The asymptotic values of response probabilities in the Audley-Jonckheere learning model

The asymptotic values of response probabilities in the Audley-Jonckheere learning model, as applied to the two-choice learning situation, are derived for (1) the experimenter-controlled events model, (2) the subject-controlled events model, and (3) the experimenter-subject-controlled events model.     

Basing Categorization on Individuals and Events

Exemplar, prototype, and connectionist models typically assume that events constitute the basic unit of learning and representation in categorization. In these models, each learning event updates a statistical representation of a category independently of other learning events. An implication is that events involving the same individual affect learning independently and are not integrated into a single structure that represents the individual in an internal model of the world. A series of experiments demonstrates that human subjects track individuals across events, establish representations of them, and use these representations in categorization. These findings are consistent with “representationalism,” the view that an internal model of the world constitutes a physical level of representation in the brain, and that the brain does not simply capture the statistical properties of events in an undifferentiated dynamical system. Although categorization is an inherently statistical process that produces generalization, pattern completion, frequency effects, and adaptive learning, it is also an inherently representational process that establishes an internal model of the world. As a result, representational structures evolve in memory to track the histories of individuals, accumulate information about them, and simulate them in events.     

Emergent Goal-Anticipatory Gaze in Infants via Event-Predictive Learning and Inference

From about 7 months of age onward, infants start to reliably fixate the goal of an observed action, such as a grasp, before the action is complete. The available research has identified a variety of factors that influence such goal-anticipatory gaze shifts, including the experience with the shown action events and familiarity with the observed agents. However, the underlying cognitive processes are still heavily debated. We propose that our minds (i) tend to structure sensorimotor dynamics into probabilistic, generative event-predictive, and event boundary predictive models, and, meanwhile, (ii) choose actions with the objective to minimize predicted uncertainty. We implement this proposition by means of event-predictive learning and active inference. The implemented learning mechanism induces an inductive, event-predictive bias, thus developing schematic encodings of experienced events and event boundaries. The implemented active inference principle chooses actions by aiming at minimizing expected future uncertainty. We train our system on multiple object-manipulation events. As a result, the generation of goal-anticipatory gaze shifts emerges while learning about object manipulations: the model starts fixating the inferred goal already at the start of an observed event after having sampled some experience with possible events and when a familiar agent (i.e., a hand) is involved. Meanwhile, the model keeps reactively tracking an unfamiliar agent (i.e., a mechanical claw) that is performing the same movement. We qualitatively compare these modeling results to behavioral data of infants and conclude that event-predictive learning combined with active inference may be critical for eliciting goal-anticipatory gaze behavior in infants.     

The tight coupling between category and causal learning

The main goal of the present research was to demonstrate the interaction between category and causal induction in causal model learning. We used a two-phase learning procedure in which learners were presented with learning input referring to two interconnected causal relations forming a causal chain (Experiment 1) or a common-cause model (Experiments 2a, b). One of the three events (i.e., the intermediate event of the chain, or the common cause) was presented as a set of uncategorized exemplars. Although participants were not provided with any feedback about category labels, they tended to induce categories in the first phase that maximized the predictability of their causes or effects. In the second causal learning phase, participants had the choice between transferring the newly learned categories from the first phase at the cost of suboptimal predictions, or they could induce a new set of optimally predictive categories for the second causal relation, but at the cost of proliferating different category schemes for the same set of events. It turned out that in all three experiments learners tended to transfer the categories entailed by the first causal relation to the second causal relation.     

Rich analysis and rational models: inferring individual behavior from infant looking data

Studies of infant looking times over the past 50 years have provided profound insights about cognitive development, but their dependent measures and analytic techniques are quite limited. In the context of infants' attention to discrete sequential events, we show how a Bayesian data analysis approach can be combined with a rational cognitive model to create a rich data analysis framework for infant looking times. We formalize (i) a statistical learning model, (ii) a parametric linking between the learning model's beliefs and infants' looking behavior, and (iii) a data analysis approach and model that infers parameters of the cognitive model and linking function for groups and individuals. Using this approach, we show that recent findings from Kidd, Piantadosi and Aslin ( 2012 ) of a U‐shaped relationship between look‐away probability and stimulus complexity even holds within infants and is not due to averaging subjects with different types of behavior. Our results indicate that individual infants prefer stimuli of intermediate complexity, reserving attention for events that are moderately predictable given their probabilistic expectations about the world.     

