When wrong predictions provide more support than right ones

Correct predictions of rare events are normatively more supportive of a theory or hypothesis than correct predictions of common ones. In other words, correct bold predictions provide more support than do correct timid predictions. Are lay hypothesis testers sensitive to the boldness of predictions? Results reported here show that participants were very sensitive to boldness, often finding incorrect bold predictions more supportive than correct timid ones. Participants were willing to tolerate inaccurate predictions only when predictions were bold. This finding was demonstrated in the context of competing forecasters and in the context of competing scientific theories. The results support recent views of human inference that postulate that lay hypothesis testers are sensitive to the rarity of data. Furthermore, a normative (Bayesian) account can explain the present results and provides an alternative interpretation of similar results that have been explained using a purely descriptive model.

Influence of stimulus distance in implicit learning of spatial and nonspatial event sequences

The serial reaction time task has been widely used to investigate implicit learning mechanisms. In the present study, we investigated the effect of stimulus distance on learning of a spatial sequence independent of a sequence of responses. Participants had to respond to objects appearing at four different locations. The objects were presented in a sequence of nine elements, whereas the location at which an object was presented followed a sequence of eight elements. Thus, the spatial and the object sequences were independent of each other. Four groups of subjects for whom the distances of the locations chosen to present objects on the computer screen (3 cm, 6 cm, 12 cm, or 22 cm) differed were tested. Only the nonspatial sequence was learned as indicated by enhanced response latencies in nonsequenced random blocks. Stimulus distance had no effect on the amount of sequence learning. Additional analyses for subgroups of subjects who did not show explicit knowledge of the sequences after completion of the task indicated that for implicit learners also, sequence learning was not influenced by stimulus distance. The results are discussed with respect to current theories of implicit serial learning.

On the impact of different number representations in the number bisection task

The number bisection task--in which the numerical middle of two other numbers has to be determined (e.g., 6 is the numerical middle of 4 and 8)--has recently been used in neuropsychological case studies in addition to the number comparison task to assess quantitative capabilities in number processing. While factors determining difficulty in normal participants have often been systematically investigated in the number comparison task, this has not yet been done in the number bisection task. Based on a pilot study by van Herten (1999), we extracted four factors that we hypothesized to modulate difficulty in a verification version of the number bisection task in normal participants: Multiplicativity (whether or not the three numbers are part of a multiplication table), range (distance between the smallest and the largest number) for bisectable number triplets as well as distance of the middle number to the numerical middle, and bisection possibility for non-bisectable triplets. In the current study, we obtained large effects for all four factors on RT and accuracy data and some interesting interactions in normal participants. In a regression analysis, we additionally observed inhibitory effects of decade crossing and of ten inclusion (whether or not one of the three numbers was a decade number). We discuss the impact of these results for the use of the number bisection task as an assessment tool in neuropsychology. Finally, we examine the consequences of these results for models of number processing.

Toward a unified theory of decision criterion learning in perceptual categorization

Optimal decision criterion placement maximizes expected reward and requires sensitivity to the category base rates (prior probabilities) and payoffs (costs and benefits of incorrect and correct responding). When base rates are unequal, human decision criterion is nearly optimal, but when payoffs are unequal, suboptimal decision criterion placement is observed, even when the optimal decision criterion is identical in both cases. A series of studies are reviewed that examine the generality of this finding, and a unified theory of decision criterion learning is described (Maddox & Dodd, 2001). The theory assumes that two critical mechanisms operate in decision criterion learning. One mechanism involves competition between reward and accuracy maximization: The observer attempts to maximize reward, as instructed, but also places some importance on accuracy maximization. The second mechanism involves a flat-maxima hypothesis that assumes that the observer's estimate of the reward-maximizing decision criterion is determined from the steepness of the objective reward function that relates expected reward to decision criterion placement. Experiments used to develop and test the theory require each observer to complete a large number of trials and to participate in all conditions of the experiment. This provides maximal control over the reinforcement history of the observer and allows a focus on individual behavioral profiles. The theory is applied to decision criterion learning problems that examine category discriminability, payoff matrix multiplication and addition effects, the optimal classifier's independence assumption, and different types of trial-by-trial feedback. In every case the theory provides a good account of the data, and, most important, provides useful insights into the psychological processes involved in decision criterion learning.

