Using Prior Learning to Facilitate the Learning of New Causal Theories

Introduction

We address the problem of learning causal knowledge by observing examples of actions and stale changes. We wish to consider the acquisition of simple causal theories such as those which describe the outcome of common events in the life of a small child (e.g., when a cup made of glass is dropped, it usually breaks and when a cup made of plastic is dropped, it. doesn't break).

We take an empirical approach to learning causal theories. A current best hypothesis [12] is formed by noticing similarities and differences among the attributeS of an obsuved event and recalled p-evious events. We choose to select a current best hypothesis rather than maintain a set of consistent hypotheses (e.g., [12]) for a numbu of reasons:

• The set of consistent hypotheses can be very large. For example, consider the following situation: Karen (a young girl with blond hair and blue eyes wearing a green sweatu) pulls on the refrigerator door but it doesn't open. Mike (an adult male with lxown hair and brown eyes wearing a blue sweat shirt) pulls on the refrigerator door and it opens. There are six attributes with different values for Karen and Mike which can genmlte consistent hypotheses. (e.g., when a person with brown eyes pulls on the refrigerator door, it opens.) In addition, these attributes may be combined conjunctively or disjunctively to form a large set of consistent hypotheses. Psychological evidence (e.g., [1, 11]) indicates that only one or a small numbu of hypotheses are considered at one time. Thus generating a causal hypothesis is treated as searching the space of possible hypotheses.
• Before a suffiCient numbu of examples have been encountered to rule out alternative consistent hypotheses, it may be necessary to predict the outcome of a new event The current best hypothesis can serve as the source of this prediction.

When a new example falsifieS the current best hypothesis, a new hypothesis .is selected from the set of consistent hypotheses. In Winston's ARCH program [11] and in RULBMOD [2] domain-specific heuristics select the new hypothesis. Howevu, since we are assuming no initial domain knowledge, our approach differs from the ARCH program and RULBMOD in the following ways:

• Initially, the current best hypothesis is selected randomly from the set of consistent hypotheses subject to the constraint that simpler hypotheses are selected first: one attribute discriminations are selected befo~ conjunctive combinations and disjunctive combinations.

Using Prior Learning to Facilitate the Learning of New Causal Theories

Michael Pazzani, Michael Dyu, Margot Flowers UCLA Artificial Intelligence Laboratory 3531 Boelter Hall Los Angeles, CA 90024

• Distinctions which have proven useful in the past influence the ordu in which causal hypotheses are generated. For example, aftu a number of examples, assume that the current hypothesis indicates that when adults pull on the refrigerator door, it opens. Latu, when presented with examples of an adult with lxown hair successfully inflating balloons, and a small child with blond hair unsuccessful at the same task, the age attribute would be p-efured to the hair-color attnbute. The hypothesis that when an adult blows into a balloon, it will inflate is considued before the hypothesis that when persons with brown hair blow into a balloon, it will inflate. As OCCAM learns about causality, domain-specific heuristics (e.g., adults are strong) are also learned which guide the search for the current best hypothesis on new problems.

In RULBMOD, all previous examples are remembered so that the set of consistent hypotheses is always consistent with previous examples. In the ARCH program, no previous examples are saved so that the set of hypotheses may contain hypotheses which are not consistent with previous examples. We take a compromise between these two extreme positions. In OCCAM, the exact numbu of previous events recalled from memory is dependent on the retrievability of each event as determined by the unique features of the events (see [8, 9, 14].) Typically, at least one positive example and at least one negative example are recalled when selecting a new hypothesis. In addition, the current example and the current incorrect hypothesis constrain the set of consistent hypotheses [1, 10].

Background: OCCAM

OCCAM [14, 15] is a program which maintains a memory of events in sevual domains. As new events are added to memory, generalizations are created which describe and explain similarities and differences between events. OCCAM integrates explanation-based and similarity-based learning techniques. For example, from a numbu of examples OCCAM induces a rule which indicates that parents have a goal of preserving the health of their children. This rule explains why a parent pays a ransom in a single example of kidnapping. This explanation is generalized by explanation-based learning techniques to create a kidnapping schema.

