Probabilistic Decision-Making in Children With Dyslexia

Background

Neurocognitive mechanisms underlying developmental dyslexia (dD) remain poorly characterized apart from phonological and/or visual processing deficits. Assuming such deficits, the process of learning complex tasks like reading requires the learner to make decisions (i.e., word pronunciation) based on uncertain information (e.g., aberrant phonological percepts)-a cognitive process known as probabilistic decision making, which has been linked to the striatum. We investigate (1) the relationship between dD and probabilistic decision-making and (2) the association between the volume of striatal structures and probabilistic decision-making in dD and typical readers.

Methods

Twenty four children diagnosed with dD underwent a comprehensive evaluation and MRI scanning (3T). Children with dD were compared to age-matched typical readers (n = 11) on a probabilistic, risk/reward fishing task that utilized a Bayesian cognitive model with game parameters of risk propensity (γ+) and behavioral consistency (β), as well as an overall adjusted score (average number of casts, excluding forced-fail trials). Volumes of striatal structures (caudate, putamen, and nucleus accumbens) were analyzed between groups and associated with game parameters.

Results

dD was associated with greater risk propensity and decreased behavioral consistency estimates compared to typical readers. Cognitive model parameters associated with timed pseudoword reading across groups. Risk propensity related to caudate volumes, particularly in the dD group.

Conclusion

Decision-making processes differentiate dD, associate with the caudate, and may impact learning mechanisms. This study suggests the need for further research into domain-general probabilistic decision-making in dD, neurocognitive mechanisms, and targeted interventions in dD.

A number-line task with a Bayesian active learning algorithm provides insights into the development of non-symbolic number estimation

To characterize numerical representations, the number-line task asks participants to estimate the location of a given number on a line flanked with zero and an upper-bound number. An open question is whether estimates for symbolic numbers (e.g., Arabic numerals) and non-symbolic numbers (e.g., number of dots) rely on common processes with a common developmental pathway. To address this question, we explored whether well-established findings in symbolic number-line estimation generalize to non-symbolic number-line estimation. For exhaustive investigations without sacrificing data quality, we applied a novel Bayesian active learning algorithm, dubbed Gaussian process active learning (GPAL), that adaptively optimizes experimental designs. The results showed that the non-symbolic number estimation in participants of diverse ages (5-73 years old, n = 238) exhibited three characteristic features of symbolic number estimation.

Data-driven experimental design and model development using Gaussian process with active learning

Interest in computational modeling of cognition and behavior continues to grow. To be most productive, modelers should be equipped with tools that ensure optimal efficiency in data collection and in the integrity of inference about the phenomenon of interest. Traditionally, models in cognitive science have been parametric, which are particularly susceptible to model misspecification because their strong assumptions (e.g. parameterization, functional form) may introduce unjustified biases in data collection and inference. To address this issue, we propose a data-driven nonparametric framework for model development, one that also includes optimal experimental design as a goal. It combines Gaussian Processes, a stochastic process often used for regression and classification, with active learning, from machine learning, to iteratively fit the model and use it to optimize the design selection throughout the experiment. The approach, dubbed Gaussian process with active learning (GPAL), is an extension of the parametric, adaptive design optimization (ADO) framework (Cavagnaro, Myung, Pitt, & Kujala, 2010). We demonstrate the application and features of GPAL in a delay discounting task and compare its performance to ADO in two experiments. The results show that GPAL is a viable modeling framework that is noteworthy for its high sensitivity to individual differences, identifying novel patterns in the data that were missed by the model-constrained ADO. This investigation represents a first step towards the development of a data-driven cognitive modeling framework that serves as a middle ground between raw data, which can be difficult to interpret, and parametric models, which rely on strong assumptions.

Rapid, precise, and reliable measurement of delay discounting using a Bayesian learning algorithm

Machine learning has the potential to facilitate the development of computational methods that improve the measurement of cognitive and mental functioning. In three populations (college students, patients with a substance use disorder, and Amazon Mechanical Turk workers), we evaluated one such method, Bayesian adaptive design optimization (ADO), in the area of delay discounting by comparing its test-retest reliability, precision, and efficiency with that of a conventional staircase method. In all three populations tested, the results showed that ADO led to 0.95 or higher test-retest reliability of the discounting rate within 10-20 trials (under 1-2 min of testing), captured approximately 10% more variance in test-retest reliability, was 3-5 times more precise, and was 3-8 times more efficient than the staircase method. The ADO methodology provides efficient and precise protocols for measuring individual differences in delay discounting.