The development of emergent differential sample behavior in pigeons

Three experiments attempted to replicate Manabe, Kawashima, and Staddon's (1995) finding of emergent differential sample behavior in budgerigars that has been interpreted as evidence of functional equivalence class formation. In Experiments 1 and 2, pigeons initially learned two-sample/ two-alternative matching to sample in which comparison presentation was contingent on pecking one sample on a differential-reinforcement-of-low-rate (DRL) schedule and the other on a fixed-ratio (FR) schedule. Later, two new samples were added to the task. Comparison presentation on these trials occurred after the first sample peck following a predetermined interval (Experiment 1) or after completion of either the DRL or FR requirement, whichever occurred first (Experiment 2). Experiment 1 found no evidence for emergent spaced versus rapid responding to the new samples as they established conditional control over the familiar choices. By contrast, differential responding did emerge for some pigeons in Experiment 2, with responding to each new sample coinciding with the pattern explicitly conditioned to the original sample occasioning the same comparison choice. This emergent effect, however, disappeared for most pigeons with continued training. Experiment 3 systematically replicated Experiment 2 using differential peck location as the sample behavior. Differential location pecking emerged to the new samples for most pigeons and remained intact throughout training. Our findings demonstrate a viable pigeon analogue to the budgerigar emergent calling paradigm and are discussed in terms of equivalence- and non-equivalence-based processes.

Memory seeding: representations underlying quantitative estimations

N. R. Brown and R. S. Siegler (1996) found that training participants on a subset of country populations improved estimations for novel transfer country populations, an effect called seeding that remained intact over time. They attributed this effect to the abstraction by participants of a general metric framework for estimating populations not dependent on specific country anchors. In a series of 3 follow-up experiments, the authors found that training on seed populations produces both general metric information and durable specific country information. Moreover, minimal amounts of general (mean or range of populations) or specific (1 or 3 countries) information made available for inspection while estimating produced a significant seeding effect. Retention over long intervals was facilitated by both presenting 3 seed countries as opposed to 1 and providing names for the seed countries.

Affective modulation of eyeblink startle with reward and threat

An emotion-modulated acoustic startle paradigm for inducing positive and negative affect was used to address pregoal and postgoal affect. Participants played a computerized lottery task in which they chose digits that could match a subsequently displayed, random set of numbers. In the positive conditions, matches led to monetary rewards. In the negative condition, matches led to an aversive noise blast. In three experiments, we found eyeblink startle magnitude was potentiated just prior to feedback concerning reward outcome, suppressed following the feedback that a monetary reward was won, and potentiated when threatened with an aversive noise. When presented with a 0%, 45%, 90%, or 100% chance of winning, higher probabilities suppressed startle response after feedback whereas the 45% trials did not. These data indicate that postgoal positive affect (winning reward) reliably suppressed the startle response whereas pregoal positive affect did not.

Contextual control of stimulus generalization and stimulus equivalence in hierarchical categorization

The purpose of this study was to determine whether hierarchical categorization would result from a combination of contextually controlled conditional discrimination training, stimulus generalization, and stimulus equivalence. First, differential selection responses to a specific stimulus feature were brought under contextual control. This contextual control was hierarchical in that stimuli at the top of the hierarchy all evoked one response, whereas those at the bottom each evoked different responses. The evocative functions of these stimuli generalized in predictable ways along a dimension of physical similarity. Then, these functions were indirectly acquired by a set of nonsense syllables that were related via transitivity relations to the originally trained stimuli. These nonsense syllables effectively served as names for the different stimulus classes within each level of the hierarchy.