In this paper, we focus on using prior learning to facilitate the learning of new causal theories. Two aspects of OCCAM relevant to learning causal knowledge are explained in this section: generalization rules and confmning causal hypotheses.

GeneraliZation Rules

In OCCAM, generalization rules postulate causal relationships. A generalization rule suggests a causal explanalion for a temporal relationship. For example, the simplest generalization rule is "If an action on an object always precedes a state change for the object, postulate the action results in the state change". Generalization rules suve a number of purposes:

• Explanation-based learning in OCCAM is initiated when a generalization rule suggests an explanation which can be confirmed and elaborated by existing causal theories. In this case, generalization rules focus the search for an explanation.
• In the absence of existing causal theories, generalization rules suggest a causal explanation which can be confmned or denied by additional examples. In this case, generalization rules serve to generate a set of plausible hypotheses which obey certain constraints on causality [3] (i.e., covariation, effects are always present when causes are present, temporal order, causes precede effects, and mechanism, a physical mediator which "connects" a cause to its effect. Generalization rules may be viewed as weak heuristics which filter the set of possible hypotheses to create a set of plausible hypotheses.

(def-gen-rule different-actor-gen-result-part ?state-1 = (state type ?stype object ?object) after ;name ;effect ?act-1 (act type ?atype ;cause object (part of ?object)) ((?act-1 result ?state-1)) (:difference ?act-1 actor) :state-action-exception-actor ;class )

A generalization rule is iUustra~ in Figure 1. ~ch generalization. rule contains a pattern for an effect (In Figure I the effect IS a state of an <;>b.JeCt), a pattern for the cause (an action perform~ on .a part of ~e object), . a temporal relation (after), a set of causal relauonsh1ps (the acuon r~ults m the state), an exceptions note (which indicates that ~e diffe~ce ~ actor may be responsible for the difference in results). Th1s general1Z8Uon rule would be responsible for generating the set of plausible hypotheses to account for the earlier example of the refrigerator opening after Mike pulls on the door, but not opening after Karen pulls on the door.

Generalization rules are divided into classes. Generalization rules which belong to the same class as the one in Figure 1 all attribu~ a differene;e in the result of an action to a difference in the actor of the acuon. They differ according to role the object of the state plays in the !!Ction. ln the rule !Jt Figure I, the action is performed on a part of ~ objeCt. ln o~er ~les m this class the action is performed on the object, or the object IS the destinatio~ of some action. The class of a generalization rule plays a part in facilitating the learning of new causal theories.

Confirming Causal Theories

In [IS], we discuss our approac~ to confirming hYJ?Oth~. We qui~kly review two strategies for confirmmg hypoth~~ ~h1ch will be ~ m a later example. First, confidence in a hypothesi~ Js mcreased :"~en. 1t makes a correct prediction [9]. Second, confidence m a hypothesiS .IS .mcreased when each alternative hypothesis is ruled out. Later, we also mdicate how prior learning can help confirm causal theories.

Facilitating the Learning of New Causal Theories

How can prior learning facilitate the selection. of the current ~t hypothesis of a set of consistent hypotheses? One Slffiple approach m1ght be to keep track of the attributes which have entered into previous successful hypotheses. For example, consider a child eating .Pieces of a pineapple The pieces can be different shapes (square or tnangular) or different ~olors (yellow or white). Eventually, ~e hypothesis that the yellow pieces of pineapple taste better may be considered and supported by a number of examples. Should color be preferred in future hypotheses? Unfortunately, preferring color indiscrimin~tely would ~inder rather than facilitate learning in many situations. Consider the earher examp~e of the refrigerator opening after Mike pulls on the door, but not operu~g ~ter Karen pulls on the door. If color were preferred, the best hypothesi~ m1ght be that when a person with a blue shirt pulls on the door, the refrigera~r will open. The problem with this simple approach is that the context m which a preference is made is ignored.

