Ulrik R. Beierholm

Causal Inference in Multisensory Perception

Perceptual events derive their significance to an animal from their meaning about the world, that is from the information they carry about their causes. The brain should thus be able to efficiently infer the causes underlying our sensory events. Here we use multisensory cue combination to study causal inference in perception. We formulate an ideal-observer model that infers whether two sensory cues originate from the same location and that also estimates their location(s). This model accurately predicts the nonlinear integration of cues by human subjects in two auditory-visual localization tasks. The results show that indeed humans can efficiently infer the causal structure as well as the location of causes. By combining insights from the study of causal inference with the ideal-observer approach to sensory cue combination, we show that the capacity to infer causal structure is not limited to conscious, high-level cognition; it is also performed continually and effortlessly in perception.

Causal inference in perception

Until recently, the question of how the brain performs causal inference has been studied primarily in the context of cognitive reasoning. However, this problem is at least equally crucial in perceptual processing. At any given moment, the perceptual system receives multiple sensory signals within and across modalities and, for example, has to determine the source of each of these signals. Recently, a growing number of studies from various fields of cognitive science have started to address this question and have converged to very similar computational models. Therefore, it seems that a common computational strategy, which is highly consistent with a normative model of causal inference, is exploited by the perceptual system in a variety of domains.

Human trimodal perception follows optimal statistical inference

Our nervous system typically processes signals from multiple sensory modalities at any given moment and is therefore posed with two important problems: which of the signals are caused by a common event, and how to combine those signals. We investigated human perception in the presence of auditory, visual, and tactile stimulation in a numerosity judgment task. Observers were presented with stimuli in one, two, or three modalities simultaneously and were asked to report their percepts in each modality. The degree of congruency between the modalities varied across trials. For example, a single flash was paired in some trials with two beeps and two taps. Cross-modal illusions were observed in most conditions in which there was incongruence among the two or three stimuli, revealing robust interactions among the three modalities in all directions. The observers bimodal and trimodal percepts were remarkably consistent with a Bayes-optimal strategy of combining the evidence in each modality with the prior probability of the events. These findings provide evidence that the combination of sensory information among three modalities follows optimal statistical inference for the entire spectrum of conditions.

Probability Matching as a Computational Strategy Used in Perception

The question of which strategy is employed in human decision making has been studied extensively in the context of cognitive tasks; however, this question has not been investigated systematically in the context of perceptual tasks. The goal of this study was to gain insight into the decision-making strategy used by human observers in a low-level perceptual task. Data from more than 100 individuals who participated in an auditory-visual spatial localization task was evaluated to examine which of three plausible strategies could account for each observers behavior the best. This task is very suitable for exploring this question because it involves an implicit inference about whether the auditory and visual stimuli were caused by the same object or independent objects, and provides different strategies of how using the inference about causes can lead to distinctly different spatial estimates and response patterns. For example, employing the commonly used cost function of minimizing the mean squared error of spatial estimates would result in a weighted averaging of estimates corresponding to different causal structures. A strategy that would minimize the error in the inferred causal structure would result in the selection of the most likely causal structure and sticking with it in the subsequent inference of location—“model selection.” A third strategy is one that selects a causal structure in proportion to its probability, thus attempting to match the probability of the inferred causal structure. This type of probability matching strategy has been reported to be used by participants predominantly in cognitive tasks. Comparing these three strategies, the behavior of the vast majority of observers in this perceptual task was most consistent with probability matching. While this appears to be a suboptimal strategy and hence a surprising choice for the perceptual system to adopt, we discuss potential advantages of such a strategy for perception.

Dopamine Modulates Reward-Related Vigor

Subjects routinely control the vigor with which they emit motoric responses. However, the bulk of formal treatments of decision-making ignores this dimension of choice. A recent theoretical study suggested that action vigor should be influenced by experienced average reward rate and that this rate is encoded by tonic dopamine in the brain. We previously examined how average reward rate modulates vigor as exemplified by response times and found a measure of agreement with the first suggestion. In the current study, we examined the second suggestion, namely the potential influence of dopamine signaling on vigor. Ninety healthy subjects participated in a double-blind experiment in which they received one of the following: placebo, L-DOPA (which increases dopamine levels in the brain), or citalopram (which has a selective, if complex, effect on serotonin levels). Subjects performed multiple trials of a rewarded odd-ball discrimination task in which we varied the potential reward over time in order to exercise the putative link between vigor and average reward rate. Replicating our previous findings, we found that a significant fraction of the variance in subjects’ responses could be explained by our experimentally manipulated changes in average reward rate. Crucially, this relationship was significantly stronger under L-Dopa than under Placebo, suggesting that the impact of average reward levels on action vigor is indeed subject to a dopaminergic influence.