Temporal dynamics of lateralized ERP components elicited during endogenous attentional shifts to relevant tactile events

To investigate the temporal dynamics of lateralized event-related brain potential (ERP) components elicited during covert shifts of spatial attention, ERPs were recorded in a task where central visual symbolic cues instructed participants to direct attention to their left or right hand in order to detect infrequent tactile targets presented to that hand, and to ignore tactile stimuli presented to the other hand, as well as all randomly intermingled peripheral visual stimuli. In different blocks, the stimulus onset asynchrony (SOA) between cue and target was 300 ms, 700 ms, or 1,100 ms. Anterior and posterior ERP modulations sensitive to the direction of an attentional shift were time-locked to the attentional cue, rather than to the anticipated arrival of a task-relevant stimulus. These components thus appear to reflect central attentional control rather than the anticipatory preparation of sensory areas. In addition, attentional modulations of ERPs to task-irrelevant visual stimuli were found, providing further evidence for crossmodal links in spatial attention between touch and vision.

Self-organizing maps with recursive neighborhood adaptation

Self-organizing maps (SOMs) are widely used in several fields of application, from neurobiology to multivariate data analysis. In that context, this paper presents variants of the classic SOM algorithm. With respect to the traditional SOM, the modifications regard the core of the algorithm, (the learning rule), but do not alter the two main tasks it performs, i.e. vector quantization combined with topology preservation. After an intuitive justification based on geometrical considerations, three new rules are defined in addition to the original one. They develop interesting properties such as recursive neighborhood adaptation and non-radial neighborhood adaptation. In order to assess the relative performances and speeds of convergence, the four rules are used to train several maps and the results are compared according to several error measures (quantization error and topology preservation criterions).

Generalized relevance learning vector quantization

We propose a new scheme for enlarging generalized learning vector quantization (GLVQ) with weighting factors for the input dimensions. The factors allow an appropriate scaling of the input dimensions according to their relevance. They are adapted automatically during training according to the specific classification task whereby training can be interpreted as stochastic gradient descent on an appropriate error function. This method leads to a more powerful classifier and to an adaptive metric with little extra cost compared to standard GLVQ. Moreover, the size of the weighting factors indicates the relevance of the input dimensions. This proposes a scheme for automatically pruning irrelevant input dimensions. The algorithm is verified on artificial data sets and the iris data from the UCI repository. Afterwards, the method is compared to several well known algorithms which determine the intrinsic data dimension on real world satellite image data.

Ecological and evolutionary validity: comments on Johnson-Laird, Legrenzi, Girotto, Legrenzi, and Caverni's (1999) mental-model theory of extensional reasoning

The mental-model account of naive probabilistic reasoning by P. N. Johnson-Laird, P. Legrenzi, V. Girotto, M. S. Legrenzi, and J.-P. Caverni (1999) provides an opportunity to clarify several similarities and differences between it and ecological rationality (frequentist) accounts. First, ambiguities in the meaning of Bayesian reasoning can lead to disagreements and inappropriate arguments. Second, 2 conflated effects of using natural frequencies are noticed but not actually tested separately because of an artificial dissociation of frequency representations and natural sampling. Third, similarities are noted between the subset principle and the principle of natural sampling. Finally, some potentially misleading portrayals of the role of evolutionary factors in psychology are corrected. Mental-model theory, rather than better explaining probabilistic reasoning, may be able to use frequency representations as a key element in clarifying its own ambiguous constructs.

Applications of the self-organising map to reinforcement learning

This article is concerned with the representation and generalisation of continuous action spaces in reinforcement learning (RL) problems. A model is proposed based on the self-organising map (SOM) of Kohonen [Self Organisation and Associative Memory, 1987] which allows either the one-to-one, many-to-one or one-to-many structure of the desired state-action mapping to be captured. Although presented here for tasks involving immediate reward, the approach is easily extended to delayed reward. We conclude that the SOM is a useful tool for providing real-time, on-line generalisation in RL problems in which the latent dimensionalities of the state and action spaces are small. Scalability issues are also discussed.

