dataesr/scientific-paragraphs-categorization huggingface dataset:
Implementation for Hierarchical (Non-)Linear Regression Modelling So far, we have looked restrictively at the case of the MLE for the DDM with only one subject, with no experimental conditions. However, in a broader setting, we would be more interested in retrieving the full posterior probability at each of the levels of the dataset (i. e. trials, subjects and population) for each condition. The first step is to specify the model at the subject level, before putting a prior on the prior of the local variables (i. e. a hyperprior). We will assume in the following that the local parameters z t,s have a Gaussian prior with subject-specific, diagonal covariance matrix σ s and trial-and subject-specific mean µ t,s = ζ(x t,s ; ω s ). ζ is a (non-)linear mapping of x t,s (i. e. the vector of the trials-subject regressors) with latent subject-specific parameters (or weights) ω s , that allows the prior to change according to condition and subject.
Simulation analysis We simulated a dataset of 64 hypothetical subjects performing a numerical Stroop task (51) of 500 trials. We considered two difficulty conditions: conflict (when the value of the numbers displayed anticorrelated with their size). Instructed response was either left or right. We therefore considered a 2x2 table of regressors. No deadline was imposed, as we did not restrain the RT to a certain range. The trial-by-trial DDM parameters were generated as follows: overall, the threshold tended to decrease with a low, fixed rate. When an error was made, this distance increased slightly, implementing post-error slowing  (52). The drift was updated from trial to trial as a function of 1) the instructed response (we considered that the drift always pointed towards the correct response), 2) the difficulty (its absolute value was higher for simple than difficult trials) and 3) the absolute value of the previous drift.
Indeed, the absolute value of the drift followed a random walk with a 1 A version of the code used for this example is available online here positive drift that reflected a training effect. The start point reflected some sort of Gambler Fallacy (53; 54; 55; 56): if the instruction was left at the trial t, subject started with the prior belief that the next instruction (at t + 1) was going to be right. This bias increased as the number of repetitions of the same instruction got higher: the rightward bias in the previous example was higher at t + 4 than at t + 1 if all the trials between t and t + 3 had the left instruction. The non-decision time was generated with a Gaussian Process with a squared exponential kernel. Simulation of the RT and choices was done according to  (10). We fitted the HLRM and the VRIN to this dataset.
As a benchmark, we also fitted this dataset to a model identical to the HLRM using a No-U-Turn Hamiltonian Monte-Carlo method  (57)  with Stan  (58). These results are reported in Appendix C. We expected that the VRIN would outperform the HLRM in term of parameter prediction and model evidence. Both optimization procedures completed in the allotted time, and reached a stable ELBO before the end of the optimization. A simple Bayesian Model Selection (BMS, (  59 )) performed on the basis of ELBO of the two models showed that the VRIN model was more likely for 62. 77 of the 64 subjects, with exceedance probability ϕ close to 1. Figure  7  and Figure  8  show the posterior probabilities of z t,s (Figure  7 ) and µ t,s = ζ(. ) (Figure  8 ) for a random subject for each of the two models. In general, the VRIN model was able to recover a more precise value for the parameters and, most importantly, to recover their individual trial-specific values.
Example from real data: Random Dot Motion Task To validate the use of the VRIN to real datasets, and show that it was able to extract relevant features of behaviour, we fitted the HLRM and the VRIN to a dataset issued from a Random Dot Motion Task where subjects had to discriminate leftward and rightward motion of the dots on the screen (60). The dots were all of the same colour but changed across trials (3 equiprobable colours). Two of these three colours predicted the motion of the dots with 80% accuracy (i. e. colour 1 = leftward motion in 80% of the trials, colour 2 = rightward motion in 80% of the trials, colour 3 = 50% of rightward motion). Hence, a table of 3x2 regressors was used in both models. In this task, subjects received immediate feedback about their performance. Each block lasted for 60 trials, and each subject (N=20) performed a total of eight blocks.