Efficient Closed-loop Maximization of Carbon Nanotube Growth Rate using Bayesian Optimization

A major technological challenge in materials research is the large and complex parameter space, which hinders experimental throughput and ultimately slows down development and implementation. In single-walled carbon nanotube (CNT) synthesis, for instance, the poor yield obtained from conventional catalysts is a result of limited understanding of input-to-output correlations. Autonomous closed-loop experimentation combined with advances in machine learning (ML) is uniquely suited for high-throughput research. Among the ML algorithms available, Bayesian optimization (BO) is especially apt for exploration and optimization within such high-dimensional and complex parameter space. BO is an adaptive sequential design algorithm for finding the global optimum of a black-box objective function with the fewest possible measurements. Here, we demonstrate a promising application of BO in CNT synthesis as an efficient and robust algorithm which can (1) improve the growth rate of CNT in the BO-planner experiments over the seed experiments up to a factor 8; (2) rapidly improve its predictive power (or learning); (3) Consistently achieve good performance regardless of the number or origin of seed experiments; (4) exploit a high-dimensional, complex parameter space, and (5) achieve the former 4 tasks in just over 100 hundred experiments (~8 experimental hours) - a factor of 5× faster than our previously reported results.

Mechanisms underlying the spacing effect in learning: A comparison of three computational models

The spacing effect is one of the most widely replicated results in experimental psychology: Separating practice repetitions by a delay slows learning but enhances retention. The current study tested the suitability of the underlying, explanatory mechanism in three computational models of the spacing effect. The relearning of forgotten material was measured, as the models differ in their predictions of how the initial study conditions should affect relearning. Participants learned Japanese-English paired associates presented in a massed or spaced manner during an acquisition phase. They were tested on the pairs after retention intervals ranging from 1 to 21 days. Corrective feedback was given during retention tests to enable relearning. The results of 2 experiments showed that spacing slowed learning during the acquisition phase, increased retention at the start of tests, and accelerated relearning during tests. Of the 3 models, only 1, the predictive performance equation (PPE), was consistent with the finding of spacing-accelerated relearning. The implications of these results for learning theory and educational practice are discussed. (PsycINFO Database Record

A model-based analysis of decision making under risk in obsessive-compulsive and hoarding disorders

Attitudes towards risk are highly consequential in clinical disorders thought to be prone to "risky behavior", such as substance dependence, as well as those commonly associated with excessive risk aversion, such as obsessive-compulsive disorder (OCD) and hoarding disorder (HD). Moreover, it has recently been suggested that attitudes towards risk may serve as a behavioral biomarker for OCD. We investigated the risk preferences of participants with OCD and HD using a novel adaptive task and a quantitative model from behavioral economics that decomposes risk preferences into outcome sensitivity and probability sensitivity. Contrary to expectation, compared to healthy controls, participants with OCD and HD exhibited less outcome sensitivity, implying less risk aversion in the standard economic framework. In addition, risk attitudes were strongly correlated with depression, hoarding, and compulsion scores, while compulsion (hoarding) scores were associated with more (less) "rational" risk preferences. These results demonstrate how fundamental attitudes towards risk relate to specific psychopathology and thereby contribute to our understanding of the cognitive manifestations of mental disorders. In addition, our findings indicate that the conclusion made in recent work that decision making under risk is unaltered in OCD is premature.

Planning Beyond the Next Trial in Adaptive Experiments: A Dynamic Programming Approach

Experimentation is at the heart of scientific inquiry. In the behavioral and neural sciences, where only a limited number of observations can often be made, it is ideal to design an experiment that leads to the rapid accumulation of information about the phenomenon under study. Adaptive experimentation has the potential to accelerate scientific progress by maximizing inferential gain in such research settings. To date, most adaptive experiments have relied on myopic, one-step-ahead strategies in which the stimulus on each trial is selected to maximize inference on the next trial only. A lingering question in the field has been how much additional benefit would be gained by optimizing beyond the next trial. A range of technical challenges has prevented this important question from being addressed adequately. This study applies dynamic programming (DP), a technique applicable for such full-horizon, "global" optimization, to model-based perceptual threshold estimation, a domain that has been a major beneficiary of adaptive methods. The results provide insight into conditions that will benefit from optimizing beyond the next trial. Implications for the use of adaptive methods in cognitive science are discussed.