Pictorial versus textual information and the ratio-bias effect

The ratio-bias effect refers to the perception that a low probability event is more likely when presented in the form of a larger, e.g., 10-in-100, than smaller, e.g., 1-in-10, numerical ratio. This phenomenon has been used to help distinguish between rational-analytic versus heuristic-automatic ways of problem solving. In the current study, responding in accordance with the ratio bias was more prevalent when choices were presented pictorially as opposed to textually. Results are discussed with respect to how various factors, including mode of information presentation, may affect whether problems are solved via heuristic, automatic processes as opposed to effortful, analytic strategies.

A self-organising network that grows when required

The ability to grow extra nodes is a potentially useful facility for a self-organising neural network. A network that can add nodes into its map space can approximate the input space more accurately, and often more parsimoniously, than a network with predefined structure and size, such as the Self-Organising Map. In addition, a growing network can deal with dynamic input distributions. Most of the growing networks that have been proposed in the literature add new nodes to support the node that has accumulated the highest error during previous iterations or to support topological structures. This usually means that new nodes are added only when the number of iterations is an integer multiple of some pre-defined constant, A. This paper suggests a way in which the learning algorithm can add nodes whenever the network in its current state does not sufficiently match the input. In this way the network grows very quickly when new data is presented, but stops growing once the network has matched the data. This is particularly important when we consider dynamic data sets, where the distribution of inputs can change to a new regime after some time. We also demonstrate the preservation of neighbourhood relations in the data by the network. The new network is compared to an existing growing network, the Growing Neural Gas (GNG), on a artificial dataset, showing how the network deals with a change in input distribution after some time. Finally, the new network is applied to several novelty detection tasks and is compared with both the GNG and an unsupervised form of the Reduced Coulomb Energy network on a robotic inspection task and with a Support Vector Machine on two benchmark novelty detection tasks.

BYY harmony learning, structural RPCL, and topological self-organizing on mixture models

The Bayesian Ying-Yang (BYY) harmony learning acts as a general statistical learning framework, featured by not only new regularization techniques for parameter learning but also a new mechanism that implements model selection either automatically during parameter learning or via a new class of model selection criteria used after parameter learning. In this paper, further advances on BYY harmony learning by considering modular inner representations are presented in three parts. One consists of results on unsupervisedmixture models, ranging from Gaussian mixture based Mean Square Error (MSE) clustering, elliptic clustering, subspace clustering to NonGaussian mixture based clustering not only with each cluster represented via either Bernoulli-Gaussian mixtures or independent real factor models, but also with independent component analysis implicitly made on each cluster. The second consists of results on supervised mixture-of-experts (ME) models, including Gaussian ME, Radial Basis Function nets, and Kernel regressions. The third consists of two strategies for extending the above structural mixtures into self-organized topological maps. All these advances are introduced with details on three issues, namely, (a) adaptive learning algorithms, especially elliptic, subspace, and structural rival penalized competitive learning algorithms, with model selection made automatically during learning; (b) model selection criteria for being used after parameter learning, and (c) how these learning algorithms and criteria are obtained from typical special cases of BYY harmony learning.

The neural basis of human error processing: reinforcement learning, dopamine, and the error-related negativity

The authors present a unified account of 2 neural systems concerned with the development and expression of adaptive behaviors: a mesencephalic dopamine system for reinforcement learning and a "generic" error-processing system associated with the anterior cingulate cortex. The existence of the error-processing system has been inferred from the error-related negativity (ERN), a component of the event-related brain potential elicited when human participants commit errors in reaction-time tasks. The authors propose that the ERN is generated when a negative reinforcement learning signal is conveyed to the anterior cingulate cortex via the mesencephalic dopamine system and that this signal is used by the anterior cingulate cortex to modify performance on the task at hand. They provide support for this proposal using both computational modeling and psychophysiological experimentation.

