A test of the optimal classifier's independence assumption in perceptual categorization

Observers completed perceptual categorization tasks that included separate base-rate/payoff manipulations, corresponding simultaneous base-rate/payoff manipulations, and conflicting simultaneous base-rate/payoff manipulations. Performance (1) was closer to optimal for 2:1 than for 3:1 base-rate/payoff ratios and when base rates as opposed to payoffs were manipulated, and (2) was more in line with the predictions from the flat-maxima hypothesis than from the independence assumption of the optimal classifier in corresponding and conflicting simultaneous base-rate/payoff conditions. A hybrid model that instantiated simultaneously the flat-maxima and the competition between reward and accuracy maximization (COBRA) hypotheses was applied to the data. The hybrid model was superior to a model that incorporated the independence assumption, suggesting that violations of the independence assumption are to be expected and are well captured by the flat-maxima hypothesis without requiring any additional assumptions. The parameters indicated that observers' reward-maximizing decision criterion rapidly approaches the optimal value and that more weight is placed on accuracy maximization in separate and corresponding simultaneous base-rate/payoff conditions than in conflicting simultaneous base-rate/payoff conditions.     

A test of the optimal classifier’s independence assumption in perceptual categorization

Observers completed perceptual categorization tasks that included separate base-rate/payoff manipulations, corresponding simultaneous base-rate/payoff manipulations, and conflicting simultaneous base-rate/payoff manipulations. Performance (1) was closer to optimal for 2:1 than for 3:1 baserate/ payoff ratios and when base rates as opposed to payoffs were manipulated, and (2) was more in line with the predictions from the flat-maxima hypothesis than from the independence assumption of the optimal classifier in corresponding and conflicting simultaneous base-rate/payoff conditions. A hybrid model that instantiated simultaneously the flat-maxima and the competition between reward and accuracy maximization (COBRA) hypotheses was applied to the data. The hybrid model was superior to a model that incorporated the independence assumption, suggesting that violations of the independence assumption are to be expected and are well captured by the flat-maxima hypothesis without requiring any additional assumptions. The parameters indicated that observers’ reward-maximizing decision criterion rapidly approaches the optimal value and that more weight is placed on accuracy maximization in separate and corresponding simultaneous base-rate/payoff conditions than in conflicting simultaneous base-rate/payoff conditions.     

Probability matching, accuracy maximization, and a test of the optimal classifier's independence assumption in perceptual categorization

Observers completed perceptual categorization tasks that included 25 base-rate/payoff conditions constructed from the factorial combination of five base-rate ratios (1:3, 1:2, 1:1, 2:1, and 3:1) with five payoff ratios (1:3, 1:2, 1:1, 2:1, and 3:1). This large database allowed an initial comparison of the competition between reward and accuracy maximization (COBRA) hypothesis with a competition between reward maximization and probability matching (COBRM) hypothesis, and an extensive and critical comparison of the flat-maxima hypothesis with the independence assumption of the optimal classifier. Model-based instantiations of the COBRA and COBRM hypotheses provided good accounts of the data, but there was a consistent advantage for the COBRM instantiation early in learning and for the COBRA instantiation later in learning. This pattern held in the present study and in a reanalysis of Bohil and Maddox (2003). Strong support was obtained for the flat-maxima hypothesis over the independence assumption, especially as the observers gained experience with the task. Model parameters indicated that observers' reward-maximizing decision criterion rapidly approaches the optimal value and that more weight is placed on accuracy maximization in separate base-rate/payoff conditions than in simultaneous base-rate/payoff conditions. The superiority of the flat-maxima hypothesis suggests that violations of the independence assumption are to be expected, and are well captured by the flat-maxima hypothesis, with no need for any additional assumptions.     

