Humans can evaluate the accuracy of their decisions by providing confidence judgements. Traditional cognitive models have tried to capture the mechanisms underlying this process but remain mostly limited to two-choice tasks with simple stimuli. How confidence is given for naturalistic stimuli with multiple choice alternatives is not well understood. We recently developed a convolutional neural network (CNN) model - RTNet - that exhibits several important signatures of human decision making and outperforms existing alternatives in predicting human responses. Here, we use RTNet's image computability to test seven different confidence strategies on a task involving digit discrimination with eight alternatives (N = 60). Specifically, we compared confidence strategies that consider the entire evidence distribution across choices against strategies that only consider a specific subset of the available evidence. We also compared strategies based on whether they compute confidence from posterior probabilities or from raw evidence. A model which derives confidence from the difference in raw evidence between the top-two choices (Top2Diff model) consistently provided the best quantitative and qualitative fits to the data and the best predictions of human confidence. These results support the notion that human confidence is based on a specific subset of available evidence, challenge prominent theories such as the Bayesian confidence hypothesis and the positive evidence heuristic, and establish CNNs as promising models for inferring the mechanisms underlying human confidence in naturalistic settings.

Prior research has shown that manipulating stimulus energy by changing both stimulus contrast and variability results in confidence-accuracy dissociations in humans. Specifically, even when performance is matched, higher stimulus energy leads to higher confidence. The most common explanation for this effect, derived from cognitive modeling, is the positive evidence heuristic where confidence neglects evidence that disconfirms the choice. However, an alternative explanation is the signal-and-variance-increase hypothesis, according to which these dissociations arise from changes in the separation and variance of perceptual representations. Because artificial neural networks lack built-in confidence heuristics, they can serve as a test for the necessity of confidence heuristics in explaining confidence-accuracy dissociations. Therefore, we tested whether confidence-accuracy dissociations induced by stimulus energy manipulations emerge naturally in convolutional neural networks (CNNs). We found that, across three different energy manipulations, CNNs produced confidence-accuracy dissociations similar to those found in humans. This effect was present for a range of CNN architectures from shallow 4-layer networks to very deep ones, such as VGG-19 and ResNet-50 pretrained on ImageNet. Further, we traced back the reason for the confidence-accuracy dissociations in all CNNs to the same signal-and-variance increase that has been proposed for humans: higher stimulus energy increased the separation and variance of evidence distributions in the CNNs' output layer leading to higher confidence even for matched accuracy. These findings cast doubt on the necessity of the positive evidence heuristic to explain human confidence and establish CNNs as promising models for testing cognitive theories of human behavior.

Sequential data with serial correlation and an unknown, unstructured, and dynamic background is ubiquitous in neuroscience, psychology, and econometrics. Inferring serial correlation for such data is a fundamental challenge in statistics. We propose a Total Variation (TV) constrained least square estimator coupled with hypothesis tests to infer the serial correlation in the presence of unknown and unstructured dynamic background. The TV constraint on the dynamic background encourages a piecewise constant structure, which can approximate a wide range of dynamic backgrounds. The tuning parameter is selected via the Ljung-Box test to control the bias-variance trade-off. We establish a non-asymptotic upper bound for the estimation error through variational inequalities. We also derive a lower error bound via Fano’s method and show the proposed method is near-optimal. Numerical simulation and a real study in psychology demonstrate the excellent performance of our proposed method compared with the state-of-the-art.