Timing in pigeons: effects of the similarity between intertrial interval and gap in a timing signal

Previous research suggests that when a fixed interval is interrupted (known as the gap procedure), pigeons tend to reset memory and start timing from 0 after the gap. However, because the ambient conditions of the gap typically have been the same as during the intertrial interval (ITI), ambiguity may have resulted. In the present experiment, the authors found that when ambient conditions during the gap were similar to the ITI, pigeons tended to reset memory, but when ambient conditions during the gap were different from the ITI, pigeons tended to stop timing, retain the duration of the stimulus in memory, and add to that time when the stimulus reappeared. Thus, when the gap was unambiguous, pigeons timed accurately.

Anterior cingulate cortex and the Stroop task: neuropsychological evidence for topographic specificity

Neuroimaging studies have implicated the anterior cingulate cortex (ACC) in many aspects of attention and cognition. Major theories of ACC function have proposed a role in conflict monitoring, executive control, response selection, and general arousal. Although the ACC is often treated as a unitary structure, extensive evidence suggests it exhibits anatomical and functional specificity. ACC activity during the Stroop color word interference task has been of particular interest. The purpose of the present study was to determine whether two different ACC subregions are necessary for intact color naming performance in the Stroop task. One experiment utilized blocked trial and mixed trial designs to emulate neuroimaging studies and to compare interference and facilitation effects, respectively. A third variant manipulated the probabilities of congruent and incongruent trials to alter levels of interference and cognitive control, or engagement of strategic processes, on a block by block basis. Two patients with focal lesions in either right mid-caudal (patient D.L.) or left rostral to mid-dorsal ACC (patient R.N.) exhibited distinctive performance profiles in these three versions of the Stroop task, providing further support for topographic specificity of function within the human ACC. Contrary to predictions from some neuroimaging experiments, damage to right mid-caudal ACC was associated with normal levels of interference and accurate performance on incongruent trials. Instead, D.L. showed reduced levels of facilitation relative to controls. Further, interference was not modulated by the probability manipulation in D.L., suggesting equivalently high levels of cognitive control in both conditions. Conversely, damage to left mid-dorsal ACC resulted in consistently lower accuracy on incongruent trials, indicating deficits in maintaining task set and inhibiting the automatic response. These results can help to constrain interpretations of ACC activations in functional imaging experiments of the Stroop task.

Probabilistic classification learning in Tourette syndrome

Tourette syndrome (TS) is characterised by stereotyped involuntary movements, called tics. Some evidence suggests that structural and functional abnormalities of the basal ganglia may explain these motor symptoms. In this study, the probabilistic classification learning (PCL) test was used to evaluate basal ganglia functions in 10 children with less severe tics (Yale Global Tic Severity Scale (YGTSS) scores<30) and in 10 children with more severe symptoms (YGTSS score>30). In the PCL task, participants are asked to decide whether different combinations of four geometric forms (cues) predict rainy or sunny weather. Each cue is probabilistically related to a weather outcome, and feedback is provided after each decision. After completion of the probabilistic stimulus-response learning procedure, subjects received a transfer test to assess explicit knowledge about the cues. The children with TS exhibited impaired learning in the PCL task in comparison with the 20 healthy control subjects. This impairment was more pronounced in the TS patients with severe symptoms, and there was a significant negative relationship between the final classification performance and the YGTSS scores. The patients showed normal learning in the transfer test. These results suggest that the neostriatal habit learning system, which may play a central role in the acquisition of probabilistic associations, is dysfunctional in TS, especially in the case of more severe motor symptoms. The classification performance and the severity of tics were independent of the explicit knowledge obtained during the test.