A theoretical framework for understanding the effects of simultaneous base-rate and payoff manipulations on decision criterion learning in perceptual categorization

Observers completed perceptual categorization tasks in which base rates and payoffs were manipulated separately or simultaneously across a range of category discriminabilities. Decision criterion estimates from the simultaneous base-rate/payoff conditions were closer to optimal than those predicted from the independence assumption, in line with predictions from the flat-maxima hypothesis. A hybrid model that instantiated the flat-maxima and competition between reward and accuracy maximization hypotheses was applied to the data as well as used in a reanalysis of C. J. Bohil and W.J. Maddox's (2001) study. The hybrid model was superior to a model that incorporated the independence assumption, suggesting that violations of the independence assumption are to be expected and are well captured by the flat-maxima hypothesis, without requiring any additional assumptions.     

Probability matching, accuracy maximization, and a test of the optimal classifier’s independence assumption in perceptual categorization

Observers completed perceptual categorization tasks that included 25 base-rate/payoff conditions constructed from the factorial combination of five base-rate ratios (1:3, 1:2, 1:1, 2:1, and 3:1) with five payoff ratios (1:3, 1:2, 1:1, 2:1, and 3:1). This large database allowed an initial comparison of the competition between reward and accuracy maximization (COBRA) hypothesis with a competition between reward maximization and probability matching (COBRM) hypothesis, and an extensive and critical comparison of the flat-maxima hypothesis with the independence assumption of the optimal classifier. Model-based instantiations of the COBRA and COBRM hypotheses provided good accounts of the data, but there was a consistent advantage for the COBRM instantiation early in learning and for the COBRA instantiation later in learning. This pattern held in the present study and in a reanalysis of Bohil and Maddox (2003). Strong support was obtained for the flat-maxima hypothesis over the independence assumption, especially as the observers gained experience with the task. Model parameters indicated that observers’ reward-maximizing decision criterion rapidly approaches the optimal value and that more weight is placed on accuracy maximization in separate base-rate/payoff conditions than in simultaneous base-rate/payoff conditions. The superiority of the flat-maxima hypothesis suggests that violations of the independence assumption are to be expected, and are well captured by the flat-maxima hypothesis, with no need for any additional assumptions.     

Linear transformations of the payoff matrix and decision criterion learning in perceptual categorization

The effects of payoff-matrix multiplication, payoff-matrix addition, the presence of long-run gains versus long-run losses, category discriminability, and base rate on decision criterion learning were examined in 2 perceptual categorization experiments. Observers were found to be sensitive to the effects of payoff-matrix multiplication (and category discriminability) on the steepness of the objective reward function in line with predictions from the flat-maxima hypothesis and contrary to the predictions from the payoff-variance hypothesis. Decision criterion learning was best in base-rate conditions, was worst when losses were associated with incorrect responding, and was intermediate when no losses were associated with incorrect responding. This performance profile was well captured by the competition between reward and accuracy (COBRA) hypothesis. A hybrid model framework that instantiates both the flat-maxima and COBRA hypotheses was necessary to account for the data from both experiments.     

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.     

On the generality of optimal versus objective classifier feedback effects on decision criterion learning in perceptual categorization

Biased category payoff matrices engender separate reward- and accuracy-maximizing decision criteria Although instructed to maximize reward, observers use suboptimal decision criteria that place greater emphasis on accuracy than is optimal. In this study, objective classifier feedback (the objectively correct response) was compared with optimal classifier feedback (the optimal classifier's response) at two levels of category discriminability when zero or negative costs accompanied incorrect responses for two payoff matrix multiplication factors. Performance was superior for optimal classifier feedback relative to objective classifier feedback for both zero- and negative-cost conditions, especially when category discriminability was low, but the magnitude of the optimal classifier advantage was approximately equal for zero- and negative-cost conditions. The optimal classifier feedback performance advantage did not interact with the payoff matrix multiplication factor. Model-based analyses suggested that the weight placed on accuracy was reduced for optimal classifier feedback relative to objective classifier feedback and for high category discriminability relative to low category discriminability. In addition, the weight placed on accuracy declined with training when feedback was based on the optimal classifier and remained relatively stable when feedback was based on the objective classifier. These results suggest that feedback based on the optimal classifier leads to superior decision criterion learning across a wide range of experimental conditions.     