Bayesian priors are encoded independently from likelihoods in human multisensory perception

It has been shown that human combination of crossmodal information is highly consistent with an optimal Bayesian model performing causal inference. These findings have shed light on the computational principles governing crossmodal integration/segregation. Intuitively, in a Bayesian framework priors represent a priori information about the environment, i.e., information available prior to encountering the given stimuli, and are thus not dependent on the current stimuli. While this interpretation is considered as a defining characteristic of Bayesian computation by many, the Bayes rule per se does not require that priors remain constant despite significant changes in the stimulus, and therefore, the demonstration of Bayes-optimality of a task does not imply the invariance of priors to varying likelihoods. This issue has not been addressed before, but here we empirically investigated the independence of the priors from the likelihoods by strongly manipulating the presumed likelihoods (by using two drastically different sets of stimuli) and examining whether the estimated priors change or remain the same. The results suggest that the estimated prior probabilities are indeed independent of the immediate input and hence, likelihood.

Vigor in the face of fluctuating rates of reward: An experimental examination

Two fundamental questions underlie the expression of behavior, namely what to do and how vigorously to do it. The former is the topic of an overwhelming wealth of theoretical and empirical work particularly in the fields of reinforcement learning and decision-making, with various forms of affective prediction error playing key roles. Although vigor concerns motivation, and so is the subject of many empirical studies in diverse fields, it has suffered a dearth of computational models. Recently, Niv et al. [Niv, Y., Daw, N. D., Joel, D., & Dayan, P. Tonic dopamine: Opportunity costs and the control of response vigor. Psychopharmacology (Berlin), 191, 507–520, 2007] suggested that vigor should be controlled by the opportunity cost of time, which is itself determined by the average rate of reward. This coupling of reward rate and vigor can be shown to be optimal under the theory of average return reinforcement learning for a particular class of tasks but may also be a more general, perhaps hard-wired, characteristic of the architecture of control. We, therefore, tested the hypothesis that healthy human participants would adjust their RTs on the basis of the average rate of reward. We measured RTs in an odd-ball discrimination task for rewards whose magnitudes varied slowly but systematically. Linear regression on the subjects individual RTs using the time varying average rate of reward as the regressor of interest, and including nuisance regressors such as the immediate reward in a round and in the preceding round, showed that a significant fraction of the variance in subjects RTs could indeed be explained by the rate of experienced reward. This validates one of the key proposals associated with the model, illuminating an apparently mandatory form of coupling that may involve tonic levels of dopamine.

The human prefrontal cortex mediates integration of potential causes behind observed outcomes

Prefrontal cortex has long been implicated in tasks involving higher order inference in which decisions must be rendered, not only about which stimulus is currently rewarded, but also which stimulus dimensions are currently relevant. However, the precise computational mechanisms used to solve such tasks have remained unclear. We scanned human participants with functional MRI, while they performed a hierarchical intradimensional/extradimensional shift task to investigate what strategy subjects use while solving higher order decision problems. By using a computational model-based analysis, we found behavioral and neural evidence that humans solve such problems not by occasionally shifting focus from one to the other dimension, but by considering multiple explanations simultaneously. Activity in human prefrontal cortex was better accounted for by a model that integrates over all available evidences than by a model in which attention is selectively gated. Importantly, our model provides an explanation for how the brain determines integration weights, according to which it could distribute its attention. Our results demonstrate that, at the point of choice, the human brain and the prefrontal cortex in particular are capable of a weighted integration of information across multiple evidences.

Separate encoding of model-based and model-free valuations in the human brain

Behavioral studies have long shown that humans solve problems in two ways, one intuitive and fast (System 1, model-free), and the other reflective and slow (System 2, model-based). The neurobiological basis of dual process problem solving remains unknown due to challenges of separating activation in concurrent systems. We present a novel neuroeconomic task that predicts distinct subjective valuation and updating signals corresponding to these two systems. We found two concurrent value signals in human prefrontal cortex: a System 1 model-free reinforcement signal and a System 2 model-based Bayesian signal. We also found a System 1 updating signal in striatal areas and a System 2 updating signal in lateral prefrontal cortex. Further, signals in prefrontal cortex preceded choices that are optimal according to either updating principle, while signals in anterior cingulate cortex and globus pallidus preceded deviations from optimal choice for reinforcement learning. These deviations tended to occur when uncertainty regarding optimal values was highest, suggesting that disagreement between dual systems is mediated by uncertainty rather than conflict, confirming recent theoretical proposals.

Pavlovian-Instrumental Interaction in ‘Observing Behavior’

Subjects typically choose to be presented with stimuli that predict the existence of future reinforcements. This so-called ‘observing behavior’ is evident in many species under various experimental conditions, including if the choice is expensive, or if there is nothing that subjects can do to improve their lot with the information gained. A recent study showed that the activities of putative midbrain dopamine neurons reflect this preference for observation in a way that appears to challenge the common prediction-error interpretation of these neurons. In this paper, we provide an alternative account according to which observing behavior arises from a small, possibly Pavlovian, bias associated with the operation of working memory.