Suboptimal Criterion Learning in Static and Dynamic Environments

Humans often make decisions based on uncertain sensory information. Signal detection theory (SDT) describes detection and discrimination decisions as a comparison of stimulus "strength" to a fixed decision criterion. However, recent research suggests that current responses depend on the recent history of stimuli and previous responses, suggesting that the decision criterion is updated trial-by-trial. The mechanisms underpinning criterion setting remain unknown. Here, we examine how observers learn to set a decision criterion in an orientation-discrimination task under both static and dynamic conditions. To investigate mechanisms underlying trial-by-trial criterion placement, we introduce a novel task in which participants explicitly set the criterion, and compare it to a more traditional discrimination task, allowing us to model this explicit indication of criterion dynamics. In each task, stimuli were ellipses with principal orientations drawn from two categories: Gaussian distributions with different means and equal variance. In the covert-criterion task, observers categorized a displayed ellipse. In the overt-criterion task, observers adjusted the orientation of a line that served as the discrimination criterion for a subsequently presented ellipse. We compared performance to the ideal Bayesian learner and several suboptimal models that varied in both computational and memory demands. Under static and dynamic conditions, we found that, in both tasks, observers used suboptimal learning rules. In most conditions, a model in which the recent history of past samples determines a belief about category means fit the data best for most observers and on average. Our results reveal dynamic adjustment of discrimination criterion, even after prolonged training, and indicate how decision criteria are updated over time

Dansk mode 1997-2007

<p>Individual DIC scores for the overt-criterion task under dynamic conditions (Expt. 2).</p

Overt-criterion data for two observers in Expt. 2.

<p><b>A</b>) The mean positions of the category <i>A</i> (solid line) and <i>B</i> (dashed line) across the overt-criterion block. <b>B</b>) Criterion placement data across the block (data points) compared to the omniscient criterion placement (solid gray line). <b>C</b>) Cross-correlation between the omniscient criterion and the observer’s criterion placement. The lag estimate is indicated by the arrow. Estimated lags for all observers ranged from 1 to 4.</p

Overt-criterion data for a representative observer in Expt. 1.

<p>Data points: Criterion placement on each trial. Lines, The mean orientation of the category <i>A</i> and <i>B</i> distributions (solid and dashed, respectively) and the optimal observer’s criterion (solid gray).</p

Model parameters for the covert-criterion task.

<p>Model parameters for the covert-criterion task.</p

Model comparison results for the covert- (dark gray) and overt-criterion (light gray) tasks in Expt. 1.

<p><b>A</b>) The bar graph depicts the relative DIC scores (i.e., DIC difference between the ideal Bayesian model and the suboptimal models) averaged across observers ±SE. Larger values indicate a better fit. <b>B</b>) To summarize the results from the group level analysis we computed exceedance probabilities for each model in each task. A model’s exceedance probability tells us how much more likely that model is compared to the alternatives, given the group data.</p

Discrimination and matching data.

<p><b>A</b>) A psychometric function for a representative observer in the orientation-discrimination task. Data points: raw data. Circle area is proportional to the number of trials completed at the corresponding orientation difference (Δ<i>θ</i>). A cumulative normal distribution was fit to the data (solid black line). The gray curves represent a 95% confidence interval on the slope parameter. <b>B</b>) One observer’s raw data from the orientation-matching task. The orientation of the matched line is shown as a function of the orientation of the displayed line. The identity line indicates a perfect match.</p

Lagged regression for the static condition (Expt. 1).

<p><b>A</b>) Covert-criterion task: Results of a logistic regression predicting the binary decision of each trial as a combination of the orientations of the current ellipse and the previous nine ellipses in each category. The solid and dashed lines represent the group average beta weights ±SE for the ellipses belonging to category <i>A</i> and category <i>B</i>, respectively. <b>B</b>) Overt-criterion task: Results of a linear regression predicting the criterion placement on each trial as a combination of the orientations of the previous nine ellipses in each category. Again, the solid and dashed lines represent the group average beta weights ±SE for the ellipses belonging to category <i>A</i> and category <i>B</i>, respectively.</p