Connecting process models to response times through Bayesian hierarchical regression analysis.

Process models specify a series of mental operations necessary to complete a task. We demonstrate how to use process models to analyze response-time data and obtain parameter estimates that have a clear psychological interpretation. A prerequisite for our analysis is a process model that generates a count of elementary information processing steps (EIP steps) for each trial of an experiment. We can estimate the duration of an EIP step by assuming that every EIP step is of random duration, modeled as draws from a gamma distribution. A natural effect of summing several random EIP steps is that the expected spread of the overall response time increases with a higher EIP step count. With modern probabilistic programming tools, it becomes relatively easy to fit Bayesian hierarchical models to data and thus estimate the duration of a step for each individual participant. We present two examples in this paper: The first example is children's performance on simple addition tasks, where the response time is often well predicted by the smaller of the two addends. The second example is response times in a Sudoku task. Here, the process model contains some random decisions and the EIP step count thus becomes latent. We show how our EIP regression model can be extended to such a case. We believe this approach can be used to bridge the gap between classical cognitive modeling and statistical inference and will be easily applicable to many use cases.

Solving Bongard Problems With a Visual Language and Pragmatic Constraints.

More than 50 years ago, Bongard introduced 100 visual concept learning problems as a challenge for artificial vision systems. These problems are now known as Bongard problems. Although they are well known in cognitive science and artificial intelligence, only very little progress has been made toward building systems that can solve a substantial subset of them. In the system presented here, visual features are extracted through image processing and then translated into a symbolic visual vocabulary. We introduce a formal language that allows representing compositional visual concepts based on this vocabulary. Using this language and Bayesian inference, concepts can be induced from the examples that are provided in each problem. We find a reasonable agreement between the concepts with high posterior probability and the solutions formulated by Bongard himself for a subset of 35 problems. While this approach is far from solving Bongard problems like humans, it does considerably better than previous approaches. We discuss the issues we encountered while developing this system and their continuing relevance for understanding visual cognition. For instance, contrary to other concept learning problems, the examples are not random in Bongard problems; instead they are carefully chosen to ensure that the concept can be induced, and we found it helpful to take the resulting pragmatic constraints into account.

Influence of reinforcement and its omission on trial-by-trial changes of response bias in perceptual decision making.

Discrimination performance in perceptual choice tasks is known to reflect both sensory discriminability and nonsensory response bias. In the framework of signal detection theory, these aspects of discrimination performance are quantified through separate measures, sensitivity (d') for sensory discriminability and decision criterion (c) for response bias. However, it is unknown how response bias (i.e., criterion) changes at the single-trial level as a consequence of reinforcement history. We subjected rats to a two-stimulus two-response conditional discrimination task with auditory stimuli and induced response bias through unequal reinforcement probabilities for the two responses. We compared three signal-detection-theory-based criterion learning models with respect to their ability to fit experimentally observed fluctuations of response bias on a trial-by-trial level. These models shift the criterion by a fixed step (1) after each reinforced response or (2) after each nonreinforced response or (3) after both. We find that all three models fail to capture essential aspects of the data. Prompted by the observation that steady-state criterion values conformed well to a behavioral model of signal detection based on the generalized matching law, we constructed a trial-based version of this model and find that it provides a superior account of response bias fluctuations under changing reinforcement contingencies.

Auditory cortex reflects goal-directed movement but is not necessary for behavioral adaptation in sound-cued reward tracking.

Mounting evidence suggests that the role of sensory cortices in perceptual decision making goes beyond the mere representation of the discriminative stimuli and additionally involves the representation of nonsensory variables such as reward expectation. However, the relevance of these representations for behavior is not clear. To address this issue, we trained rats to discriminate sounds in a single-interval forced-choice task and then confronted the animals with unsignaled blockwise changes of reward probabilities. We found that unequal reward probabilities for the two choice options led to substantial shifts in response bias without concomitant reduction in stimulus discrimination. Although decisional biases were on average less extreme than required to maximize overall reinforcement, a model-based analysis revealed that rats managed to harvest >97% of rewards. Neurons in auditory cortex recorded during task performance weakly differentiated the discriminative stimuli but more strongly the subsequent goal-directed movement. Although 10-20% of units exhibited significantly different firing rates between task epochs with different response biases, control experiments showed this to result from inflated false positive rates due to unspecific temporal correlations of spiking activity rather than changing reinforcement contingencies. Transient pharmacological inactivation of auditory cortex reduced sound discriminability without affecting other measures of performance, whereas inactivation of medial prefrontal cortex affected both discriminability and bias. Together, these results suggest that auditory cortex activity only weakly reflects decisional variables during flexible updating of stimulus-response-outcome contingencies and does not play a crucial role in sound-cued adaptive behavior, beyond the representation of the discriminative stimuli.NEW & NOTEWORTHY Recent evidence suggests that sensory cortex represents nonsensory variables such as reward expectation, but the relevance of these representations for behavior is not well understood. We show that rat auditory cortex (AC) is modulated during movement and reward anticipation in a sound-cued reward tracking task, whereas AC inactivation only impaired discrimination without affecting reward tracking, consistent with a predominantly sensory role of AC.