Dissociating habit and recollection: evidence from Parkinson's disease, amnesia and focal lesion patients

We investigated the role played by the striatum and the medial temporal lobes (MTL) in memory performance by testing patients with Parkinson's disease (PD) and amnesia with Hay and Jacoby's habit-learning task [Journal of Experimental Psychology: Learning, Memory and Cognition 22 (1996) 1323]. Using equations from Jacoby's process-dissociation procedure [Journal of Memory and Language 30 (1991) 513], we were able to separate out the contribution of habit (automatic memory) and recollection (intentional memory) to performance within a single probability-learning paradigm. Amnesics showed the expected dissociation of impaired recollection and intact habit, highlighting the important role of the MTL in recollective processing. Mild PD patients did not perform differently than matched controls for habit or recollection, however, moderate PD patients were impaired in their ability to rely on habit and in their ability to recollect specific information. The performance of focal lesion patients further supported the interpretation that PD patients have a significant deficit in automatic, habit-learning due to striatal dysfunction while their deficit in recollection may arise from impoverished frontal lobe contributions.

The effect of category variability in perceptual categorization

Exemplar and distributional accounts of categorization make differing predictions for the classification of a critical exemplar precisely halfway between the nearest exemplars of 2 categories differing in variability. Under standard conditions of sequential presentation, the critical exemplar was classified into the most similar, least variable category, consistent with an exemplar account. However, if the difference in variability is made more salient, then the same exemplar is classified into the more variable, most likely category, consistent with a distributional account. This suggests that participants may be strategic in their use of either strategy. However, when the relative variability of 2 categories was manipulated, participants showed changes in the classification of intermediate exemplars that neither approach could account for.

Representation facilitates reasoning: what natural frequencies are and what they are not

A good representation can be crucial for finding the solution to a problem. Gigerenzer and Hoffrage (Psychol. Rev. 102 (1995) 684; Psychol. Rev. 106 (1999) 425) have shown that representations in terms of natural frequencies, rather than conditional probabilities, facilitate the computation of a cause's probability (or frequency) given an effect--a problem that is usually referred to as Bayesian reasoning. They also have shown that normalized frequencies--which are not natural frequencies--do not lead to computational facilitation, and consequently, do not enhance people's performance. Here, we correct two misconceptions propagated in recent work (Cognition 77 (2000) 197; Cognition 78 (2001) 247; Psychol. Rev. 106 (1999) 62; Organ. Behav. Hum. Decision Process. 82 (2000) 217): normalized frequencies have been mistaken for natural frequencies and, as a consequence, "nested sets" and the "subset principle" have been proposed as new explanations. These new terms, however, are nothing more than vague labels for the basic properties of natural frequencies.

Chances and frequencies in probabilistic reasoning: rejoinder to Hoffrage, Gigerenzer, Krauss, and Martignon

Do individuals unfamiliar with probability and statistics need a specific type of data in order to draw correct inferences about uncertain events? Girotto and Gonzalez (Cognition 78 (2001) 247) showed that naive individuals solve frequency as well as probability problems, when they reason extensionally, in particular when probabilities are represented by numbers of chances. Hoffrage, Gigerenzer, Krauss, and Martignon (Cognition 84 (2002) 343) argued that numbers of chances are natural frequencies disguised as probabilities, though lacking the properties of true probabilities. They concluded that we failed to demonstrate that naive individuals can deal with true probabilities as opposed to natural frequencies. In this paper, we demonstrate that numbers of chances do represent probabilities, and that naive individuals do not confuse numbers of chances with frequencies. We conclude that there is no evidence for the claim that natural frequencies have a special cognitive status, and the evolutionary argument that the human mind is unable to deal with probabilities.

Dynamics and constraints in insight problem solving

This article reports 2 experiments that investigated performance on a novel insight problem, the 8-coin problem. The authors hypothesized that participants would make certain initial moves (strategic moves) that seemed to make progress according to the problem instructions but that nonetheless would guarantee failure to solve the problem. Experiment 1 manipulated the starting state of the problem and showed that overall solution rates were lower when such strategic moves were available. Experiment 2 showed that failure to capitalize on visual hints about the correct first move was also associated with the availability of strategic moves. The results are interpreted in terms of an information-processing framework previously applied to the 9-dot problem. The authors argue that in addition to the operation of inappropriate constraints, a full account of insight problem solving must incorporate a dynamic that steers solution-seeking activity toward the constraints.