Applications based on machine learning models have now become an indispensable part of the everyday life and the professional world. As a consequence, a critical question has recently arose among the population: Do algorithmic decisions convey any type of discrimination against specific groups of population or minorities? In this article, we show the importance of understanding how bias can be introduced into automatic decisions. We first present a mathematical framework for the fair learning problem, specifically in the binary classification setting. We then propose to quantify the presence of bias by using the standard disparate impact index on the real and well-known adult income dataset. Finally, we check the performance of different approaches aiming to reduce the bias in binary classification outcomes. Importantly, we show that some intuitive methods are ineffective with respect to the statistical parity criterion. This sheds light on the fact that trying to make fair machine learning models may be a particularly challenging task, in particular when the training observations contain some bias.

Key questions in paleoneurology concern the timing and emergence of derived cerebral features within the human lineage. Endocasts are replicas of the internal table of the bony braincase that are widely used in paleoneurology as a proxy for reconstructing a timeline for hominin brain evolution in the fossil record. The accurate identification of cerebral sulci imprints in endocasts is critical for assessing the topographic extension and structural organisation of cortical regions in fossil hominins. High‐resolution imaging techniques combined with established methods based on population‐specific brain atlases offer new opportunities for tracking detailed endocranial characteristics. This study provides the first documentation of sulcal pattern imprints from the superolateral surface of the cerebrum using a population‐based atlas technique on extant human endocasts. Human crania from the Pretoria Bone Collection (South Africa) were scanned using micro‐CT. Endocasts were virtually extracted, and sulci were automatically detected and manually labelled. A density map method was applied to project all the labels onto an averaged endocast to visualise the mean distribution of each identified sulcal imprint. This method allowed for the visualisation of inter‐individual variation of sulcal imprints, for example, frontal lobe sulci, correlating with previous brain‐MRI studies and for the first time the extensive overlapping of imprints in historically debated areas of the endocast (e.g. occipital lobe). In providing an innovative, non‐invasive, observer‐independent method to investigate human endocranial structural organisation, our analytical protocol introduces a promising perspective for future research in paleoneurology and for discussing critical hypotheses on the evolution of cognitive abilities among hominins.

As part of fMRI data analysis, the pyhrf package provides a set of tools for addressing the two main issues involved in intra-subject fMRI data analysis: (i) the localization of cerebral regions that elicit evoked activity and (ii) the estimation of activation dynamics also known as Hemodynamic Response Function (HRF) recovery. To tackle these two problems, pyhrf implements the Joint Detection-Estimation framework~(JDE) which recovers parcel-level HRFs and embeds an adaptive spatio-temporal regularization scheme of activation maps. With respect to the sole detection issue~(i), the classical voxelwise GLM procedure is also available through nipy, whereas Finite Impulse Response~(FIR) and temporally regularized FIR models are concerned with HRF estimation~(ii) and are specifically implemented in pyhrf. Several parcellation tools are also integrated such as spatial and functional clustering. Parcellations may be used for spatial averaging prior to FIR/RFIR analysis or to specify the spatial support of the HRF estimates in the JDE approach. These analysis procedures can be applied either to volumic data sets or to data projected onto the cortical surface. For validation purpose, this package is shipped with artificial and real fMRI data sets, which are used in this paper to compare the outcome of the different available approaches. The artificial fMRI data generator is also described to illustrate how to simulate different activation configurations, HRF shapes or nuisance components. To cope with the high computational needs for inference, pyhrf handles distributing computing by exploiting cluster units as well as multi-core machines. Finally, a dedicated viewer is presented, which handles $n$-dimensional images and provides suitable features to explore whole brain hemodynamics~(time series, maps, ROI mask overlay).

Discrete structures like graphs make it possible to naturally and flexibly model complex phenomena. Since graphs that represent various types of information are increasingly available today, their analysis has become a popular subject of research. Yet, even an algorithm for locating the average position in graphs is lacking although this knowledge would be of primary interest for statistical analysis or representation problems. In this work, we develop a stochastic algorithm for finding the Fréchet mean of weighted undirected metric graphs. This method relies on a noisy simulated annealing algorithm dealt with using homogenization. We then illustrate our algorithm with three examples (subgraphs of a social network, subgraph of a collaboration and citation network, and a transport network).

Automatic recommendation systems based on deep neural networks have become extremely popular during the last decade. Some of these systems can, however, be used in applications that are ranked as High Risk by the European Commission in the AI act—for instance, online job candidate recommendations. When used in the European Union, commercial AI systems in such applications will be required to have proper statistical properties with regard to the potential discrimination they could engender. This motivated our contribution. We present a novel optimal transport strategy to mitigate undesirable algorithmic biases in multi-class neural network classification. Our strategy is model agnostic and can be used on any multi-class classification neural network model. To anticipate the certification of recommendation systems using textual data, we used it on the Bios dataset, for which the learning task consists of predicting the occupation of female and male individuals, based on their LinkedIn biography. The results showed that our approach can reduce undesired algorithmic biases in this context to lower levels than a standard strategy.