Probability Learning Research Articles

Learning temporal probabilistic causal models from longitudinal data

Medical problems often require the analysis and interpretation of large collections of longitudinal data in terms of a structural model of the underlying physiological behavior. A suitable way to deal with this problem is to identify a temporal causal model that may effectively explain the patterns observed in the data. Here we will concentrate on probabilistic models, that provide a convenient framework to represent and manage underspecified information; in particular, we will consider the class of Causal Probabilistic Networks (CPN). We propose a method to perform structural learning of CPNs representing time-series through model selection. Starting from a set of plausible causal structures and a collection of possibly incomplete longitudinal data, we apply a learning algorithm to extract from the data the conditional probabilities describing each model. The models are then ranked according to their performance in reconstructing the original time-series, using several scoring functions, based on one-step ahead predictions. In this paper we describe the proposed methodology through an example taken from the diabetes monitoring domain. The selection process is applied to a set of input-output models that generalize the class of ARX models, where the inputs are the insulin and meal intakes and the outputs are the blood glucose levels. Although the physiological process underlying this particular application is characterized by strong non-linearities and low data reliability, we show that it is possible to obtain meaningful results, in terms of conditional probability learning and model ranking power.

Use of external frames of reference and dead reckoning in toddlers' coding of spatial location

Recent research has expanded the list of factors that control spatial attention. Beside current goals and perceptual salience, statistical learning, reward, motivation and emotion also affect attention. But do these various factors influence spatial attention in the same manner, as suggested by the integrated framework of attention, or do they target different aspects of spatial attention? Here I present evidence that the control of attention may be implemented in two ways. Whereas current goals typically modulate where in space attention is prioritized, search habits affect how one moves attention in space. Using the location probability learning paradigm, I show that a search habit forms when people frequently find a visual search target in one region of space. Attentional cuing by probability learning differs from that by current goals. Probability cuing is implicit and persists long after the probability cue is no longer valid. Whereas explicit goal-driven attention codes space in an environment-centered reference frame, probability cuing is viewer-centered and is insensitive to secondary working memory load and aging. I propose a multi-level framework that separates the source of attentional control from its implementation. Similar to the integrated framework, the multi-level framework considers current goals, perceptual salience, and selection history as major sources of attentional control. However, these factors are implemented in two ways, controlling where spatial attention is allocated and how one shifts attention in space.

Goal Setting Effects on Implicit and Explicit Learning of Complex Tasks

The robust finding that setting difficult, specific goals leads to increased performance on simple tasks has not generalized to complex task performance. The results of the present research suggest that the moderating effect of task complexity on the goal–performance relationship is due to confounding goal difficulty with explicit and implicit learning. Two multiple cue probability learning studies were performed keeping the learning mode constant while varying goal difficulty. Study 1 examined goal setting effects on performance when task processing was implicit. Consistent with previous research on complex tasks, setting difficult, specific goals did not result in performance gains. Study 2 demonstrated that when complex task processing is explicit, goal setting results in gradual but steady improvements in complex task performance. Protocol analysis of strategies used by participants indicate that goal setting resulted in increased performance through the development of better strategies.

The Learning of Natural Configural Strategies

The learning of natural configural strategies, strategies that match people intuitive theories about configural relationship between variables, is studied in a two-cue probability learning paradigm. The main focus is the learning of disjunctive strategy, a strategy in which response depends primarily on the high cue, and conjunctive strategy, a strategy in which response depends primarily on the low cue. We find that people learn disjunctive strategy better when the target of the prediction is human than when it is non-human, and that they learn conjunctive strategy better when the target is non-human. In addition, in a meaningful context, conjunctive strategy is learned better in the short run, but after a prolonged feedback, disjunctive strategy is learned better. In an abstract context, disjunctive strategy is learned better both in the short run and in the long run. The processes that lead to these differences in the learning of conjunctive and disjunctive strategies are discussed.