Models in search of a brain

Mental localization efforts tend to stress the where more than the what. We argue that the proper targets for localization are well-specified cognitive models. We make this case by relating an existing cognitive model of category learning to a learning circuit involving the hippocampus, perirhinal, and prefrontal cortices. Results from groups varying in function along this circuit (e.g., infants, amnesics, and older adults) are successfully simulated by reducing the model’s ability to form new clusters in response to surprising events, such as an error in supervised learning or an unfamiliar stimulus in unsupervised learning. Clusters in the model are akin to conjunctive codes that are rooted in an episodic experience (the surprising event) yet can develop to resemble abstract codes as they are updated by subsequent experiences. Thus, the model holds that the line separating episodic and semantic information can become blurred. Dissociations (categorization vs. recognition) are explained in terms of cluster recruitment demands.     

No two cues are alike: Depth of learning during infancy is dependent on what orients attention

Human infants develop a variety of attentional mechanisms that allow them to extract relevant information from a cluttered multimodal world. We know that both social and nonsocial cues shift infants’ attention, but not how these cues differentially affect learning of multimodal events. Experiment 1 used social cues to direct 8- and 4-month-olds’ attention to two audiovisual events (i.e., animations of a cat or dog accompanied by particular sounds) while identical distractor events played in another location. Experiment 2 directed 8-month-olds’ attention with colorful flashes to the same events. Experiment 3 measured baseline learning without attention cues both with the familiarization and test trials (no cue condition) and with only the test trials (test control condition). The 8-month-olds exposed to social cues showed specific learning of audiovisual events. The 4-month-olds displayed only general spatial learning from social cues, suggesting that specific learning of audiovisual events from social cues may be a function of experience. Infants cued with the colorful flashes looked indiscriminately to both cued locations during test (similar to the 4-month-olds learning from social cues) despite attending for equal duration to the training trials as the 8-month-olds with the social cues. Results from Experiment 3 indicated that the learning effects in Experiments 1 and 2 resulted from exposure to the different cues and multimodal events. We discuss these findings in terms of the perceptual differences and relevance of the cues.     

A sequence of limiting distributions of response probabilities

Explicit solutions are obtained for a sequence of limiting distributions of response probabilities for the two experimenter-controlled events learning model of Bush and Mosteller [2]. A generalization to thes experimenter-controlled events model is found.     

Inferring interventional predictions from observational learning data

Previous research has shown that people are capable of deriving correct predictions for previously unseen actions from passive observations of causal systems (Waldmann & Hagmayer, 2005). However, these studies were limited, since learning data were presented as tabulated data only, which may have turned the task more into a reasoning rather than a learning task. In two experiments, we therefore presented learners with trial-by-trial observational learning input referring to a complex causal model consisting of four events. To test the robustness of the capacity to derive correct observational and interventional inferences, we pitted causal order against the temporal order of learning events. The results show that people are, in principle, capable of deriving correct predictions after purely observational trial-by-trial learning, even with relatively complex causal models. However, conflicting temporal information can impair performance, particularly when the inferences require taking alternative causal pathways into account.     

Direct Associations or Internal Transformations? Exploring the Mechanisms Underlying Sequential Learning Behavior

We evaluate two broad classes of cognitive mechanisms that might support the learning of sequential patterns. According to the first, learning is based on the gradual accumulation of direct associations between events based on simple conditioning principles. The other view describes learning as the process of inducing the transformational structure that defines the material. Each of these learning mechanisms predicts differences in the rate of acquisition for differently organized sequences. Across a set of empirical studies, we compare the predictions of each class of model with the behavior of human subjects. We find that learning mechanisms based on transformations of an internal state, such as recurrent network architectures (e.g., Elman, 1990), have difficulty accounting for the pattern of human results relative to a simpler (but more limited) learning mechanism based on learning direct associations. Our results suggest new constraints on the cognitive mechanisms supporting sequential learning behavior.     

