Fig 1.
Illustration of the personalized Bayesian optimization procedure of theoretical values.
a) The Gaussian process (GP) is fitted to the existing data and models the expected performance along parameter and personalized dimensions. b) The acquisition function identifies the next point to evaluate along the value of the personalized variable relevant to the participant. c) Once the data is collected at this new point the GP is updated and a new point selected. d) This cycle continues until either a new subject is tested, in which case a different value for the personalized variable will be recorded. e) a pre-set stopping criterion is reached, such as the number of subjects to be tested; or until the potential improvement is considered negligible (convergence). In this study, we utilized a pre-set stopping criterion of 50 subjects, after which testing was ceased.
Fig 2.
An overview of the experimental paradigm.
a) An overview of the behavioral paradigm. Subjects (n = 50) watched a fixation point that indicated the start of a trial. After 3000 ms an arithmetic multiplication was shown with two possible answer options on the left and right side with a difference of 10 to keep consistency in task difficulty. Subjects responded by pressing either the left or right button on a response box as quickly and accurately with no time limit present. Lastly, subjects received either ‘correct’ or ‘incorrect’ as feedback to continuously capture attention. b) Subjects first completed a baseline rs-EEG of four minutes, after which 10 practice trials of multi-digit times single-digit multiplications were presented of four minutes. This was followed by the baseline task of 10 minutes, which comprised five blocks of 10 different multiplications. Subjects had a short break (~3 minutes) between baseline and the pBO. Three different tACS frequency-current combinations were proposed by the pBO algorithm after the completion of each sequence of 50 trials of the multiplication task which was approximately 30 minutes in total. Between these tACS combinations, post-block rs-EEGs of four minutes were recorded before the subjects moved on to the next tACS combination. Validation of the blinding of the stimulation and perceived sensations were assessed after completion of a stimulation block. c) An illustration of the tACS electrode montage. Stimulation was applied over the left frontoparietal area (F3 and P3) with one return electrode (Cz). d) A top down topoplot showing both the stimulation electrodes (red and blue) and the EEG electrode placing (turquoise).
Fig 3.
Results of the personalized Bayesian optimization model at several different baseline abilities (n = 49).
The figure shows the predictions from the Gaussian process model for low baseline ability (panel a: 1 standard deviation (SD) below the mean), mean baseline ability (panel b: mean = 0.055), and for high baseline ability (panel c: 1 SD above the mean). The y-axis shows the frequency range of the applied stimulation (0–50 Hz) and the x-axis the current of the stimulation (0–1.6 mA, peak-to-peak). Arithmetic performance is indicated in color based on the normalized drift rates (tACS block/baseline block). Low drift rates are shown in dark blue and high drift rates in yellow. A best-inferred point for arithmetic performance according to a specific frequency-current combination is indicated by a red square in all three panels. Note that this figure is not based on different groups of participants as in moderation analysis, but represents a three dimensional view of the GP’s surrogate surface at three different points for visualization purposes.
Fig 4.
Results of optimizing behavior with personalized Bayesian optimization (pBO) (n = 49).
a) In-depth visualization of the normalized performance according to baseline ability during pBO. Normalized performance was calculated as the drift rate of the performance block divided by the drift rate of the baseline block. Subjects on the lower part of the baseline ability spectrum showed a similar arithmetic performance improvement during tACS compared to subjects on the higher baseline ability spectrum. Note that a normalized performance score of 1 indicates no difference with baseline arithmetic performance when no stimulation was applied. A normalized performance score higher than 1 indicates improved performance as measured with drift rate. The blue shaded area indicates 95% credibility intervals. b) The change in frequency-amplitude tACS parameters proposed by the pBO algorithm based on the individualized baseline ability in arithmetic at the end of optimization. c) Predicted best performance at each iteration (i.e., different blocks), calculated as the best performance predicted by the GP at any parameter combination. Subjects were added sequentially, with three subsequent iterations were assessed for each participant. For example, iterations 148–150, represents blocks 1–3 for the 50th subject. Surrogate uncertainty is shown by the shaded area in pink. Note that during some iterations uncertainty is higher due to new baseline abilities introduced in the pBO and due to outliers. These outliers are retested later which then reduces uncertainty.
Fig 5.
Results of simulating the ability of pBO, BO and random search algorithms on identifying the optima in the Hartmann 3-dimensional surface.
The simulation was run 30 times on each of the six different levels of noise, lines represent the mean performance and shaded areas the standard deviation of 30 repeats. a) Shows the best found value identified by each algorithm at each iteration, demonstrating that the pBO algorithm is able to find higher values more quickly than the BO and random search algorithms. b) Shows the Euclidean distance of the identified optima from the true optima of the Hartmann function (i.e., accuracy of the algorithm). The pBO algorithm is shown to be more accurate than the BO and random search algorithms, except at very high levels of noise, where they are comparable.