A nonlinear updating algorithm captures suboptimal inference in the presence of signal-dependent noise

Abstract

Bayesian models of behavior have advanced the idea that humans combine prior beliefs and sensory observations to minimize uncertainty. How the brain implements Bayes-optimal inference, however, remains poorly understood. Simple behavioral tasks suggest that the brain can flexibly represent and manipulate probability distributions. An alternative view is that brain relies on simple algorithms that can implement Bayes-optimal behavior only when the computational demands are low. To distinguish between these alternatives, we devised a task in which Bayes-optimal performance could not be matched by simple algorithms. We asked subjects to estimate and reproduce a time interval by combining prior information with one or two sequential measurements. In the domain of time, measurement noise increases with duration. This property makes the integration of multiple measurements beyond the reach of simple algorithms. We found that subjects were able to update their estimates using the second measurement but their performance was suboptimal, suggesting that they were unable to update full probability distributions. Instead, subjects' behavior was consistent with an algorithm that predicts upcoming sensory signals, and applies a nonlinear function to errors in prediction to update estimates. These results indicate that inference strategies humans deploy may deviate from Bayes-optimal integration when the computational demands are high.

Metamers of Bayesian computation

“…For the original pair, participants' t p increased with t s , and exhibited systematic biases toward the mean of the prior (Figure 2d, red). Similar to numerous previous studies 40,41,[43][44][45][46] , this behavior was consistent with predictions of the ideal observer model ( Supplementary Figure 1).…”

A neural circuit model for human sensorimotor timing

“…Second, the interaction of α with the level of noise caused the model to occasionally skip a beat ( Supplementary Fig. 6), which occurs occasionally in humans performing similar tasks 31 .…”

Neural structure of a sensory decoder for motor control

“…Thus, our conclusion, that the computation of sensory-motor gain is subject to an independent source of noise that arises from gain control, does not contradict previous data, only previous conclusions. Several lines of evidence argue against the logical idea that integration of the additional information associated with increasing target size should decrease the effective Weber fraction in behavior 72 , and therefore explain our behavioral results. First, due to surround suppression 40 , the average MT neuron exhibits decreased precision as target size increases beyond the classical receptive field 41 , not the increased precision that would be required to explain our data.…”

“…Gain adjustment is a critical feature of optimal estimation by Bayesian integration, where the weight given to a sensory cue depends on the relative reliability of each potential source of information. Reliability-based weighting strategies operate when subjects integrate sensory cues 72,[75][76][77][78][79] or combine measurements with prior knowledge based on past experience 29,33,80,81 . Therefore, neural mechanisms must exist for appropriately applying sensory gain during estimation.…”

“…The first two terms of the equation cause the variance of motor output to depend on the derivative of f , d f /ds, in the vicinity of s. The last term of the equation causes the output variance to depend on the mean gain when gain noise is non-zero. Panel B illustrates the effect of a nonlinear transformation, f , based on the Bayesian least squares (BLS) estimator for signal-dependent sensory noise (w = 0.1) 9,72,88 . In the vicinity of s + η s = 10, df/ds is near 1.…”