A hierarchical Bayesian approach to adaptive vision testing: A case study with the contrast sensitivity function

Measurement efficiency is of concern when a large number of observations are required to obtain reliable estimates for parametric models of vision. The standard entropy-based Bayesian adaptive testing procedures addressed the issue by selecting the most informative stimulus in sequential experimental trials. Noninformative, diffuse priors were commonly used in those tests. Hierarchical adaptive design optimization (HADO; Kim, Pitt, Lu, Steyvers, & Myung, 2014) further improves the efficiency of the standard Bayesian adaptive testing procedures by constructing an informative prior using data from observers who have already participated in the experiment. The present study represents an empirical validation of HADO in estimating the human contrast sensitivity function. The results show that HADO significantly improves the accuracy and precision of parameter estimates, and therefore requires many fewer observations to obtain reliable inference about contrast sensitivity, compared to the method of quick contrast sensitivity function (Lesmes, Lu, Baek, & Albright, 2010), which uses the standard Bayesian procedure. The improvement with HADO was maintained even when the prior was constructed from heterogeneous populations or a relatively small number of observers. These results of this case study support the conclusion that HADO can be used in Bayesian adaptive testing by replacing noninformative, diffuse priors with statistically justified informative priors without introducing unwanted bias.

On the Functional Form of Temporal Discounting: An Optimized Adaptive Test

The tendency to discount the value of future rewards has become one of the best-studied constructs in the behavioral sciences. Although hyperbolic discounting remains the dominant quantitative characterization of this phenomenon, a variety of models have been proposed and consensus around the one that most accurately describes behavior has been elusive. To help bring some clarity to this issue, we propose an Adaptive Design Optimization (ADO) method for fitting and comparing models of temporal discounting. We then conduct an ADO experiment aimed at discriminating among six popular models of temporal discounting. Rather than supporting a single underlying model, our results show that each model is inadequate in some way to describe the full range of behavior exhibited across subjects. The precision of results provided by ADO further identify specific properties of models, such as accommodating both increasing and decreasing impatience, that are mandatory to describe temporal discounting broadly.

Evaluating the performance of the quick CSF method in detecting contrast sensitivity function changes

The contrast sensitivity function (CSF) has shown promise as a functional vision endpoint for monitoring the changes in functional vision that accompany eye disease or its treatment. However, detecting CSF changes with precision and efficiency at both the individual and group levels is very challenging. By exploiting the Bayesian foundation of the quick CSF method (Lesmes, Lu, Baek, & Albright, 2010), we developed and evaluated metrics for detecting CSF changes at both the individual and group levels. A 10-letter identification task was used to assess the systematic changes in the CSF measured in three luminance conditions in 112 naïve normal observers. The data from the large sample allowed us to estimate the test-retest reliability of the quick CSF procedure and evaluate its performance in detecting CSF changes at both the individual and group levels. The test-retest reliability reached 0.974 with 50 trials. In 50 trials, the quick CSF method can detect a medium 0.30 log unit area under log CSF change with 94.0% accuracy at the individual observer level. At the group level, a power analysis based on the empirical distribution of CSF changes from the large sample showed that a very small area under log CSF change (0.025 log unit) could be detected by the quick CSF method with 112 observers and 50 trials. These results make it plausible to apply the method to monitor the progression of visual diseases or treatment effects on individual patients and greatly reduce the time, sample size, and costs in clinical trials at the group level.

A hierarchical adaptive approach to optimal experimental design

Experimentation is at the core of research in the behavioral and neural sciences, yet observations can be expensive and time-consuming to acquire (e.g., MRI scans, responses from infant participants). A major interest of researchers is designing experiments that lead to maximal accumulation of information about the phenomenon under study with the fewest possible number of observations. In addressing this challenge, statisticians have developed adaptive design optimization methods. This letter introduces a hierarchical Bayes extension of adaptive design optimization that provides a judicious way to exploit two complementary schemes of inference (with past and future data) to achieve even greater accuracy and efficiency in information gain. We demonstrate the method in a simulation experiment in the field of visual perception.

Analytical Expressions for the REM Model of Recognition Memory

An inordinate amount of computation is required to evaluate predictions of simulation-based models. Following Myung et al (2007), we derived an analytic form expression of the REM model of recognition memory using a Fourier transform technique, which greatly reduces the time required to perform model simulations. The accuracy of the derivation is verified by showing a close correspondence between its predictions and those reported in Shiffrin and Steyvers (1997). The derivation also shows that REM's predictions depend upon the vector length parameter, and that model parameters are not identifiable unless one of the parameters is fixed.