A stochastic model of myeloid cell lineages in hematopoiesis and pathway mutations in acute myeloid leukemia.

A model for hematopoiesis is presented that explicitly includes the erythrocyte, granulocyte, and thrombocyte lineages and their common precursors. A small number of stem cells proliferate and differentiate through different compartments to produce the vast number of blood cells needed every day. Growth factors regulate the proliferation of cells dependent on the current demand. We provide a steady state analysis of the model and rough parameter estimates. Furthermore, we extend the model to include mutations that alter the replicative capacity of cells and introduce differentiation blocks. With these mutations the model develops signs of acute myeloid leukemia.

Descending Marr's levels: Standard observers are no panacea.

According to Marr, explanations of perceptual behavior should address multiple levels of analysis. Rahnev & Denison (R&D) are perhaps overly dismissive of optimality considerations at the computational level. Also, an exclusive reliance on standard observer models may cause neglect of many other plausible hypotheses at the algorithmic level. Therefore, as far as explanation goes, standard observer modeling is no panacea.

An overview of quantitative approaches in Gestalt perception.

Gestalt psychology is often criticized as lacking quantitative measurements and precise mathematical models. While this is true of the early Gestalt school, today there are many quantitative approaches in Gestalt perception and the special issue of Vision Research "Quantitative Approaches in Gestalt Perception" showcases the current state-of-the-art. In this article we give an overview of these current approaches. For example, ideal observer models are one of the standard quantitative tools in vision research and there is a clear trend to try and apply this tool to Gestalt perception and thereby integrate Gestalt perception into mainstream vision research. More generally, Bayesian models, long popular in other areas of vision research, are increasingly being employed to model perceptual grouping as well. Thus, although experimental and theoretical approaches to Gestalt perception remain quite diverse, we are hopeful that these quantitative trends will pave the way for a unified theory.

Discovering hierarchical motion structure.

Scenes filled with moving objects are often hierarchically organized: the motion of a migrating goose is nested within the flight pattern of its flock, the motion of a car is nested within the traffic pattern of other cars on the road, the motion of body parts are nested in the motion of the body. Humans perceive hierarchical structure even in stimuli with two or three moving dots. An influential theory of hierarchical motion perception holds that the visual system performs a "vector analysis" of moving objects, decomposing them into common and relative motions. However, this theory does not specify how to resolve ambiguity when a scene admits more than one vector analysis. We describe a Bayesian theory of vector analysis and show that it can account for classic results from dot motion experiments, as well as new experimental data. Our theory takes a step towards understanding how moving scenes are parsed into objects.

A Statistical Framework to Infer Delay and Direction of Information Flow from Measurements of Complex Systems.

In neuroscience, data are typically generated from neural network activity. The resulting time series represent measurements from spatially distributed subsystems with complex interactions, weakly coupled to a high-dimensional global system. We present a statistical framework to estimate the direction of information flow and its delay in measurements from systems of this type. Informed by differential topology, gaussian process regression is employed to reconstruct measurements of putative driving systems from measurements of the driven systems. These reconstructions serve to estimate the delay of the interaction by means of an analytical criterion developed for this purpose. The model accounts for a range of possible sources of uncertainty, including temporally evolving intrinsic noise, while assuming complex nonlinear dependencies. Furthermore, we show that if information flow is delayed, this approach also allows for inference in strong coupling scenarios of systems exhibiting synchronization phenomena. The validity of the method is demonstrated with a variety of delay-coupled chaotic oscillators. In addition, we show that these results seamlessly transfer to local field potentials in cat visual cortex.

