Likelihood-free Bayesian analysis of memory models

Parameter Inference for Computational Cognitive Models with Approximate Bayesian Computation

This paper addresses a common challenge with computational cognitive models: identifying parameter values that are both theoretically plausible and generate predictions that match well with empirical data. While computational models can offer deep explanations of cognition, they are computationally complex and often out of reach of traditional parameter fitting methods. Weak methodology may lead to premature rejection of valid models or to acceptance of models that might otherwise be falsified. Mathematically robust fitting methods are, therefore, essential to the progress of computational modeling in cognitive science. In this article, we investigate the capability and role of modern fitting methods—including Bayesian optimization and approximate Bayesian computation—and contrast them to some more commonly used methods: grid search and Nelder–Mead optimization. Our investigation consists of a reanalysis of the fitting of two previous computational models: an Adaptive Control of Thought—Rational model of skill acquisition and a computational rationality model of visual search. The results contrast the efficiency and informativeness of the methods. A key advantage of the Bayesian methods is the ability to estimate the uncertainty of fitted parameter values. We conclude that approximate Bayesian computation is (a) efficient, (b) informative, and (c) offers a path to reproducible results.

The Cognitive Lens: a primer on conceptual tools for analysing information processing in developmental and regenerative morphogenesis

Brains exhibit plasticity, multi-scale integration of information, computation and memory, having evolved by specialization of non-neural cells that already possessed many of the same molecular components and functions. The emerging field of basal cognition provides many examples of decision-making throughout a wide range of non-neural systems. How can biological information processing across scales of size and complexity be quantitatively characterized and exploited in biomedical settings? We use pattern regulation as a context in which to introduce the Cognitive Lens-a strategy using well-established concepts from cognitive and computer science to complement mechanistic investigation in biology. To facilitate the assimilation and application of these approaches across biology, we review tools from various quantitative disciplines, including dynamical systems, information theory and least-action principles. We propose that these tools can be extended beyond neural settings to predict and control systems-level outcomes, and to understand biological patterning as a form of primitive cognition. We hypothesize that a cognitive-level information-processing view of the functions of living systems can complement reductive perspectives, improving efficient top-down control of organism-level outcomes. Exploration of the deep parallels across diverse quantitative paradigms will drive integrative advances in evolutionary biology, regenerative medicine, synthetic bioengineering, cognitive neuroscience and artificial intelligence. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Thermodynamic integration via differential evolution: A method for estimating marginal likelihoods

A typical goal in cognitive psychology is to select the model that provides the best explanation of the observed behavioral data. The Bayes factor provides a principled approach for making these selections, though the integral required to calculate the marginal likelihood for each model is intractable for most cognitive models. In these cases, Monte Carlo techniques must be used to approximate the marginal likelihood, such as thermodynamic integration (TI; Friel & Pettitt, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(3), 589-607 2008; Lartillot & Philippe, Systematic Biology, 55(2), 195-207 2006), which relies on sampling from the posterior at different powers (called power posteriors). TI can become computationally expensive when using population Markov chain Monte Carlo (MCMC) approaches such as differential evolution MCMC (DE-MCMC; Turner et al., Psychological Methods, 18(3), 368 2013) that require several interacting chains per power posterior. Here, we propose a method called thermodynamic integration via differential evolution (TIDE), which aims to reduce the computational burden associated with TI by using a single chain per power posterior (R code available at https://osf.io/ntmgw/ ). We show that when applied to non-hierarchical models, TIDE produces an approximation of the marginal likelihood that closely matches TI. When extended to hierarchical models, we find that certain assumptions about the dependence between the individual- and group-level parameters samples (i.e., dependent/independent) have sizable effects on the TI approximated marginal likelihood. We propose two possible extensions of TIDE to hierarchical models, which closely match the marginal likelihoods obtained through TI with dependent/independent sampling in many, but not all, situations. Based on these findings, we believe that TIDE provides a promising method for estimating marginal likelihoods, though future research should focus on a detailed comparison between the methods of estimating marginal likelihoods for cognitive models.

Approximating Bayesian Inference through Model Simulation

The ultimate test of the validity of a cognitive theory is its ability to predict patterns of empirical data. Cognitive models formalize this test by making specific processing assumptions that yield mathematical predictions, and the mathematics allow the models to be fitted to data. As the field of cognitive science has grown to address increasingly complex problems, so too has the complexity of models increased. Some models have become so complex that the mathematics detailing their predictions are intractable, meaning that the model can only be simulated. Recently, new Bayesian techniques have made it possible to fit these simulation-based models to data. These techniques have even allowed simulation-based models to transition into neuroscience, where tests of cognitive theories can be biologically substantiated.