SUSTAIN: a network model of category learning

SUSTAIN (Supervised and Unsupervised STratified Adaptive Incremental Network) is a model of how humans learn categories from examples. SUSTAIN initially assumes a simple category structure. If simple solutions prove inadequate and SUSTAIN is confronted with a surprising event (e.g., it is told that a bat is a mammal instead of a bird), SUSTAIN recruits an additional cluster to represent the surprising event. Newly recruited clusters are available to explain future events and can themselves evolve into prototypes-attractors-rules. SUSTAIN's discovery of category substructure is affected not only by the structure of the world but by the nature of the learning task and the learner's goals. SUSTAIN successfully extends category learning models to studies of inference learning, unsupervised learning, category construction, and contexts in which identification learning is faster than classification learning.     

The relation between memory and expectancy as revealed by percentage and sequence of reward investigations

There is growing agreement that to explain instrumental learning properly, one should emphasize memory as well as expectancy. I call this approachmemory-expectancy theory. Amsel’s (1992) frustration theory is one variety of memory-expectancy theory. Capaldi’s (1994) sequential theory is another. In this report, I examine in considerable detail the effects of percentage and sequence of reward on extinction following different levels of acquisition training. These extinction findings, taken together with certain serial learning acquisition findings, seem to support a novel version of memory-expectancy theory, one that in some respects is similar to and in some respects is different from that suggested by Amsel. First, on the basis of this analysis, we may reject two ideas: that animals remember only the prior reward event and that animals anticipate only the reward event contingent upon the current response. Second, the analysis supports three salient propositions of the present memory-expectancy approach. Memories of reward events may serve as conditioned stimuli for expectancies of reward events. On any current trial, the animal may remember each of the reward events associated with one or more prior trials. On any current trial, the animal may anticipate not only the current reward event, but also reward events contingent upon subsequent trials. Essentially, according to this model, the stimuli that elicit expectancies, as well as the expectancies themselves, may change progressively over a series of learning trials.     

A model for predicting the outcomes of basketball games

We investigated the task of predicting the outcomes of sporting events, in particular, basketball games. In two experiments, college students predicted the outcomes of a series of National Basketball Association (NBA) games. Following each prediction, the subject received feedback in the form of the actual outcome of the NBA game. After a period of initial learning about the relative strengths of the teams, the subjects were surprisingly successful in their predictions. We examined expert–novice differences by comparing the published predictions of professional oddsmakers to the predictions of the experimental subjects. The average predictions by the subjects were approximately as accurate as the predictions of experts. Finally, we applied a mathematical model, developed originally as an account of simpler learning experiments, to the subjects' responses. We found that the course of the subjects' learning about the teams was well-described by this model.     

The identity model and factors controlling the superiority of the study-test method over the anticipation method

Short-term memory (STM) and long-term memory (LTM) components are assumed to overlap in such a way that the response reflects predominantly STM components in short retention intervals but LTM ones in long retention intervals. Based on the STM and LTM overlap hypothesis, the identity model postulates that basic processes per study, test, and intervening study and test events as well as intercycle intervals, respectively, are the same for both anticipation and study-test methods in cued (paired-associate) recall and recognition (verbal discrimination learning). A crucial difference between the two methods is the differential retention interval distribution (containing an overlap area). Amounts of STM components in the short-term store (STS), that is, critical items, seem to control the varied superiority of the study-test method over the anticipation method. This is directly linked to the learning difficulty dimension, which in turn is determined by such variables as list length, learning materials, exposure durations (presentation rates), acquisition stages, learning ability, developmental stages (ages), and others.     