The ELBO estimate was, however, stable at this point. Another difference between this dataset and the previous example is that, here, we had to use a uniform approximate posterior over t 0 to avoid the posterior expected value of t 0t,s tending to the value of RT t,s (see Appendix A). When performing a BMS between the two, we could see that the VRIN outperformed the HLRM (number of subject where VRIN was preferred: 12. 43, ϕ = 0. 85). The first interesting observation we can make about the fit of the VRIN is that, unlike the HLRM, it was able to account for the post-error slowing phenomenon. Analyzing the trial-to-trial changes in the posterior mean of the threshold (µ a t,s = ζ(z <t,s , x ≤t,s , s, σ s ; ψ)), we observed that the value of µ a t+1,s -µ a t,s was significantly lower after a correct response than after an error: after an accurate trial, threshold decreased slightly but significantly (average = -0.
009, 95% CI =[-0. 012, -007]), whereas after error, this difference was positive (average = 0. 042 95% CI =[0. 036, 0. 048]). The difference between the two was also significant (z = -18. 3608, p < 1e -74) (Figure  10 ). When applied on the fitted HLRM parameters, this analysis showed a similar pattern, although of much lower magnitude (average effect of errors: 0. 001, CI = [0. 0005, 0. 002], effect for accurate trials not significant, difference magnitude z = -3. 99539, p < 1e -4). The fact that this effect emerged (even slightly) with the HLRM fit should not surprise the reader: errors were more likely during some trial categories (color and motion direction) than others, and the result was that the regression weights of the HLRM encoded a larger mean threshold value for these trials. To show this, we executed the same test on our dataset, while shuffling the trials for each subject, and then subtracting the average per-category value.
The larger overlap observed with HLRM indicates a lower capacity of this model to discriminate between errors and correct trials. A similar pattern was found for the start-point, where the value of E q [µ w t,s ] tended to anticorrelate with the motion at the previous trial for the VRIN model only (Figure  11 ), reflecting some kind of Gambler Fallacy. Finally, subjects executed more right than left clicks (an overall proportion of 0. 4622 left clicks). This was reflected by a slight, average, positive bias (mean value of E q [µ w t,s ] = 0. 143, 95% CI = [-0. 014, 0. 301], since the convention used in our dataset encoded rightward choice at the lower boundary).
Discussion In this paper, we show that the Drift Diffusion Model (DDM) is well suited to be used in combination with Variational Inference. We present two ways of using VB in this context: the first approach is a classical hierarchical regression model that goes deep in the data structure, with latent variables coming from every level of the hierarchy (trial, subject and population). The second approach takes advantage of the time series of the dataset to build a precise posterior probability distribution of the parameters at each trial. Our approaches are data-driven and can, therefore, be applied to a very broad range of datasets with little or no tuning. The only features the user needs to define are the regressors. Many routines have been proposed to optimize the DDM. Ratcliff and Tuerlinckx  (10)  Finally, the VRIN model, besides its ability to account for trial-by-trial variability in the threshold values, can also provide a more precise estimate of the posterior distribution of local parameters, as it conditions this posterior on more information than just the RT, the choice and the prior by adding the previous trials as regressors for the value of the prior.
Therefore, adjusting the trade-off between accuracy of posterior estimates and computational cost is an important challenge for future developments of our models. A potential improvement of the present approaches would be to broaden the models to other sequential sampling models (SSM). Many of them have a closed-form FPT density function formula  (74) , allowing our models to extend to these other frameworks. In the presence of missing trials or blocks of variable length, the gradient function cannot be prerecorded 2. This makes the evaluation of the gradient much slower than without missing trials. This constitutes another crucial issue to improve in the future. Finally, informative priors should probably be included for the variance parameters σ s , or another level of inference should be implemented to adjust this prior to the dataset.
