Confidence of probabilistic predictions modulates the cortical response to pain

Significance The functional significance of EEG responses to pain has long been debated because of their dramatic variability. This study indicates that such variability can be partly related to the confidence of probabilistic predictions emerging from sequences of pain inputs. The confidence of pain predictions is negatively associated with the cortical EEG responses to pain. This indicates that the brain relies less on sensory inputs when confidence is higher and shows us that confidence-weighted statistical learning modulates the cortical response to pain.


Participants and task
Thrity-six participants were recruited for this study. As described in the manuscript, 5 subjects were excluded from the analyses because 2 of them made 1-2 errors in the pre-or postcheck sessions (most likely due to distraction), 2 of them fell asleep during the task and the task had different parameters for 1 pilot participant. Table S1 indicates, for all participants, the temperatures employed throughout the experiment (stimuli of intensities I1 and I2), the outcomes of the check stimulus discrimination sessions and the exclusion reasons.
During the experiments, all participants received 10 sequences of 100 stimuli from two intensities I1 (cool) and I2 (warm). Each sequence was generated according to a Markovian process. As illustrated in Fig. S1, similar numbers of stimuli from both intensities were delivered to all participants (a), and they all predicted similar numbers of transitions from both intensities (b).

EEG modulation using alternative inference models
In order to identify how inferring the sequence statistics modulates the EEG responses, these signals can be regressed on the confidence and prediction error (PE) obtained trial-by-trial from a learning model. In the manuscript, this is done using the model which best approximates the participants' probability estimates, i.e. a Bayesian model learning the sequence TPs with a time constant of 8 stimuli (Figs. 5 and 6). This analysis reveals a strong negative association between the vertex potential (VP) and confidence. Hereunder, we show that these modulations are preserved if other plausible models are employed to derive the confidence and PE. First, if the raw confidence is used as regressor instead of the residual confidence (as defined in (14)), the main results remain unchanged (Fig. S2).
Likewise, Fig. S3 illustrates similar findings if the 'preferred' learning model of each participant (based on the fitting of the behavioral reports) is considered to obtain the regressors. Because only a minority of participants preferred to learn the IF or AF rather than the TPs, it does not significantly affect the outcomes shown in Figs. 5 and 6.
Finally, if the second model which best approximates the overall participants' behavior is considered, i.e. a Bayesian model learning the sequence IF with a time constant of 8 stimuli, Fig. S4 shows that the correlation between the VP and confidence is preserved (b), and that the PE modulates late EEG responses more strongly (c).

Bayesian model updates
In Bayesian models, a sequence transition probability (TP) is continuously estimated through the computation of the posterior distribution of this TP given the past stimuli y1:n (see equations [1]- [2]). Before receiving stimulus yn+1, a prediction about the forthcoming intensity is hence available and corresponds to the mean of the posterior distribution given y1:n (see [6]). Examples of posterior distributions and their mean before (gray) and after (black) receiving a stimulus within a sequence are shown in

Parameter and model recovery analyses
In order to assess the robustness of our model and parameter selection procedures, we conducted parameter and model recovery analyses. The idea is to generate data using the true models and to determine to which extent the selection procedures can recover the true models and their parameters (2, 3). Here, with the Bayesian models (learning AF, IF or TPs), the parameters are the integration time constant. Because the model predictions (i.e. probability estimates) are deterministic for a given sequence, data were simulated by sampling probability estimates from the Beta distribution estimated at each time step (see [3]-[4]- [5]). Results of the parameter and model recovery analyses can be found in Fig. S6. For all three models, Fig. S6a shows the recovered integration time constants (y-axis) for 30 simulations using all N = 31 parameters fitted to the participants' reports (true parameters, x-axis). Then, Fig. S6b illustrates that the three models themselves can be reliably re-identified when fitting noisy data. ω) are identifiable, we simulated data using each model with different parameters and fitted the models to these synthetic data like we did it to the behavioral reports. Since the model predictions (i.e. probability estimates) are deterministic for a given sequence, data were simulated by sampling probability estimates from the Beta distribution estimated at each time step (see Methods). For each model (learning AF, IF or TPs), we consider all the optimal time constants that were fitted to the individual behavioral data (2). Using each time constant and model, 30 synthetic data sets were built based on the same number of sequences and probability estimates as for the real participants (10 sequences were generated with the TPs indicated in Fig. 1d and probability estimates were sampled every 15±3 stimuli).

Gamma-band oscillations (GBOs) induced by the stimuli
Using the epochs before applying the low-pass filter described in the Materials and Methods section of the article, we checked whether the hot stimuli induced more GBOs than the cool ones, a typical EEG correlate of pain perception (4,5).
To this aim, we first computed short-time Fourier transforms (STFTs) of the amplitudes of each trial for each participant at FCz, from 40 to 140 Hz in steps of 2 Hz and from −1 to 1.5 seconds after stimulus onset. We considered 100ms width Gaussian windows for the STFTs to reach a reasonable time resolution for GBOs. We then averaged the single-trial STFTs per participant and computed the percentage of stimulus-induced changes of amplitude as (5,6): where S(t, f ) is the signal amplitude at time t and frequency f , R(f ) is the average baseline amplitude at frequency f , obtained by averaging the amplitude in the [−0.5, −0.1] seconds time window, and ER is expressed in %.
Although we could not reliably detect GBOs in all participants (as it is commonly the case), the hot stimuli induced significantly more GBOs than the cool ones (in the interval [60, 90] Hz -[0.15, 1.5] s for I2 vs. I1: mean difference of 0.81%, t30 = 2.46, p = 0.02, Cohen's d = 0.44). The grand averaged STFTs are displayed in Fig. S7. These maps suggest that the larger GBOs in response to warm I2 stimuli mostly occurred in late time windows. Following previous works (5,7,8) suggesting that pain-induced GBOs can occur concomitantly with the VPs, we also compared the amplitudes of GBOs induced by the cool and hot stimuli along the time intervals defined by their respective grand mean N2 waves, i.e. width Gaussian windows were used.

EEG modulation by the inference over all electrodes
In the manuscript, we reported how confidence and BPE modulate the VP (by focusing on central electrodes). Here, we also assessed the effects of these inferential parameters on the EEG responses from all the electrodes, using cluster-based significance tests (by shuffling the regressors across trials). Results are displayed in Figs. S8 and S9 for the Bayesian TP and IF models respectively, with one sub-plot for each significant cluster found, ordered in decreasing order of cluster-level significance. These analyses validate our main findings: using both models, the largest significant clusters are concentrated around (1) the N2-P2 components for confidence and (2)  a, t-statistics for the regression coefficients associated with the confidence, I1 stimuli. b, t-statistics for the regression coefficients associated with the confidence, I2 stimuli. c, t-statistics for the regression coefficients associated with the prediction error, I1 stimuli. d, t-statistics for the regression coefficients associated with the prediction error, I2 stimuli.