Overestimation of base-rate differences in complex perceptual categories

The optimality of multidimensional perceptual categorization performance was examined for several base-rate ratios, for both integral and separable dimension stimuli, and for complex category structures. In all cases, the optimal decision bound was highly nonlinear. Observers completed several experimental sessions, and all analyses were performed at the single-observer level using a series of nested models derived from decision-bound theory (Maddox, 1995; Maddox & Ashby, 1993). In every condition, all observers were found to be sensitive to the base-rate manipulations, but the majority of observers appeared to overestimate the base-rate difference. These findings converge with those for cases in which the optimal decision bound was linear (Maddox, 1995) and suggest that base-rates are learned in a similar fashion regardless of the complexity of the optimal decision bound. Possible explanations for the consistent overestimate of the base-rate difference are discussed. Several continuous-valued analogues of Kruschke’s (1996) theory of base-rate learning with discrete-valued stimuli were tested. These models found some support, but in all cases were outperformed by a version of decision-bound theory that assumed accurate knowledge of the category structure and an overestimate of the base-rate difference.     

Pseudodiagnosticity in judgment under uncertainty

The study investigates the extent to which the false alarm (i.e., ) is utilized in judgment under uncertainty. The main findings are (1) this cue is utilized by subjects when provided with a numerically low base-rate (i.e., P(H)) and a high hit-rate (i.e., P(D/H)). Under these conditions the false alarm helps resolve the inconsistency between the implications of these probabilistic cues. (2) The false alarm is ignored by subjects when provided with a numerically high base-rate and a high hit-rate. Under these conditions both latter probabilities are consistent and imply strong support for the focal hypothesis. The false alarm is either not consistent with these cues or redundant and ignored. In addition, three experiments provided evidence regarding base-rate utilization. When comparing conditions (1) and (2) it is demonstrated that the base-rate has a significant effect on judgments. Finally, the experiments provided evidence suggesting that the base-rate is not ignored when the datum is not diagnostic. The results are discussed in relation to the base-rate fallacy, pseudodiagnosticity, and cue consistency.     

On the relation between base-rate and cost-benefit learning in simulated medical diagnosis.

Observers completed a series of simulated medical diagnosis tasks that differed in category discriminability and base-rate/cost-benefit ratio. Point, accuracy, and decision criterion estimates were closer to optimal (a) for category d' = 2.2 than for category d' = 1.0 or 3.2, (b) when base-rates as opposed to cost-benefits were manipulated, and (c) when the cost of an incorrect response resulted in no point loss (nonnegative cost) as opposed to a point loss (negative cost). These results support the "flat-maxima" and competition between reward and accuracy (COBRA) hypotheses. A hybrid model that instantiated simultaneously both hypotheses was applied to the data. The model parameters indicated that (a) the reward-maximizing decision criterion quickly approached the optimal criterion, (b) the importance placed on accuracy maximization early in learning was larger when the cost of an incorrect response was negative as opposed to nonnegative, and (c) by the end of training the importance placed on accuracy was equal for negative and nonnegative costs.     

Dissociable influences of reward motivation and positive emotion on cognitive control