(20)d others(61; 62; 9)have used a numerical quadrature (NQ) algorithm with a numerical estimate of the gradient to optimize the likelihood function at the subject level. The computational cost of this method is extremely high, justifying the development of less flexible, but simpler methods (63; 64; 7; 65). Vandekerckhove et al. (20)used a Markov Chain Monte Carlo (MCMC) technique to estimate each trial distribution in a fully Bayesian setting. Our approach differs in several ways from the work of Vandekerckhove et al. : first, the method we used to make inference about the generative model allows us to extend it to large (or very large) datasets with limited cost, as the gradient of the ELBO is estimated stochastically. The use of Variational Inference makes it also possible to control the convergence of the algorithm, which is challenging with MCMC techniques.
Measures All data were collected during a single meeting. Each participant completed a self-report questionnaire and was assessed by an investigator through a semi-structured interview. To the best of our knowledge, there was no tool available to examine the subjective experiences of former cult members. Therefore, part of the interview was designed specifically for this study, based on the methodological and clinical experiences of a panel of experts, including psychiatrists, methodologists, sociologists and experts in the field of cults.
The analysis was completed independently and a consensus was necessary for classification. The interview was performed chronologically from the year preceding the commitment to the effective departure from the group. Data collected regarding the characteristics of the cultic group included the size of the group, its organization, its creed  (Commission d'enquête parlementaire, 1995) , the frequency of meetings with the cult leader, the abilities of the cult leader (including supernatural or magical abilities or power in the form of knowledge), and the incurred risk in the case of opposition. Additionally, it included the presence of cultic group description criteria  (Gest and Guyard, 1996) : group elitism, exorbitant financial demands, severing of ties with the member's original social environment, attacks on physical and/or psychological integrity, indoctrination of children, antisocial discourse, breaches of public order, legal problems, bypassing of traditional economic networks and infiltration of the authorities, alternative lifestyle, cult of personality of the leader, and the initial seduction of members.
Data collected regarding the experience of a member in the group included age at the time of the commitment, the time between first contact and commitment, the life events in the year preceding commitment that facilitated it, the length of cult membership, the investment in the group, the impact of cult membership, the life events that were an obstacle to departure and the life events that aided in departure, the time interval between the first desire to leave and actual departure, and the method of departure (personal initiative, group dissolution, or outside intervention).
Statistical Analysis Data were entered into Microsoft Excel and summarised using Pivot tables to describe the demographic variables. The number and percentage of students selecting each term for each video was calculated. For each video, the median score and interquartile range (IQR) for each term was calculated to describe the strength of the selected term. Multiple Correspondence Analysis (MCA), with the joint option in Stata, was used to visualise the relationship between the students' previous experience and the terms selected (in binary form presence or absence of behaviour) for each video. MCA is a descriptive technique used to visualise binary and categorical variables of interest (student experience) as points on a two-dimensional plot to describe how strongly and in which way the variables are related or cluster together  [27].
Results Data were collected from 127 students that agreed to take part in the study. Most students were female, aged <20 years old, and enrolled in the veterinary science or technology programme (Table  3 ). Just under half of the students rated themselves as being either Experienced or Very Experienced, with 10% of students indicating they had no previous experience with horses (Table  3 ). The number of students selecting each term and the median score for each selected term for each video is shown in Table  4. The students selected 13/15 terms for Video 1, of which most students strongly perceived the horse as being Alert (80%) and Curious (84%), and 81% of students scored the horse as moderately Friendly (Table  4 ). Just over half of students (54%) gave moderate scores for At Ease, and 30% of students gave moderate scores for Happy.
The main objective of the present study is to provide the first fine-grained description of the evolution over the lifespan of the (algorithmic) complexity of human pseudo-random productions. Secondary objectives are to demonstrate that, across a variety of different tasks of random generation, the novel measure of behavioral complexity does not rely on the collection of tediously long response sequences as hitherto required. The playful instructions to produce brief response sequences by randomizing a given set of alternatives are suitable for children and elderly people alike, can be applied in work with various patient groups and are convenient for individual testing as well as Internet-based data collection. Participants with ages ranging from 4 to 91 performed a series of RIG tasks online.