Suboptimal criterion setting in a perceptual choice task with asymmetric reinforcement.

Performance on psychophysical tasks is influenced by a variety of non-sensory factors, most notably the magnitude or probability of reinforcement following correct responses. When reinforcement probability is unequal for hits and correct rejections, signal detection theory specifies an optimal decision criterion which maximizes the number of reinforcers. We subjected pigeons to a task in which six different stimuli (shades of gray) had to be assigned to one of two categories. Animals were confronted with asymmetric reinforcement schedules in which correct responses to five of the stimuli were reinforced with a probability of 0.5, while correct responses to the remaining stimulus were extinguished. The subjects' resultant choice probabilities clearly deviated from those predicted by a maximization account. More specifically, the magnitude of the choice bias increased with the distance of the to-be-extinguished stimulus to the category boundary, a pattern opposite to that posited by maximization. The present and a previous set of results in which animals performed optimally can be explained by a simple choice mechanism in which a variable decision criterion is constantly updated according to a leaky integration of incomes attained from both response options.

Mapping spikes to sensations.

Single-unit recordings conducted during perceptual decision-making tasks have yielded tremendous insights into the neural coding of sensory stimuli. In such experiments, detection or discrimination behavior (the psychometric data) is observed in parallel with spike trains in sensory neurons (the neurometric data). Frequently, candidate neural codes for information read-out are pitted against each other by transforming the neurometric data in some way and asking which code's performance most closely approximates the psychometric performance. The code that matches the psychometric performance best is retained as a viable candidate and the others are rejected. In following this strategy, psychometric data is often considered to provide an unbiased measure of perceptual sensitivity. It is rarely acknowledged that psychometric data result from a complex interplay of sensory and non-sensory processes and that neglect of these processes may result in misestimating psychophysical sensitivity. This again may lead to erroneous conclusions regarding the adequacy of candidate neural codes. In this review, we first discuss requirements on the neural data for a subsequent neurometric-psychometric comparison. We then focus on different psychophysical tasks for the assessment of detection and discrimination performance and the cognitive processes that may underlie their execution. We discuss further factors that may compromise psychometric performance and how they can be detected or avoided. We believe that these considerations point to shortcomings in our understanding of the processes underlying perceptual decisions, and therefore offer potential for future research.

Visual perception of thick transparent materials.

Under typical viewing conditions, human observers readily distinguish between materials such as silk, marmalade, or granite, an achievement of the visual system that is poorly understood. Recognizing transparent materials is especially challenging. Previous work on the perception of transparency has focused on objects composed of flat, infinitely thin filters. In the experiments reported here, we considered thick transparent objects, such as ice cubes, which are irregular in shape and can vary in refractive index. An important part of the visual evidence signaling the presence of such objects is distortions in the perceived shape of other objects in the scene. We propose a new class of visual cues derived from the distortion field induced by thick transparent objects, and we provide experimental evidence that cues arising from the distortion field predict both the successes and the failures of human perception in judging refractive indices.

Does cognitive science need kernels?

Kernel methods are among the most successful tools in machine learning and are used in challenging data analysis problems in many disciplines. Here we provide examples where kernel methods have proven to be powerful tools for analyzing behavioral data, especially for identifying features in categorization experiments. We also demonstrate that kernel methods relate to perceptrons and exemplar models of categorization. Hence, we argue that kernel methods have neural and psychological plausibility, and theoretical results concerning their behavior are therefore potentially relevant for human category learning. In particular, we believe kernel methods have the potential to provide explanations ranging from the implementational via the algorithmic to the computational level.

Generalization and similarity in exemplar models of categorization: insights from machine learning.

Exemplar theories of categorization depend on similarity for explaining subjects' ability to generalize to new stimuli. A major criticism of exemplar theories concerns their lack of abstraction mechanisms and thus, seemingly, of generalization ability. Here, we use insights from machine learning to demonstrate that exemplar models can actually generalize very well. Kernel methods in machine learning are akin to exemplar models and are very successful in real-world applications. Their generalization performance depends crucially on the chosen similarity measure. Although similarity plays an important role in describing generalization behavior, it is not the only factor that controls generalization performance. In machine learning, kernel methods are often combined with regularization techniques in order to ensure good generalization. These same techniques are easily incorporated in exemplar models. We show that the generalized context model (Nosofsky, 1986) and ALCOVE (Kruschke, 1992) are closely related to a statistical model called kernel logistic regression. We argue that generalization is central to the enterprise of understanding categorization behavior, and we suggest some ways in which insights from machine learning can offer guidance.