The approach that we take in OCCAM differs from the above simple approach in two ways:

1. Attributes which have entered into previous successful hypotheses are preferred in more restricted situations. These situations are determined by the type of the cause in a the generali~tion .rule and the cias;s of the generalization rule. For example, af~r mducmg that the refrige~r door will open after an adult pulls on 1~ the preference for .age. applies only to the actor of this type of the acuon (propel, an applicauon o.f a force) and to the same class of generalization rules (i.e., those wh1ch attribute a difference in a result to a difference in the actor).
2. The attributes which have entered into previous successful hypotheses are used to create disposi~o~l attribut~ These dispositional attributes represent capac1t~s or potent18~ For example, after OCCAM induces that the refrigerator d~r w1~l open when an adult pulls on it, a dispositional attribute wh1ch m1ght be

called "strength" is created, where strength is the tendency for an application of force by a particular actor to result in a state change. Dispositional attributes serve a number of purposes:

• Distributional attributes serve as intermediate conclusions [6]. Like Fu and Buchanan's intermediate concepts, these dispositional predicates often correspond to named concepts in our domain (see Figure 2). If further information is found out about a dispositional attribute, it applies to all future and past examples. For example, in OCCAM, age is initially associated with strength. If other attributes are found which are indicators of strength (e.g., size of arms), they enter into future predictions.

Figure 2: Dispositional attributes. "propel" is the conceptual dependency act for the application or a physical force, "move" is a movement or a body part, "mbuild" is the making or a decision. Note that the attribute listed for each disposition is only the initial attribute associated with the disposition.

• Distributional attributes can viewed as parent predicates [7]. It is in this manner, that distributional attributes facilitate learning new causal theories. When learning that a refrigerator will open after an adult pulls on the door, two hypotheses are created:
• Adults are strong enough to open a refrigerator door.
• Adults are strong.

It is this second more general hypothesis which facilitates learning in new domains. For example, this hypothesis can be specialized to indicate that adults are strong enough to inflate balloons. Note that OCCAM does not start with dispositional attributes such as "strength". Instead, dispositional attributes are created to account for differences in capabilities (for actors) or tendencies (for objects). These dispositional attributes serve as domain-specific knowledge which guide the search for causal hypotheses.

• More support is given to hypotheses which are formed by making use of existing dispositional attributes. It is in this manner that prior learning also facilitates confirming hypotheses.

There are a number of issues which arise when using dispositional attributes to facilitate the search for causal hypotheses:

• When are dispositional attributes created? Dispositional attributes are created to account for a difference in the result of two (or more) actions.
• How do we avoid creating a new dispositional attribute for each new example? The reuse of existing dispositional attributes is preferred to the creation of new ones.

An Example

In this section we demonstrate how learning dispositional attributes facilitates learning new causal theories. The example we consid~r is the refrigerator opening after Mike pulls on the door, but not operung after Karen pulls on the door. In this case there are two events in ~e~ory. Events are input to occ~ in conce~tual de~~dency [16). ~ Simplified representation of Mike opemng the refrigerator IS Illustrated m Figure 3.

The generalization rule in Figure I suggest that a difference in the actor accounts for the different results when Mike or Karen pulls on the door. Since there are not yet any applicable dispositional attributes, OCCAM randomly selects one attribute of the actor which is different in Karen and Mike: eye-color. OCCAM creates a new dispositional attribute 1 (disp-I)

1 This rcndency doesn't have a name in Englilh, 10 we'll have to refer to it by OCCAM' I nune: disp-1.

which represents the tendency for an application of a force by a person with brown eyes to result in a state change. The current best llypothesis is that pexsons with brown eyes are disp-1 enough to open a refrigerator.