Measures For each task, CT (in seconds) was recorded. The sum of CTs (total CT) was also used in the analyses. An estimate of the algorithmic complexity of participants' responses was computed using the acss function included in the freely publicly available acss R-package  [42]  that implements the complexity methods used in this project. Complexities were then normalized, using the mean and standard deviation of all possible strings with the given length and number of possible symbols, so that a complexity of 0 corresponds to the mean complexity of all possible strings. For each participant, the mean normalized complexity (averaged over the five tasks) was also computed, serving as a global measure of complexity.
This allowed us to assess the semantic priming effect (unrelated condition-related condition) and the possible modulation of this semantic priming effect by auditory attention. Participants. Sixty-two psychology students from the University of Grenoble Alpes (46 females, M age = 22 years, SD = 6; 16 males, M age = 21 years, SD = 2) participated in this experiment. All were native French speakers and reported no known language or auditory disorder. All participants gave written informed consent and received course credit for their participation. Stimuli. First, 360 words and 120 pseudo-words (according to the French orthographic rules) were selected. The words included 120 targets, 120 semantically related and 120 unrelated prime words. They were selected from both a preceding study  [13]  and a verbal association database  [48].
Pairs of primes (semantically related and unrelated) were matched in terms of lexical frequency (according to the French database, Lexique 3  [49] ) and number of syllables. Table  1  shows the psycholinguistic characteristic of the target and prime words used. Table  1  shows the means (in bold) and standard deviations (in parentheses) of psycholinguistic variables, controlled for each type of verbal stimulus. Second, 840 sentences were constructed and recorded with an OLYMPUS LS100 recorder. To allow participants to perform stream segregation easily, sentences recorded were uttered by one male (mean of F 0 = 137. 27 Hz) and one female voice (mean of F 0 = 238. 21 Hz). Each sentence was composed of 18 syllables and had a comparable duration (for the male speaker, M = 2916 ms, SD = 235; female, M = 3237 ms, SD = 361).
Each recorded sentence underwent noise-reduction processing, intensity calibration in dB-A and normalization at 80dB-A. SiS stimuli were built by merging one sentence produce by the male speaker and one produced by the female speaker. Both male and female speakers' sentences started simultaneously after 200 ms of silence. Sentences were processed with Audacity software (2. 1. 1. Version, http://www. audacityteam. org/). During the experiment the sound tracks were presented to participants over headphone at 60 dB-A. Among these 840 sentences, 480 were used for the relevant speech stream (i. e. containing the experimental primes), 240 for the irrelevant speech stream, and 120 for the pseudo-words' presentation. Half of the 480 sentences used as relevant speech stream contained the semantically related prime, and the other half contained the unrelated one.
Data analysis Semantic priming task The dataset comported 7440 observations. We excluded two participants; the first one was slow (M = 973 ms, SD = 423) compared with the group mean reaction time (M = 686 ms, SD = 217), and the second one had an error rate that exceeded 15% (M = 16. 66% SD =. 36), three times greater than the group mean (M = 5. 91%, SD = 3. 86). Moreover, three items were removed from the dataset because they induced high error rates (more than 40%: fiasco, pagaie, tempo) compared to the other items (M = 4. 23%, SD = 4. 18). Finally, outliers, i. e. , latencies less than 300 ms and greater than 1500 ms, were also removed from data. Overall, a total of 6. 64% of the original data was discarded for the data analysis. The mean of RTs for correct responses on the word targets was 621 ms (SD = 75), and there was an ER of 4.
Executive function assessment For the anti-saccade task, the dataset consisted of 22016 observations. Half of these observations corresponded to the straight-gaze condition; the other half, to the changed-gaze condition. For the straight-gaze condition, 31 observations were absent responses and were consequently removed from the dataset as 4 anticipation responses (RTs lower than 80 ms  [42] ). Thus, 0. 31% of the original straight-gaze condition data were removed from the data analysis. For the changed-gaze condition, 66 absent responses and 17 anticipation responses (corresponding to 0. 75% of the initial dataset of the condition) were also removed. An ANOVA was conducted for each condition (straight-gaze and changed-gaze) in terms of RTs and ERs. The straight-gaze ANOVA included Switching (blocked and mixed conditions) and Response suppression (PRO and ANTI conditions) variables as within-participant factors.
