Thesis defended in 2020.

If you were a realtor, how would you take a customer on a tour of a house ? Would you start with the nicest rooms before ending up with the ugliest — based on the idea that the ﬁrst impressions are primary — or would you choose the opposite tour to leave the potential client with a ﬁnal good impression ? We believe that these alternative sequences inevitably leave a different mental representation of the house, like it is clearly the case for diagnoses [1] (based on a simple manipulated checklist of symptoms) or police lineups [2], and categorization.

Categorization is a domain that requires to model the memory of naive or expert classifiers for which the task is to group stimuli into classes. These learning models for humans can not only model the brain capacity but also help improve human-machine cooperative classification (for instance when machines can facilitate the task of humans by determining a subset of references for each category), and even improve pattern recognition by machines using machine-learning algorithms [3,4].

However the vast majority of studies in the categorization domain in both computer science and psychology draw the to-be-categorized stimuli in random order in order to avoid a list of potentially confounding variables. As a result, the inﬂuence of presentation order is understudied and scarcely addressed at all in standard models, which sometimes end up by giving similar predictions. Random orders hinder the precise modeling of a true incremental learning process (and subsequently the performance curves).

In cognitive psychology, the literature has shown that order does matter in categorization, as it does change both the quality and rapidity of a learning session in humans [5]. For instance, distributed practice aims at alternating categories, which invites the participants to find dissimilarities between categories, whereas massed learning rather involve finding similarities between the stimuli of the same category when grouped temporarily. However, fewer studies focus on more refine types of orderings of stimuli within a given category. A few preliminary results suggest that participants perform better when stimuli follow an abstract rule [6,7]. This result has gone beyond previous research that has only reported a benefit of using similarity-based presentation orders [8,9]. Overall, all of these results suggest that the orders based on similarity, although more effective than random orders, tend to induce the formation of too specific hypotheses that slows down the learning process.

The main objective of this PhD proposal is to model the temporal effects of presentation orders, to simulate the behavior of participants, and to compare existing models. This work should aim to model not only the learning and classification times but also the qualitative aspects of the representations in the learner’s mind (i. e., such as the formation of clusters or exemplars) using more specific statistical procedures. So far, an extension of the exemplar model developed by Nosofsky (GCM, General Context Model) has been developed by F. Mathy (co director, psychologist), by adding to the previous model a computation based on the discriminability of the memory traces based on the temporal distances between stimuli, by analogy with a recent short-term memory model [10]. However, this model is limited to predicting serial order, not temporal order.

The subject of this PhD is to develop further these models thanks to marked counting processes. This kind of probability models allows to precisely model the interactions between response delays, order/time of stimulus apparition, using a distance between stimulus that has yet to be defined. Some of these counting processes (such as Hawkes processes) are already used in neuroscience to model interactions between neurons and P. Reynaud-Bouret (director, mathematician) has already developed statistical tests in this case (both goodness-of-fit test and dependency detection [11,12]). Thus we want to create new models of marked counting processes allowing to model the impact of a presentation based on a similarity order, thanks to a distance for example based on this similarity. According to the different envisioned models, we may model the learning (of rules) associated to a presentation of the biggest cluster (i.e., the rule) followed by the smallest clusters (i.e., exceptions), and compare to a random presentation of clusters (promoting the abstraction of the diagnostic features). A third person, Thomas Laloë, specialist in statistical learning (in particular in k nearest neighbors methods) and in level set estimation [13,14], will participate to this PhD supervision to create for example models based on commonly used distances in machine learning and to perform statistical comparisons with more psychologically inspired models (as [10]) in order to check which approaches are more adapted to model the learning process of human beings.

**Bibliography :**

[1] Kwan, V. S. Y., Wojcik, S. P., Miron-Shatz, T., Votruba, A. M., & Olivola, C. Y. (2012). Effects of symptom presentation orderonperceived disease risk. Psychological science, 23, 381–385.

[2] Wells, G. L. (2014). Eyewitness identiﬁcation : Probative value, criterion shifts, and policy regarding the sequential lineup. Current Directions in Psychological Science, 23, 11-16.

[3] Duda, Hart (2000), Pattern Classification.

[4] Pothos, Wills (2011), Formal approaches of classification.

[5] Kornell, N., Bjork, R. A. (2008). Learning concepts and categories : is spacing the ”enemy of induction” ? Psychological Science, 19, 585-592.

[6] Kang, S. H. K., Pashler, H. (2012). Learning painting styles : Spacing is advantageous when it promotes discriminative contrast. Applied Cognitive Psychology, 26, 97-103.

[7] Mathy, F., Feldman, J. (2009). A rule-based presentation order facilitates category learning. Psychonomic Bulletin & Review, 16, 1050-1057.

[8] Elio, R., Anderson, J. R. (1981). Effects of category generalizations and instance similarity on schema abstraction. Journal of Experimental Psychology : Human Learning and Memory, 7, 397-417.

[9] Medin, D. L., Bettger, J. G. (1994). Presentation order and recognition of categorically related examples. Psychonomic Bulletin & Review, 1, 250-254.

[10] Brown, G. D. A., Neath, I., Chater, N. (2007). A temporal ratio model of memory. Psychological Review, 114, 539-576.

[11] Reynaud-Bouret, P. , Rivoirard, V., Grammont , F., Tuleau-Malot, C. (2014)

Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis, Journal of Mathematical Neuroscience, 4:3.

[12] Albert, M., Bouret, Y., Fromont, M., Reynaud-Bouret, P. (2015) Bootstrap and permutation tests of independence for point processes, Annals of Statistics, 43(6), 2537-2564.

[13] Laloë, T. (2008). A k-nearest neighbor approach for functional regression , Statistics & probability letters.

[14] Di Bernardino, E., Laloë, T., Servien, R. (2015). Estimating covariate functions associated to multivariate risks : a level sets approach, Metrika.