On the Role of Fragmentary Knowledge in a Sequence Learning Task

There has been considerable debate about whether or not we need to distinguish between the acquisition of implicit-and, independently thereof, the acquisition of explicit-knowledge in sequence learning tasks. Proponents of the view that a unitary knowledge base is formed assume (a) that the knowledge acquired is explicitly available, and (b) that information about sequence fragments forms the core of this explicit knowledge. Both of these issues are addressed empirically in the present article. In two experiments, an adapted process dissociation procedure and a suitable measurement model were used to separate recollective (explicit) and fluency-based (implicit) memory processes in a sequence learning task. Experiment 1 demonstrated that fluency-based processes came into play much later than recollective processes. Such recollective processes have been conceptualized as being based on simple knowledge about sequence fragments or chunks. Indeed, Experiment 2 showed that recollective processes are more likely to contribute to sequence judgements if chunks are readily available at test than if they are not. Together, these results are in line with the view that the learning of an event systematicity can be conceived of as the memorization of chunks of events that support both the speedingup of reaction times to systematic events and explicit, recollective memory processes even after relatively little training.     

Symmetric limiting distributions of response probabilities

Necessary and sufficient conditions for the symmetry of the limiting distributions of response probabilities are derived for the Bush and Mosteller two experimenter-controlled events learning model [Bush and Mosteller, 1955].     

Prediction during statistical learning, and implications for the implicit/explicit divide

Accounts of statistical learning, both implicit and explicit, often invoke predictive processes as central to learning, yet practically all experiments employ non-predictive measures during training. We argue that the common theoretical assumption of anticipation and prediction needs clearer, more direct evidence for it during learning. We offer a novel experimental context to explore prediction, and report results from a simple sequential learning task designed to promote predictive behaviors in participants as they responded to a short sequence of simple stimulus events. Predictive tendencies in participants were measured using their computer mouse, the trajectories of which served as a means of tapping into predictive behavior while participants were exposed to very short and simple sequences of events. A total of 143 participants were randomly assigned to stimulus sequences along a continuum of regularity. Analysis of computer-mouse trajectories revealed that (a) participants almost always anticipate events in some manner, (b) participants exhibit two stable patterns of behavior, either reacting to vs. predicting future events, (c) the extent to which participants predict relates to performance on a recall test, and (d) explicit reports of perceiving patterns in the brief sequence correlates with extent of prediction. We end with a discussion of implicit and explicit statistical learning and of the role prediction may play in both kinds of learning.     

Stress-enhanced fear learning in rats is resistant to the effects of immediate massed extinction

Enhanced fear learning occurs subsequent to traumatic or stressful events and is a persistent challenge to the treatment of post-traumatic stress disorder (PTSD). Facilitation of learning produced by prior stress can elicit an exaggerated fear response to a minimally aversive event or stimulus. Stress-enhanced fear learning (SEFL) is a rat model of PTSD; rats previously exposed to the SEFL 15 electrical shocks procedure exhibit several behavioral responses similar to those seen in patients with PTSD. However, past reports found that SEFL is not mitigated by extinction (a model of exposure therapy) when the spaced extinction began 24?h after stress. Recent studies found that extinction from 10?min to 1?h subsequent to fear conditioning "erased" learning, whereas later extinction, occurring from 24 to 72?h after conditioning did not. Other studies indicate that massed extinction is more effective than spaced procedures. Therefore, we examined the time-dependent nature of extinction on the stress-induced enhancement of fear learning using a massed trial's procedure. Experimental rats received 15 foot shocks and were given either no extinction or massed extinction 10?min or 72?h later. Our present data indicate that SEFL, following traumatic stress, is resistant to immediate massed extinction. Experimental rats showed exaggerated new fear learning regardless of when extinction training occurred. Thus, post-traumatic reactivity such as SEFL does not seem responsive to extinction treatments.     

Influence of correlated visual cues on auditory signal detection

Two experiments investigated the effects on auditory signal detection of introducing visual cues that were partially correlated with the signal events. The results were analyzed in terms of a detection model that assumes that such cue-signal correlations will not affect sensitivity, but will instead cause the subject to develop separate response biases for each cue. The model specifies a functional relationship between the asymptotic values of these cuecontingent biases. The overall results of the experiments supported the detection assumptions of the model and the general bias learning assumption, but indicated a more complex learning process than that specified by the model.