Acknowledgments This work was supported by the  Rhone-Alpes Region, France  attributed through the " ARC2: Qualitede vie et Vieillissement ". We would like to thank the 62 students of the  University of Grenoble Alpes  for their participation on the study. We are also grateful to  Michel Hoen  who was involved in this project and  Gustavo Estivalet  for his contribution and advice on data analysis.
For procedure details, see Lefevre and colleagues  29. Simultaneously, 1 mL of blood was withdrawn from the saphenous vein. Immediately after collection, samples were centrifuged during 10 minutes at 2000 × g at 4 °C, and stored at -80 °C until assay. The experiment and all of the involved procedures were performed in accordance with the relevant guidelines and regulations (European Community standards for the care and use of laboratory animals) and approved by the animal ethical committee CELYNE n°42 (ref 02075-01) and the French Ministry of agriculture and environment. Sample and data processing. Oxytocin assay. Three different methods were used to measure OT in human samples, and one for macaques' samples. They will be referred as, respectively, OT ELS (Enzo Life Science), OT Lg (the method from Geenen's lab in Liège  28  ), OT RIA (the method from Landgraf 's lab  18  ), OT M (macaques).
Moreover, we also tested correlations between methods for both CSF and plasma OT values. To complement this analysis, we also used Spearman rank correlation tests on raw values, as non-parametric statistics are not sensitive to biased distribution and outliers. Our sample size of 22-25 patients (depending on the assay) has 80% power (20% chance to fail rejecting the null hypothesis) to detect r = 0. 57-0. 54. We consider however that correlation coefficient lower than 0. 5 would not be strong enough to use plasma OT as a reliable indicator of central OT. All statistical tests were performed with STATISTICA 8 or MATLAB 2013a. For cases of non-significant correlations between the methods, we used equivalence tests based on the two-one sided test procedure  33  to determine if we could conclude statistical equivalence for the correlation between methods.
Acknowledgements This research was funded by  CNRS  and  Labex  Cortex  ANR-11-LABEX-0042  grant from the  University of Lyon  I within the program " Investissement d' Avenir ") to AS. AL was supported by a doctoral fellowship from  Labex  Cortex  ANR-11-LABEX-0042  grant from the  University of Lyon  I. We thank  A. Szathmari ,  G. Deiana  and the clinical staff for assistance during patients' clinical exams. We are also grateful to  V. Geenen ,  H. Martens  and  C. Renard  for their suggestions and comments on oxytocin assay technical procedures. This work was supported by  CNRS  and  Labex Cortex "Investissement d' Avenir" ANR  grant to AS.
Data analysis For each assessor, results of the free sorting tasks were encoded in individual distance matrices where the rows and the columns are the whiskies. For each individual distance matrix, a value of 1 between a row and a column indicates that the assessor put the two whiskies together, whereas a value of 0 indicates that the whiskies were not put together. For each group of assessors (i. e. French, UK, US, experts and non-experts) and each condition (orthonasal and full tasting conditions), the individual distance matrices obtained from the sorting data were computed in a global similarity matrices. These global similarity matrices were then submitted to non-metric multidimensional scaling (MDS). In addition, hierarchical ascending classifications (HAC) were performed on each MDS coordinate to identify groups of whiskies.
Results: Socioeconomic, family or school variables were associated with levels of physical activity and sedentary behaviour for both boys and girls, but no factor, except perceived parental physical activity level, was associated with total energy expenditure (total physical activity) for either gender. Adolescents with privileged and less privileged socioeconomic status reported the same total amount of energy expenditure. Conclusions: Total physical activity score alone is not sufficient to assess the physical activity of adolescents. These findings may have implications for better understanding of social inequalities in this context and recommendations to prevent overweight. Trial registration: This trial is registered at ClinicalTrials. gov (NCT00814554). The date of registration: 23 December 2008.