Structure of mental models, problem solving, and learning of probability

Structure of mental models, problem solving, and learning of probability

Feedback Representation and Prediction Strategies

The influence of feedback representation on prediction is examined in a single cue probability learning paradigm. Two types of feedback representation are examined: deviation representation, in which the feedback is the magnitude, or even just the sign, of the prediction error, and standard representation, in which the feedback is the outcome itself. It is found that when the predictor is represented visually (rather than numerically), and when the outcome scale is unknown, deviation representation results in higher prediction extremity than standard representation. In addition, deviation representation results in higher prediction consistency than standard representation. These findings are explained as resulting from more reliance on the representativeness heuristic in the deviation representation conditions.

Using Lotteries to Improve Students' Number Sense and Understanding of Probability

This article examines ways in which a discussion of lotteries can be integrated into a classroom lesson on combinatorics and probability and be used to enhance the teaching and learning of number sense and probability of winning various lottery games, and facts and myths about lotteries. Instructional tips for incorporating discussions of lotteries into lesson plans are also given.

A turning point in mathematical learning theory.

This target article by Estes (1950) sparked the mathematical learning theory movement, which took seriously the goal of predicting quantitative details of behavioral data from standard learning experiments. The central constructs of Estes's theory were stimulus variability, stimulus sampling, and stimulus-response association by contiguity, all cast within a framework enabling predictions of response probabilities and latencies. The math models enterprise flourished during the period 1950-1975 and provided successful quantitative accounts of data from Pavlovian and instrumental conditioning, probability learning, verbal learning, concept identification, and other standard learning paradigms. The techniques have been assimilated into the armamentarium of theoretical psychology. Stimulus sampling theory has faded away as it has been transformed into modern descendants such as connectionism and information-processing models of cognition.

Statistical Decision Task in Probability Learning Situation

Statistical Decision Task in Probability Learning Situation

確率学習場面における精神遅滞児の問題解決過程と発達-差異論争

精神遅滞児の心理学研究において、学校や家庭での精神遅滞児の行動が、ほとんど問題解決行動として注目されてこなかったのは、一種の驚きである。確かに、一般的にも問題解決の検討は、種々な要因が関与するだけに困難を極める。その上、精神遅滞児の場合、彼らの問題解決行動を分析しようとすると、健常児以上に認知要因および情緒的動機づけ的要因の連関性が強く、実験統制の難しさのみならず、個人間・個人内差が大きくなるだろう。しかしながら、とくに精神遅滞児の教育の手がかりをもつためには、もっとこの問題解決行動の研究が進歩する必要がある。本稿では、確率学習課題を用い、その基礎心理機制を検討してきた諸研究を概観して、精神遅滞児の特徴を知る。そして、精神遅滞児の認知機能に関して、1960年代から続いている論争に、この問題解決過程からの接近を試み解決の方向を探る。

Attenuation by contextual cues of retroactive interference of a conditional discrimination in rats

We investigated the effect of associating unique contextual cues with an interpolated learning task on retroactive interference in long-term memory. Rats were originally trained in a two-bar operant chamber with an auditory conditional discrimination stimulus. During interpolated learning, which occurred in either the original or a new context, some rats were trained on a probability learning task that did not include the auditory stimuli present during original learning. Subsequent retraining on the original conditional discrimination task in the original context showed that (1) significant retroactive interference occurs in rats, and (2) the presence of unique contextual cues during interpolated learning significantly reduces this interference. These results extend the conditions under which the susceptibility to retroactive interference can be altered by contextual cues.

Review: Cognitive Snapshots of the Stochastic River

A tour through seven different perspectives on the learning of probability offered by the chapter authors of Chance Encounters is simultaneously enlightening and frustrating. It is enlightening because each perspective provides some conceptual morsels for researchers in probability to assimilate or to reject. It is frustrating because no synthesis of the perspectives, no careful distillation of the major ideas in the book, was attempted either by the editors or by any chapter author. The book can be thought of as a series of cognitive photographs from a river tour of stochastic thinking. Like real photos, some of the pictures we receive are in crystalline focus, whereas others are either underdeveloped or overdeveloped. Each reader will have to construct an overall perspective for himself or herself in order to bring the main ideas into focus.

Task information, cognitive information, or functional validity information: Which components of cognitive feedback affect performance?

