Performance in terms of training set size Gains: time saving, less chance to overfit Other issues about relevance based learning noise handling using other prior knowledge Semi-supervised learning Expert knowledge as constraints from attribute-based to FOL CSE 471/598 by H. Liu

Inductive logic programming It combines inductive methods with FOL. ILP represents theories as logic programs. ILP offers complete algorithms for inducing general, first-order theories from examples. It can learn successfully in domains where attribute-based algorithms fail completely. An example - a typical family tree (Fig 19.11) CSE 471/598 by H. Liu

Inverse resolution If Classifications follow from B^H^D, then we can prove this by resolution with refutation (completeness). The normal resolution is C1 and C2 -> C where C is the resolvent If we run the proof backwards, we can find a H such that the proof goes through. C -> C1 and C2 C and C2 -> C1 Generating inverse proofs A family tree example (Fig 19.13) CSE 471/598 by H. Liu

Inverse resolution also involves search Each inverse resolution (IR) step is nondeterministic For any C and C1, there can be many C2 Discovering new knowledge with IR It’s not easy - a monkey and a typewriter Discovering new predicates with IR Fig 19.14 The ability to use background knowledge provides significant advantages CSE 471/598 by H. Liu

Top-down learning (FOIL) A generalization of DT induction to the first-order case by the same author of C4.5 Starting with a general rule and specialize it to fit data Now we use first-order literals instead of attributes, and H is a set of clauses instead of a decision tree. Example: =>grandfather(x,y) (page 701) positive and negative examples adding literals one at a time to the left-hand side e.g., Father (x,y) => Grandfather(x,y) How to choose literal? (Algorithm on page 702) the rule should agree with some + examples, none of – examples FOIL removes the covered + examples, repeats CSE 471/598 by H. Liu

Summary Using prior knowledge in cumulative learning Prior knowledge allows for shorter H’s. Prior knowledge plays different logical roles as in entailment constraints EBL, RBL, KBIL ILP generates new predicates so that concise new theories can be expressed. CSE 471/598 by H. Liu