Modeling the dynamics of recognition memory testing with an integrated model of retrieval and decision making

A robust finding in recognition memory is that performance declines monotonically across test trials. Despite the prevalence of this decline, there is a lack of consensus on the mechanism responsible. Three hypotheses have been put forward: (1) interference is caused by learning of test items (2) the test items cause a shift in the context representation used to cue memory and (3) participants change their speed-accuracy thresholds through the course of testing. We implemented all three possibilities in a combined model of recognition memory and decision making, which inherits the memory retrieval elements of the Osth and Dennis (2015) model and uses the diffusion decision model (DDM: Ratcliff, 1978) to generate choice and response times. We applied the model to four datasets that represent three challenges, the findings that: (1) the number of test items plays a larger role in determining performance than the number of studied items, (2) performance decreases less for strong items than weak items in pure lists but not in mixed lists, and (3) lexical decision trials interspersed between recognition test trials do not increase the rate at which performance declines. Analysis of the model's parameter estimates suggests that item interference plays a weak role in explaining the effects of recognition testing, while context drift plays a very large role. These results are consistent with prior work showing a weak role for item noise in recognition memory and that retrieval is a strong cause of context change in episodic memory.

Approaches to Analysis in Model-based Cognitive Neuroscience

Our understanding of cognition has been advanced by two traditionally nonoverlapping and non-interacting groups. Mathematical psychologists rely on behavioral data to evaluate formal models of cognition, whereas cognitive neuroscientists rely on statistical models to understand patterns of neural activity, often without any attempt to make a connection to the mechanism supporting the computation. Both approaches suffer from critical limitations as a direct result of their focus on data at one level of analysis (cf. Marr, 1982), and these limitations have inspired researchers to attempt to combine both neural and behavioral measures in a cross-level integrative fashion. The importance of solving this problem has spawned several entirely new theoretical and statistical frameworks developed by both mathematical psychologists and cognitive neuroscientists. However, with each new approach comes a particular set of limitations and benefits. In this article, we survey and characterize several approaches for linking brain and behavioral data. We organize these approaches on the basis of particular cognitive modeling goals: (1) using the neural data to constrain a behavioral model, (2) using the behavioral model to predict neural data, and (3) fitting both neural and behavioral data simultaneously. Within each goal, we highlight a few particularly successful approaches for accomplishing that goal, and discuss some applications. Finally, we provide a conceptual guide to choosing among various analytic approaches in performing model-based cognitive neuroscience.

Double jeopardy in inferring cognitive processes

Inferences we make about underlying cognitive processes can be jeopardized in two ways due to problematic forms of aggregation. First, averaging across individuals is typically considered a very useful tool for removing random variability. The threat is that averaging across subjects leads to averaging across different cognitive strategies, thus harming our inferences. The second threat comes from the construction of inadequate research designs possessing a low diagnostic accuracy of cognitive processes. For that reason we introduced the systems factorial technology (SFT), which has primarily been designed to make inferences about underlying processing order (serial, parallel, coactive), stopping rule (terminating, exhaustive), and process dependency. SFT proposes that the minimal research design complexity to learn about n number of cognitive processes should be equal to 2ⁿ. In addition, SFT proposes that (a) each cognitive process should be controlled by a separate experimental factor, and (b) The saliency levels of all factors should be combined in a full factorial design. In the current study, the author cross combined the levels of jeopardies in a 2 × 2 analysis, leading to four different analysis conditions. The results indicate a decline in the diagnostic accuracy of inferences made about cognitive processes due to the presence of each jeopardy in isolation and when combined. The results warrant the development of more individual subject analyses and the utilization of full-factorial (SFT) experimental designs.

Hierarchical approximate Bayesian computation

Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model's parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper, we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function.

A generalized, likelihood-free method for posterior estimation

Recent advancements in Bayesian modeling have allowed for likelihood-free posterior estimation. Such estimation techniques are crucial to the understanding of simulation-based models, whose likelihood functions may be difficult or even impossible to derive. However, current approaches are limited by their dependence on sufficient statistics and/or tolerance thresholds. In this article, we provide a new approach that requires no summary statistics, error terms, or thresholds and is generalizable to all models in psychology that can be simulated. We use our algorithm to fit a variety of cognitive models with known likelihood functions to ensure the accuracy of our approach. We then apply our method to two real-world examples to illustrate the types of complex problems our method solves. In the first example, we fit an error-correcting criterion model of signal detection, whose criterion dynamically adjusts after every trial. We then fit two models of choice response time to experimental data: the linear ballistic accumulator model, which has a known likelihood, and the leaky competing accumulator model, whose likelihood is intractable. The estimated posterior distributions of the two models allow for direct parameter interpretation and model comparison by means of conventional Bayesian statistics-a feat that was not previously possible.

A method for efficiently sampling from distributions with correlated dimensions

Bayesian estimation has played a pivotal role in the understanding of individual differences. However, for many models in psychology, Bayesian estimation of model parameters can be difficult. One reason for this difficulty is that conventional sampling algorithms, such as Markov chain Monte Carlo (MCMC), can be inefficient and impractical when little is known about the target distribution--particularly the target distribution's covariance structure. In this article, we highlight some reasons for this inefficiency and advocate the use of a population MCMC algorithm, called differential evolution Markov chain Monte Carlo (DE-MCMC), as a means of efficient proposal generation. We demonstrate in a simulation study that the performance of the DE-MCMC algorithm is unaffected by the correlation of the target distribution, whereas conventional MCMC performs substantially worse as the correlation increases. We then show that the DE-MCMC algorithm can be used to efficiently fit a hierarchical version of the linear ballistic accumulator model to response time data, which has proven to be a difficult task when conventional MCMC is used.