One piece at a time: Learning complex rules through self-directed sampling

One piece at a time: Learning complex rules through self-directed sampling Doug Markant (doug.markant@nyu.edu) Todd M. Gureckis (todd.gureckis@nyu.edu) New York University Department of Psychology 6 Washington Place, New York, NY 10003 USA Abstract How do people make information sampling decisions? Self-directed information sampling—the ability to collect in- formation that one expects to be useful—has been shown to improve the eﬃciency of concept acquisition for both human and machine learners. However, little is known about how peo- ple decide which information is worth learning about. In this study, we examine self-directed learning in a relatively complex rule learning task that gave participants the ability to “design and test” stimuli they wanted to learn about. On a subset of trials we recorded participants’ uncertainty about how to clas- sify the item they had just designed. Analyses of these uncer- tainty judgments show that people prefer gathering informa- tion about items that help re ne one rule at a time (i.e., those that fall close to a pairwise category “margin”) rather than items that have the highest overall uncertainty across all relevant hy- potheses or rules. Our results give new insight into how people gather information to test currently entertained hypotheses in complex problem solving tasks. Keywords: self-directed learning, categorization, active learn- ing, information search, rule learning In light of evidence that self-directed sampling can speed learning, it is important to understand how people decide what data to collect. Given a potential observation, what in- formation do people rely on to decide if it will be useful? One aspect that may help explain a person’s decision to sample an item is their uncertainty in how to classify it (or more generally, their uncertainty about the outcome of any test performed on the item). Intuitively, a self-directed learner should direct their attention to items that are high in uncer- tainty while ignoring items that can already be con dently classi ed or predicted. Consistent with this strategy, the pat- tern of stimuli sampled by self-directed learners in our pre- vious study (see Figure 1) revealed that participants system- atically directed their samples toward the category boundary as the task progressed. Intuitively, the learner is mostly likely to be uncertain about these items (e.g., most of the errors in classi cation occur near the category boundary). In the current study, we examine how subjective uncer- tainty in how to classify an item can be used to predict whether or not it is sampled. We begin by presenting three psycholog- ically motivated proposals for how sampling decisions relate to judgments of uncertainty, and then test these models in a new experiment that extends the “self-directed” classi cation learning paradigm used in Markant and Gureckis (2010). Our results highlight the need for models of sampling behavior that go beyond monolithic measures of information value to con- sider how people collect and use data during the sequential learning of concepts. Introduction A cornerstone of many educational philosophies is that people learn more eﬀectively when they direct or control their own learning experiences (Bruner, 1961). While there are many ways that control might in uence learning, an important fac- tor is the ability to actively gather information that one con- siders potentially useful while avoiding data that is poten- tially redundant, a behavior referred to as self-directed sam- pling (Gureckis & Markant, in revision). One recent study directly examined the interaction of self-directed information sampling and learning (Markant & Gureckis, 2010, in revision). In this study, people attempted to learn simple dichotomous categories of objects that varied along two perceptual dimensions (circles that diﬀered in size and the orientation of a central line segment, see Figure 1). In contrast to traditional categorization training procedures, we allowed participants to “design” stimuli that they wanted to learn more about on each trial. Like a child asking their parent to label an unfamiliar object, self-directed “designing” or “sampling” allows the learner to focus on information they want rather than be limited by the ow of passive experience. e major nding from this study was that for simple uni- dimensional rules, self-directed learners acquired the correct category rule faster than “passive” participants who were pro- vided samples from an experimenter-de ned distribution. In addition, self-directed learners out-performed a set of “yoked” learners who viewed the same examples but did not get to make information sampling decisions themselves (consistent with studies of causal learning with similar yoked compar- isons, Lagnado and Sloman, 2004; Sobel and Kushnir, 2006). ree models for relating uncertainty and information sampling decisions e following sections lay out three possible ways in which uncertainty might guide information sampling decisions. Model 1: Sampling to reduce global uncertainty Prior work on how people gather information has oen fo- cused on diagnostic reasoning problems in which the learner is given a set of alternatives (e.g., diﬀerent diseases) and asked to sample observable features (e.g., symptoms) in order to identify the true diagnosis (Nelson, McKenzie, Cottrell, & Se- jnowski, 2010; Skov & Sherman, 1986; Trope & Bassok, 1982). From a computational perspective, various authors have pro- posed sampling norms that attempt to predict information sampling decisions based on a learner’s representation of the task (Nelson, 2005; Nelson et al., 2010; Oaksford & Chater,