Soon, OCCAM is presented with a countereumple of a small child with brown eyes and blond hair who cannot open the refripator. This contradicts a prediction made by the current hypothesis. Smce vt:ry linle confidence had been built up for the current hypothesis and disp-1 they are abandoned, and a new current best hypothesis must be generated. There are at least two possible hypotheses: persons with b:own hair can open refrigerators, or adults can open refrigerators. OCCAM randomly selects adults to form a new dispositional attributel (strength) which represents the tendency for an application of a force by an adult to result in a state change. The current best hypothesis is that adults are strong enough to open a refrigerator. Further examples give a great deal of support to this hypothesis and to the dispositional attribute called strength. 3

Once OCCAM has learned a dispositional attribute, future learning is ~acili~ted. OCCAM is next presented ~ an example of Mike successfully mflatmg a round yellow balloon, while Karen cannot inflate a long blue balloon. This time, two generalization rules apply, one which would attribute the difference in the result to a difference in the object (round yellow balloon vs. long blue balloon) and one which would attribute the difference to the actor (Mike vs. Karen). Since thele are no dispositional attributes for the object difference, one attribute (color) is randomly selected. For the acta" difference, the strength dispositional attribute applies (since the generalization rule class, and the act type are the same as the refrigerator example), and the age attribute is selected over other attrib~tes such as hair color. These two competing hypothesis are compared, and smce the strength (and, thelefore, the age) of the actor has more support than the color of the object, 4 it is favored. The current beSt hypothesis is that adults are strong enough to inflate balloons. Further examples add support to this hypothesis.

Conclusions

We have presented one point on w~t appears to be a continuum between explanation-based learning and empiricallearnin' methods. The technique presented in this paper appears limited to domams that have a reason for their regularity (i.e., dispositional attributes). For example, it would not apply to concept learnin$ of physical objects (i.e., there is no reason that color is significant in distmguishing a horse from a zebra, but not significant in distinguishing an arch from a house).

There are a number of possible extensions to this walt. Fust, OCCAM contains generalization rules which attribute the difference of a result to a difference in the acta" or the obJect These rules could also be learned as dispositional attributes represenung internal and external causes for ~ or failure. This distinction is quite important in determining the affective response to an outcome [S]. Second, the dispositional attributes in OCCAM are learned at a fixed level . of generality (i.e., the type of conceptual dependency action.) This works well for the examples we have encountered, but a more general approach would be to learn the level of generality of a dispositional attribute by keeping track of the instances in which it has applied successfully and unsuccessfully. This would be more in the spirit o( Goodman's parent predicates and over-hypodleses. Finally the cases of a dispositional attribute being abandoned can be recorded ~ that learning is also facilitated by avoiding the same mislakc in future cases.

"occ..M'o name fe< lhi.o allribule i.o di.op-2.

3N01e that an event ouch u an odult not bein& oble to lift a car would not clecreue ouppo1t for the exi.otmce of the otrm&lh cli.opooiticnal allribute. Only a COUIIIeniUIIIpl oudl u a child liftin& a car which an adult could not would ftllllC>Ye ouppo1t hem tbi.o hypotheoi.o since this counterexample would use lhe same aeneralization rule.

4 Recall thatlhe re-use of a cliopooitional auributes inc:reuea the support fe< a hypooheoio

We have presented an approach to learning causal theories which creates disJ)ositional attributes such as "strength" to facilitate future learning. This technique has been applied successfully to a number of examples of causal theories and an example of a social theory: OCCAM required many examples to induce that parents (as opposed to any adult) have a goal of satisfying the hunger of their children. A dispositional attribute (which might be called "affection") was formed which facilitated learning that parents have a goal of preserving the health of their children. This social ~ow~ge pro":ided an explanation for a parent ~ying the ransom in kidnappmg, wh1ch enabled OCCAM to create a kidnapping schema by explanation-based learning techniques.