Representations of uncertainty: where art thou?

Abstract

Perception is often described as probabilistic inference requiring an internal representation of uncertainty. However, it is unknown whether uncertainty is represented in a task-dependent manner, solely at the level of decisions, or in a fully Bayesian manner, across the entire perceptual pathway. To address this question, we first codify and evaluate the possible strategies the brain might use to represent uncertainty, and highlight the normative advantages of fully Bayesian representations. In such representations, uncertainty information is explicitly represented at all stages of processing, including early sensory areas, allowing for flexible and efficient computations in a wide variety of situations. Next, we critically review neural and behavioral evidence about the representation of uncertainty in the brain agreeing with fully Bayesian representations. We argue that sufficient behavioral evidence for fully Bayesian representations is lacking and suggest experimental approaches for demonstrating the existence of multivariate posterior distributions along the perceptual pathway.

Figure 1

Taxonomy of generative and recognition models in decision making. Blue and green backgrounds correspond to the two components of Bayesian decision theory: the observation and decision processes of the generative model (orange), and the perception and action selection modules of the recognition model (purple), respectively. Note that ‘perception’ here is broadly construed to include all cognitive processes (e.g. sensory perception or memory) that have access to information (‘observations’) that is relevant for the decision making task. Rectangles indicate observed variables ($x$), circles indicate latent variables (including the decision variable, $z$) which are part of the generative model and are probabilistically computed in a recognition model, diamonds indicate non-probabilistically computed internal variables of a recognition models, hexagons indicate variables specific to the decision process: the action ($a$) and the utility obtained ($u$). The utility function ($\mathcal{U}$) is shown without a bounding box to indicate that it is a parameter that is constant across trials or time steps, while other quantities change over time or trials. Left: generative models. All generative models describe how $z$ is related to $x$, and how it (exclusively) determines the $u$ obtained for a given $a$ (as parameterized by $\mathcal{U}$). Simple generative models only have a single latent variable, $z$. Complex generative models have multiple latent variables beside $z$. Right: recognition models. All recognition models compute action $a$ from observations $x$. Probabilistic recognition models compute a posterior over $z$ given $x$ (Equation 1), which they then combine with $\mathcal{U}$ to compute $a$ (Equations 2a and 2b). The non-probabilistic recognition model computes $a$ directly from $x$, without computing a posterior over $z$, and without explicitly representing $\mathcal{U}$. Probabilistic recognition models are further subdivided based on what other variables are computed probabilistically while computing the posterior over $z$: simple models do not have any other variables, complex models do, with fully Bayesian, hybrid, and task-dependent models probabilistically computing all variables, a subset of them, or none of them, respectively.