Fig 1.
Examples of three trials from the [42] dataset.
Each trial is from the same condition (feature) but with a different participant. We can clearly see that there are some large individual differences. The first two participants appear to prioritise a horizontal scanning strategy, although the second implements this as two long runs (one colour, and then the next). The third participant de-emphasies a directional strategy and instead focuses on collecting nearby items of the same colour whenever possible.
Fig 2.
FoMo v1.0 inter-item selection results for the [42] dataset.
Histograms comparing the absolute directions (). Green indicates overlap of overlap of the two distributions. We can see that while the model favours the cardinal directions - presumably due to a proximity bias combined with grid-like stimuli - it fails to capture the strong left to right peak we see in the human data.
Fig 3.
The original [7] model parameters.
From left to right: stick/switch rate, class weights, proximity tuning, and direction tuning.
Table 1.
Overview of notation used to define FoMo. Concepts are split into four components: stimulus definition; derived features; free parameters; and likelihood calculation.
Fig 4.
(top): Illustratifiguon of four von Mises distributions (top) that can be summed to give (middle) a multi-model distribution that is able to flexibly weight horizontal and vertical directions.
(bottom): How these weights could encode different strategies.
Fig 5.
Illustration of three different values.
We used a value of in the work presented here, which strikes a balance between minimising the overlap between our four components without assigning angles around the oblique directions all to 0.
Table 2.
Table with a full overview of the different model versions, detailing which model components are included in each version.
Table 3.
Table overviewing the data used in this paper. The ‘trials’ column indicates the number of trials in each condition, and the ‘target items’ column indicates how many targets the participant had to collect (all were exhaustive search tasks, apart from [73]). The ‘conditions’ column indicates the comparisons that were looked at in our analysis, and do not necessarily reflect the full range of conditions that were tested in the original papers.
Table 4.
Mean test set accuracy for each dataset. The difference in the hance baselines reflects the fact that some experiments involved different numbers of target items. The prior model is based on FoMo v1.0. Note: these overall accuracy scores are relatively insensitive to the differences between models, as accuracy rates vary within trials, between conditions and from person to person, as illustrated in Fig 6.
Fig 6.
(left): Comparison in accuracy between FoMo v1.0 and 1.3 for the [42] and [74] data.
Each point represents an individual participant, and the crosshairs provide the 95% Highest Posterior Density Interval (HPDI). Colours indicate the improvement in accuracy between models. (right): 95% HPDI for accuracy throughout a trial for FoMo v1.3. The dotted line indicates chance performance.
Table 5.
Comparison between FoMo and the classifier developed by [55] on the [37] dataset. We report their intial and final (post feature pruning and oversampling) modelling results, and compare them to FoMo v1.0 and v1.3. The difference coloumn compares performance between v1.3 and the final classifier from [55].
Fig 7.
Posterior densities for FoMo v1.3, applied to the [74] dataset.
(top): Posterior estimates for the four core FoMo parameters. (bottom): Illustration of the 4 direction weights, for each of our two conditions. The shaded bar indicates the 97%HPDI, with the dark inner region giving the 53% interval. We can see that in both conitions there is a preference for horizontal directions, and stronger directional effects in the feature condition.
Fig 8.
Comparison of simulated paths from FoMo v1.0 and v1.3 with observed data from a human participant from the [74] dataset.
The items are illustrated as red triangle and pale blue circles, and the white line illustrates the order in which the human particpant selected the items. The purple lines indicate the weightings that the model assigns to each possible next target (thicker means more weight).
Fig 9.
Comparison of predicted and observed path statistics (FoMo v1.3) over a range of datasets.
Each dot represents an individual participant in a condition, the dotted line indicates the y = x identity line, while the solid black lines give the best fit linear regression. Note that the poorer performance for the [73] is almost certainly due (at least in part) to our use of an exhaustive foraging model to account for an inexhastive paradigm.
Fig 10.
The items are illustrated as red triangle and pale blue circles.
(left) The while line illustrates the order in which the human particpant selected the items in a trial from the Hughes et al dataset [74]. (right) Six example predictions, shown in purple, of predictions from FoMo v1.3. The three plots in the top row represent simulations in which we have constrained the initial item selection to match the item selected by the human participant on this trial. The three plots on the bottom are simulations in which the initial item selection is unconstrained.
Fig 11.
(top): estimate of scaled absolute error averaged across first selection variants and statistics, for each dataset and model version.
(bottom): estimate of scaled absolute error averaged across datasets for model v1.3, for fixed and free first selection and for each statistic.