Multimodal similarity and categorization of novel, three-dimensional objects.

Similarity has been proposed as a fundamental principle underlying mental object representations and capable of supporting cognitive-level tasks such as categorization. However, much of the research has considered connections between similarity and categorization for tasks performed using a single perceptual modality. Considering similarity and categorization within a multimodal context opens up a number of important questions: Are the similarities between objects the same when they are perceived using different modalities or using more than one modality at a time? Is similarity still able to explain categorization performance when objects are experienced multimodally? In this study, we addressed these questions by having subjects explore novel, 3D objects which varied parametrically in shape and texture using vision alone, touch alone, or touch and vision together. Subjects then performed a pair-wise similarity rating task and a free sorting categorization task. Multidimensional scaling (MDS) analysis of similarity data revealed that a single underlying perceptual map whose dimensions corresponded to shape and texture could explain visual, haptic, and bimodal similarity ratings. However, the relative dimension weights varied according to modality: shape dominated texture when objects were seen, whereas shape and texture were roughly equally important in the haptic and bimodal conditions. Some evidence was found for a multimodal connection between similarity and categorization: the probability of category membership increased with similarity while the probability of a category boundary being placed between two stimuli decreased with similarity. In addition, dimension weights varied according to modality in the same way for both tasks. The study also demonstrates the usefulness of 3D printing technology and MDS techniques in the study of visuohaptic object processing.

Spatial four-alternative forced-choice method is the preferred psychophysical method for naïve observers.

H. R. Blackwell (1952) investigated the influence of different psychophysical methods and procedures on detection thresholds. He found that the temporal two-interval forced-choice method (2-IFC) combined with feedback, blocked constant stimulus presentation with few different stimulus intensities, and highly trained observers resulted in the "best" threshold estimates. This recommendation is in current practice in many psychophysical laboratories and has entered the psychophysicists' "folk wisdom" of how to run proper psychophysical experiments. However, Blackwell's recommendations explicitly require experienced observers, whereas many psychophysical studies, particularly with children or within a clinical setting, are performed with naïve observers. In a series of psychophysical experiments, we find a striking and consistent discrepancy between naïve observers' behavior and that reported for experienced observers by Blackwell: Naïve observers show the "best" threshold estimates for the spatial four-alternative forced-choice method (4-AFC) and the worst for the commonly employed temporal 2-IFC. We repeated our study with a highly experienced psychophysical observer, and he replicated Blackwell's findings exactly, thus suggesting that it is indeed the difference in psychophysical experience that causes the discrepancy between our findings and those of Blackwell. In addition, we explore the efficiency of different methods and show 4-AFC to be more than 3.5 times more efficient than 2-IFC under realistic conditions. While we have found that 4-AFC consistently gives lower thresholds than 2-IFC in detection tasks, we have found the opposite for discrimination tasks. This discrepancy suggests that there are large extrasensory influences on thresholds--sensory memory for IFC methods and spatial attention for spatial forced-choice methods--that are critical but, alas, not part of theoretical approaches to psychophysics such as signal detection theory.

Bayesian inference for psychometric functions.

In psychophysical studies, the psychometric function is used to model the relation between physical stimulus intensity and the observer's ability to detect or discriminate between stimuli of different intensities. In this study, we propose the use of Bayesian inference to extract the information contained in experimental data to estimate the parameters of psychometric functions. Because Bayesian inference cannot be performed analytically, we describe how a Markov chain Monte Carlo method can be used to generate samples from the posterior distribution over parameters. These samples are used to estimate Bayesian confidence intervals and other characteristics of the posterior distribution. In addition, we discuss the parameterization of psychometric functions and the role of prior distributions in the analysis. The proposed approach is exemplified using artificially generated data and in a case study for real experimental data. Furthermore, we compare our approach with traditional methods based on maximum likelihood parameter estimation combined with bootstrap techniques for confidence interval estimation and find the Bayesian approach to be superior.