It is becoming increasingly appreciated that affective and/or motivational influences contribute strongly to goal-oriented cognition and behavior. An unresolved question is whether emotional manipulations (i.e., direct induction of affectively valenced subjective experience) and motivational manipulations (e.g., delivery of performance-contingent rewards and punishments) have similar or distinct effects on cognitive control. Prior work has suggested that reward motivation can reliably enhance a proactive mode of cognitive control, whereas other evidence is suggestive that positive emotion improves cognitive flexibility, but reduces proactive control. However, a limitation of the prior research is that reward motivation and positive emotion have largely been studied independently. Here, we directly compared the effects of positive emotion and reward motivation on cognitive control with a tightly matched, within-subjects design, using the AX-continuous performance task paradigm, which allows for relative measurement of proactive versus reactive cognitive control. High-resolution pupillometry was employed as a secondary measure of cognitive dynamics during task performance. Robust increases in behavioral and pupillometric indices of proactive control were observed with reward motivation. The effects of positive emotion were much weaker, but if anything, also reflected enhancement of proactive control, a pattern that diverges from some prior findings. These results indicate that reward motivation has robust influences on cognitive control, while also highlighting the complexity and heterogeneity of positive-emotion effects. The findings are discussed in terms of potential neurobiological mechanisms.     

Diagnosticity and the base-rate effect

A common judgmental task involves predicting the category membership of an individual on the basis of information specific to that individual and background information regarding the base rate of different categories. According to statistical theory, predictions may deviate from base rates only to the extent that the individuating information is diagnostic. Previous research has demonstrated that diagnosticity is often judged by “representativeness,” the degree to which the individuating information is differentially suggestive of the different possible categories. Thus, information with high differential representativeness will swamp base-rate information even if it is almost worthless (e.g., because its source is unreliable). The present studies varied differential representativeness by manipulating the prediction categories’ similarity to one another vis-a-vis the individuating information. It was found that the effect of the base rate increased systematically as differential representativeness decreased. Representativeness was measured independently by several converging techniques. These measures predicted the magnitude of the base-rate effect, supporting the hypothesis that neutral stimuli are assigned to categories in proportion to the base rates.     

I'm worth more than you! Effects of reward interdependence on performance,cohesion, emotion and effort during team competition

ObjectivesTo examine the effects of reward structures on the performance of a motor task. To evaluate the effects of reward interdependence on performance, cohesion, emotion, and effort during intergroup (team) competition.DesignAn experimental design was used to compare the effects of reward interdependence (no, low, high) on performance of a strength and endurance task.MethodParticipants (N = 111) performed a 3-min handgrip task as a member of a team of four under three reward interdependence conditions (no; low, with an even split of prize money; high, with an uneven split of prize money) in head-to-head competitions against another team. Task performance was assessed using the cumulative force production total. Task-related cohesion, enjoyment, anxiety and effort were measured using self-report scales.ResultsPerformance was better with rewards than no reward, and better with high than low reward interdependence. Team cohesion was highest with low reward interdependence. Effort was greater with rewards than no reward. Anxiety and enjoyment did not vary among the reward conditions. Mediation analyses indicated that increased cohesion mediated improvements in performance from no reward to low reward interdependence conditions, and increased effort mediated improvements in performance from no reward to both low and high reward interdependence conditions.ConclusionPerformance of a simple physical task in team competition was facilitated by rewards, with optimal performance associated with unequal rewards (i.e., performance-related pay). The benefits of performing with rewards compared to no rewards were explained by increased cohesion and effort. Social interdependence theory can help explain performance of simple motor tasks during team-based competitions. The findings have implications for the pay structures adopted by sports teams.     

When, what, and how much to reward in reinforcement learning-based models of cognition

Reinforcement learning approaches to cognitive modeling represent task acquisition as learning to choose the sequence of steps that accomplishes the task while maximizing a reward. However, an apparently unrecognized problem for modelers is choosing when, what, and how much to reward; that is, when (the moment: end of trial, subtask, or some other interval of task performance), what (the objective function: e.g., performance time or performance accuracy), and how much (the magnitude: with binary, categorical, or continuous values). In this article, we explore the problem space of these three parameters in the context of a task whose completion entails some combination of 36 state-action pairs, where all intermediate states (i.e., after the initial state and prior to the end state) represent progressive but partial completion of the task. Different choices produce profoundly different learning paths and outcomes, with the strongest effect for moment. Unfortunately, there is little discussion in the literature of the effect of such choices. This absence is disappointing, as the choice of when, what, and how much needs to be made by a modeler for every learning model.     