A recent review by Balzer, Doherty, and O'Connor (1989) decomposed cognitive feedback (CFB) into three conceptually distinct components: information about the task system (task information, TI), information about the subject's cognitive system (cognitive information, CI), and information about the relationship of the task system to the cognitive system (functional validity information, FVI). Their review suggested that the TI component of CFB appeared to be the component responsible for improvements in performance on multiple cue probability learning (MCPL) tasks. A laboratory experiment was designed to test whether different combinations of CFB components lead to different levels of performance. Undergraduates ( N = 133) were randomly assigned to one of five CFB conditions (TI only, CI only, TI + CI, TI + CI + FVI, or no feedback (NF)). Subjects completed a MCPL task, predicting number of wins for major league baseball teams. Subjects returned a week later, received the CFB appropriate for their experimental condition, and repeated the judgment task. Traditional measures of performance on MCPL tasks (e.g., r a ) were collected, along with measures of the accuracy of predictions and self-report measures of the understandability and helpfulness of feedback. Results indicated that subjects who received TI (i.e., TI, TI + CI, or TI + CI + FVI feedback conditions) showed significantly better performance than subjects who received no feedback as indicated by validity and accuracy measures of performance. In no instance did the CI condition show better performance the the NF condition, nor did the TI + CI or TI + CI + FVI conditions show better performance then the TI condition. No differences were found in subjects' self-reported reactions to CFB. Overall, TI was found to be the CFB component that improved the validity and accuracy of judgement performance.

The Positive Effects of Easy Goals on Decision Quality and Risk Propensity in an MCPLP Task

ABSTRACTIn this study the potential performance benefits of easy goals were examined within the multiple cue probability learning paradigm (MCPLP). Specifically, the effects of varying levels of goal difficulty on performance and risk propensity (used to define a form of commitment) were investigated. With few exceptions, previous studies demonstrated support for difficult goals. In this study, contrary to the majority of past evidence, as goals became easier decision quality significantly improved. Moreover, risk propensity increased with easier goals and, as suggested by a post‐hoc analysis, had more direct impact on decision makers’ behaviors than goal levels. Goal‐related behavior in complex MCPLP tasks appears to significantly differ from the majority of goal evidence in other types of research due to the tendency for subjects to view complex task properties in the same context as goal levels.

Separable and unitary stimuli in nonmetric multiple-cue probability learning

Two experiments were run to study the effects of separable and unitary stimuli dimensions in a probabilistic, decision-making-like environment. Using a nonmetric multiple-cue probability learning task with two relevant dimensions and additional relevant configural information, no differences in utilization were found for these two types of stimuli. However, in an environment that subjects find more difficult, one in which one dimension is relevant along with the pattern of two additional dimensions, an effect was found. Unitary stimuli were found to facilitate utilization of configural information, but no difference was found for utilization of dimensional information.

An adaptive approach to human decision making: Learning theory, decision theory, and human performance.

This article describes a general model of decision rule learning, the rule competition model, composed of 2 parts: an adaptive network model that describes how individuals learn to predict the payoffs produced by applying each decision rule for any given situation and a hill-climbing model that describes how individuals learn to fine tune each rule by adjusting its parameters. The model was tested and compared with other models in 3 experiments on probabilistic categorization. The first experiment was designed to test the adaptive network model using a probability learning task, the second was designed to test the parameter search process using a criterion learning task, and the third was designed to test both parts of the model simultaneously by using a task that required learning both category rules and cutoff criteria. Probabilistic categorization is an important class of decision problems in which stimuli are sampled from a number of categories and the decision maker must decide the category from which each stimulus was sampled. Payoffs depend on both the true category membership and the decision maker's response for each stimulus. Examples are found in all areas of psychology: In perception, auditory or visual stimuli are categorized as signal or noise, and in memory recognition, verbal items are categorized as old or new. In cognition, exemplar patterns are assigned to conceptual categories, and in industrial psychology, job applicants are categorized as acceptable or unacceptable. Finally, in clinical psychology, patient symptom patterns are assigned to disease categories. For the past 35 years, the general theory of signal detection (Peterson, Birdsall, & Fox, 1954) has served as the most prominent model of probabilistic categorization. It has been successfully applied to all of the areas of psychology mentioned (see Green & Swets, 1966; for perception; Bernbach, 1967, and Wickelgren & Norman, 1966, for memory recognition; Ashby & Gott, 1988, for conceptual categorization; Cronbach & Gleser, 1965, for industrial psychology; and Swets & Pickett, 1982, for medical diagnosis). The core idea is that (a) each stimulus is represented as a point within a multidimensional stimulus space, (b) this multidimensional space is partitioned into response regions, and (c) a stimulus is categorized according to the region within which it lies. Simple decision rules are normally used to describe how the stimulus space is partitioned.' For example, unidimensional stimuli can be divided into two categories by either a cutoff rule (all points above a cutoff go into one category) or by an interval rule (all points inside an interval go into one category). Two-dimensional stimuli can be partitioned into