Discriminating Among Probability Weighting Functions Using Adaptive Design Optimization

Probability weighting functions relate objective probabilities and their subjective weights, and play a central role in modeling choices under risk within cumulative prospect theory. While several different parametric forms have been proposed, their qualitative similarities make it challenging to discriminate among them empirically. In this paper, we use both simulation and choice experiments to investigate the extent to which different parametric forms of the probability weighting function can be discriminated using adaptive design optimization, a computer-based methodology that identifies and exploits model differences for the purpose of model discrimination. The simulation experiments show that the correct (data-generating) form can be conclusively discriminated from its competitors. The results of an empirical experiment reveal heterogeneity between participants in terms of the functional form, with two models (Prelec-2, Linear in Log Odds) emerging as the most common best-fitting models. The findings shed light on assumptions underlying these models.

How do PDP models learn quasiregularity?

Parallel distributed processing (PDP) models have had a profound impact on the study of cognition. One domain in which they have been particularly influential is learning quasiregularity, in which mastery requires both learning regularities that capture the majority of the structure in the input plus learning exceptions that violate the regularities. How PDP models learn quasiregularity is still not well understood. Small- and large-scale analyses of a feedforward, 3-layer network were carried out to address 2 fundamental issues about network functioning: how the model can learn both regularities and exceptions without sacrificing generalizability and the nature of the hidden representation that makes this learning possible. Results show that capacity-limited learning pressures the network to form componential representations, which ensures good generalizability. Small and highly local perturbations of this representational system allow exceptions to be learned while minimally disrupting generalizability. Theoretical and methodological implications of the findings are discussed.

A Tutorial on Adaptive Design Optimization

Experimentation is ubiquitous in the field of psychology and fundamental to the advancement of its science, and one of the biggest challenges for researchers is designing experiments that can conclusively discriminate the theoretical hypotheses or models under investigation. The recognition of this challenge has led to the development of sophisticated statistical methods that aid in the design of experiments and that are within the reach of everyday experimental scientists. This tutorial paper introduces the reader to an implementable experimentation methodology, dubbed Adaptive Design Optimization, that can help scientists to conduct "smart" experiments that are maximally informative and highly efficient, which in turn should accelerate scientific discovery in psychology and beyond.

Optimal Decision Stimuli for Risky Choice Experiments: An Adaptive Approach

Collecting data to discriminate between models of risky choice requires careful selection of decision stimuli. Models of decision making aim to predict decisions across a wide range of possible stimuli, but practical limitations force experimenters to select only a handful of them for actual testing. Some stimuli are more diagnostic between models than others, so the choice of stimuli is critical. This paper provides the theoretical background and a methodological framework for adaptive selection of optimal stimuli for discriminating among models of risky choice. The approach, called Adaptive Design Optimization (ADO), adapts the stimulus in each experimental trial based on the results of the preceding trials. We demonstrate the validity of the approach with simulation studies aiming to discriminate Expected Utility, Weighted Expected Utility, Original Prospect Theory, and Cumulative Prospect Theory models.

Model discrimination through adaptive experimentation

An ideal experiment is one in which data collection is efficient and the results are maximally informative. This standard can be difficult to achieve because of uncertainties about the consequences of design decisions. We demonstrate the success of a Bayesian adaptive method (adaptive design optimization, ADO) in optimizing design decisions when comparing models of the time course of forgetting. Across a series of testing stages, ADO intelligently adapts the retention interval in order to maximally discriminate power and exponential models. Compared with two different control (non-adaptive) methods, ADO distinguishes the models decisively, with the results unambiguously favoring the power model. Analyses suggest that ADO's success is due in part to its flexibility in adjusting to individual differences. This implementation of ADO serves as an important first step in assessing its applicability and usefulness to psychology.

Adaptive design optimization: a mutual information-based approach to model discrimination in cognitive science

Discriminating among competing statistical models is a pressing issue for many experimentalists in the field of cognitive science. Resolving this issue begins with designing maximally informative experiments. To this end, the problem to be solved in adaptive design optimization is identifying experimental designs under which one can infer the underlying model in the fewest possible steps. When the models under consideration are nonlinear, as is often the case in cognitive science, this problem can be impossible to solve analytically without simplifying assumptions. However, as we show in this letter, a full solution can be found numerically with the help of a Bayesian computational trick derived from the statistics literature, which recasts the problem as a probability density simulation in which the optimal design is the mode of the density. We use a utility function based on mutual information and give three intuitive interpretations of the utility function in terms of Bayesian posterior estimates. As a proof of concept, we offer a simple example application to an experiment on memory retention.