Cognitive load causes kinematic changes in both elite and non-elite rowers

The current motor literature suggests that extraneous cognitive load may affect performance and kinematics in a primary motor task. A common response to increased cognitive demand, as observed in past studies, might be to reduce movement complexity and revert to previously learned movement patterns, in line with the progression-regression hypothesis. However, according to several accounts of automaticity, motor experts should be able to cope with dual task demands without detriment to their performance and kinematics. To test this, we conducted an experiment asking elite and non-elite rowers to use a rowing ergometer under conditions of varying task load. We employed single-task conditions with low cognitive load (i.e., rowing only) and dual-task conditions with high cognitive load (i.e., rowing and solving arithmetic problems). The results of the cognitive load manipulations were mostly in line with our hypotheses. Overall, participants reduced movement complexity, for example by reverting towards tighter coupling of kinematic events, in their dual-task performance as compared to single-task performance. The between-group kinematic differences were less clear. In contradiction to our hypotheses, we found no significant interaction between skill level and cognitive load, suggesting that the rowers' kinematics were affected by cognitive load irrespective of skill level. Overall, our findings contradict several past findings and automaticity theories, and suggest that attentional resources are required for optimal sports performance.     

Base-rate effects in category learning: a comparison of parallel network and memory storage-retrieval models

Exemplar-memory and adaptive network models were compared in application to category learning data, with special attention to base rate effects on learning and transfer performance. Subjects classified symptom charts of hypothetical patients into disease categories, with informative feedback on learning trials and with the feedback either given or withheld on test trials that followed each fourth of the learning series. The network model proved notably accurate and uniformly superior to the exemplar model in accounting for the detailed course of learning; both the parallel, interactive aspect of the network model and its particular learning algorithm contribute to this superiority. During learning, subjects' performance reflected both category base rates and feature (symptom) probabilities in a nearly optimal manner, a result predicted by both models, though more accurately by the network model. However, under some test conditions, the data showed substantial base-rate neglect, in agreement with Gluck and Bower (1988b).     

Allocation of effort as a function of payoffs for individual tasks in a multitasking environment

SYNWORK1 software allows the examination of how payoffs affect the allocation of effort by people when they perform four different tasks (memory search, arithmetic, visual monitoring, and auditory monitoring). In a previous study (Wang, Proctor, & Pick, 2007), we showed that participants adopted multitasking strategies allocating relative effort appropriate to payoff differences between the arithmetic and memory tasks, but that they exhibited residual effects of prior payoffs when the payoffs were switched. In the present study, we varied the payoff in two different experiments for only one of these tasks, the memory task in Experiment 1 and the arithmetic task in Experiment 2. Doing this allowed consideration of performance for both the task for which payoff changed explicitly and the other cognitive task, for which the payoff difference was implicit (i.e., relative to the explicit payoff that was manipulated). Although participants adjusted performance on the task for which the payoff explicitly varied, the payoff manipulation had less effect than did the explicit payoff manipulations for both tasks used previously. Also, the change in effort on a task resulting from explicitly increasing its payoff was less than that from decreasing the payoff. SYNWORK1 is a good environment for studying multitasking, but has several limitations that need to be addressed to provide a synthetic work environment that allows investigation of a wider range of theoretically relevant issues.     

On the positive and negative effects of self-efficacy on performance: Reward as a moderator

We address the controversy regarding the sign of the effect of self-efficacy on performance. We propose that when reward is high, self-efficacy has a positive effect on performance, whereas when reward is low, it has a negative effect. This hypothesis was tested in three experiments (with sample sizes of 76, 99, and 111) in which reward and self-efficacy were manipulated and performance was measured using different manipulations and tasks in both within-factor and between-factor designs. The results supported the hypothesis that reward moderates the effect of self-efficacy on performance. When reward was high, the effect of self-efficacy on performance was positive, whereas when reward was low, the effect of self-efficacy on performance was negative.