CHOICE AS A FUNCTION OF LOCAL VERSUS MOLAR REINFORCEMENT CONTINGENCIES

Rats were trained on a discrete-trial probability learning task. In Experiment 1, the molar reinforcement probabilities for the two response alternatives were equal, and the local contingencies of reinforcement differentially reinforced a win-stay, lose-shift response pattern. The win-stay portion was learned substantially more easily and appeared from the outset of training, suggesting that its occurrence did not depend upon discrimination of the local contingencies but rather only upon simple strengthening effects of individual reinforcements. Control by both types of local contingencies decreased with increases in the intertrial interval, although some control remained with intertrial intervals as long as 30 s. In Experiment 2, the local contingencies always favored win-shift and lose-shift response patterns but were asymmetrical for the two responses, causing the molar reinforcement rates for the two responses to differ. Some learning of the alternation pattern occurred with short intertrial intervals, although win-stay behavior occurred for some subjects. The local reinforcement contingencies were discriminated poorly with longer intertrial intervals. In the absence of control by the local contingencies, choice proportion was determined by the molar contingencies, as indicated by high exponent values for the generalized matching law with long intertrial intervals, and lower values with short intertrial intervals. The results show that when molar contingencies of reinforcement and local contingencies are in opposition, both may have independent roles. Control by molar contingencies cannot generally be explained by local contingencies.

Hindsight bias in a very sparse environment

Hindsight bias, the inability to ignore outcome information, was studied in a sparse and abstract environment, that of a probability learning task. Following the probability learning task, the subjects were asked to estimate the probability of the events. The subjects in the hindsight conditions were provided outcome information. They were unable to ignore the outcome information even though they were instructed to do so. Their mean probability estimates deviated in the direction of the outcome information they received. This was found for subjects who received the “actual probabilities” as outcome information as well as for subjects who were only given what the event on the next trial would have been.

Interaction of data and hypotheses in probabilistic inference tasks: Rejection of the hypothesis sampling model?

The problem of whether or not data influence subjects’ sampling of hypotheses about functional relations in the probabilistic inference tasks was examined. The results of the experiment show first, a considerable impact of data on subjects’ hypothesis selection and second, that the subjects significantly modify their hypothesis selection from one part of the experiment to the other. Thus, there is an interaction of data and hypotheses in cue probability learning (CPL) tasks regarding the hypothesis sampling process and an execution of cognitive control over the subjects’ hypothesis pool.

Motivational Determinants of Children's Probability Learning

Abstract We studied performance on the probability-learning task, a discrimination task with three alternatives, only one of which gets 66% reinforcement. The goals were to examine the relations of maximizing—namely, choosing the reinforced alternative—to success-oriented motivational variables and IQs in the two genders and in two age groups. The Wechsler-Bellevue test (Lieblich, Ben-Shahar, & Ninio, 1975) and tasks assessing probability learning, expectancy of success, delay of gratification, and risk-taking were administered individually. Correlations, factor analyses, and multiple regression analyses showed that maximizing was correlated negatively with the motivational variables in both age groups and that in combination with them it accounted for the bulk of the variance. It also correlated negatively with IQ more in older subjects than in younger subjects. We also addressed the multiple motivational determinants of maximizing and the direct cognitive and indirect motivational impact of IQ on perfor...