On the Minimum Description Length Complexity of Multinomial Processing Tree Models

Multinomial processing tree (MPT) modeling is a statistical methodology that has been widely and successfully applied for measuring hypothesized latent cognitive processes in selected experimental paradigms. This paper concerns model complexity of MPT models. Complexity is a key and necessary concept to consider in the evaluation and selection of quantitative models. A complex model with many parameters often overfits data beyond and above the underlying regularities, and therefore, should be appropriately penalized. It has been well established and demonstrated in multiple studies that in addition to the number of parameters, a model's functional form, which refers to the way by which parameters are combined in the model equation, can also have significant effects on complexity. Given that MPT models vary greatly in their functional forms (tree structures and parameter/category assignments), it would be of interest to evaluate their effects on complexity. Addressing this issue from the minimum description length (MDL) viewpoint, we prove a series of propositions concerning various ways in which functional form contributes to the complexity of MPT models. Computational issues of complexity are also discussed.

Optimal experimental design for model discrimination

Models of a psychological process can be difficult to discriminate experimentally because it is not easy to determine the values of the critical design variables (e.g., presentation schedule, stimulus structure) that will be most informative in differentiating them. Recent developments in sampling-based search methods in statistics make it possible to determine these values and thereby identify an optimal experimental design. After describing the method, it is demonstrated in 2 content areas in cognitive psychology in which models are highly competitive: retention (i.e., forgetting) and categorization. The optimal design is compared with the quality of designs used in the literature. The findings demonstrate that design optimization has the potential to increase the informativeness of the experimental method.

Evaluation and comparison of computational models

Computational models are powerful tools that can enhance the understanding of scientific phenomena. The enterprise of modeling is most productive when the reasons underlying the adequacy of a model, and possibly its superiority to other models, are understood. This chapter begins with an overview of the main criteria that must be considered in model evaluation and selection, in particular explaining why generalizability is the preferred criterion for model selection. This is followed by a review of measures of generalizability. The final section demonstrates the use of five versatile and easy-to-use selection methods for choosing between two mathematical models of protein folding.

Modeling the word recognition data of Vitevitch and Luce (1998): is it ARTful?

Vitevitch and Luce (1998) showed that the probability with which phonemes co-occur in the language (phonotactic probability) affects the speed with which words and nonwords are named. Words with high phonotactic probabilities between phonemes were named more slowly than words with low probabilities, whereas with nonwords, just the opposite was found. To reproduce this reversal in performance, a model would seem to require not merely sublexical representations, but sublexical representations that are relatively independent of lexical representations. ARTphone (Grossberg, Boardman, & Cohen, 1997) is designed to meet these requirements. In this study, we used a technique called parameter space partitioning to analyze ARTphone's behavior and to learn if it can mimic human behavior and, if so, to understand how. To perform best, differences in sublexical node probabilities must be amplified relative to lexical node probabilities to offset the additional source of inhibition (from top-down masking) that is found at the sublexical level.

Analytic Expressions for the BCDMEM Model of Recognition Memory

We introduce a Fourier Transformation technique that enables one to derive closed-form expressions of performance measures (e.g., hit and false alarm rates) of simulation-based models of recognition memory. Application of the technique is demonstrated using the bind cue decide model of episodic memory (BCDMEM; Dennis & Humphreys, 2001). In addition to reducing the time required to test the model, which for models like BCDMEM can be excessive, asymptotic expressions of the measures reveal heretofore unknown properties of the model, such as model predictions being dependent on vector length.

Global model analysis by parameter space partitioning

To model behavior, scientists need to know how models behave. This means learning what other behaviors a model can produce besides the one generated by participants in an experiment. This is a difficult problem because of the complexity of psychological models (e.g., their many parameters) and because the behavioral precision of models (e.g., interval-scale performance) often mismatches their testable precision in experiments, where qualitative, ordinal predictions are the norm. Parameter space partitioning is a solution that evaluates model performance at a qualitative level. There exists a partition on the model's parameter space that divides it into regions that correspond to each data pattern. Three application examples demonstrate its potential and versatility for studying the global behavior of psychological models.