Unsupervised Learning is one of the most fundamental problem of machine learning, and more generally, of artificial intelligence. In a broad sense, it amounts to learning some unobserved latent structure over data. This structure may be of interest per se, or may serve as an important stepping stone integrated in a complex data analysis pipe-line - since large amounts of unlabeled data are more common than costly labeled data. Arguably, one the cornerstones of unsupervised learning is clustering, where the aim is to recover a partition of the data into homogeneous groups. Beside vanilla clustering, unsupervised learning encompasses a large variety of related other problems such as hierarchical clustering, where the group structure is more complex and reveals both the backbone and fine-grain organization of the data, segmentation where the shape of the clusters is constrained by side information, or ranking or seriation problems where where no actual cluster structure exists, but where there is some implicit ordering between the data. All these problems have already found countless applications and interest in these methods is even strengthening due to the amount of available unlabelled data. We can for instance cite crowdsourcing - where individuals answer to a subset of questions, and where, depending on the context, one might want to e.g. cluster them depending on their field of expertise, rank them depending on their performances, or seriate them depending on their affinities. Such problems are extremely relevant for recommender systems - where individuals are users, and questions are items - and for social network analyses. The analysis of unsupervised learning procedures has a long history that takes its roots both in the computer science and in mathematical communities. In response to recent bridges between these two communities, groundbreaking advances have been made in the theoretical foundations of vanilla clustering. We believe that these recent advances hold the key for deep impacts on the broader field of unsupervised learning because of the pervasive nature of clustering. In this proposal, we first aim at propagating these recent ground-breaking advances in vanilla clustering to problems where the latent structure is either more complex or more constrained. We will consider problems of increasing latent structure complexity - starting from hierarchical clustering and heading toward ranking, seriation, and segmentation - and propose new algorithms that will build on each other, focusing on the interfaces between these problems. As a result, we expect to provide new methods that are valid under weaker assumptions in comparison to what is usually done - e.g. parametric assumptions - while being also able to adapt to the unknown intrinsic difficulty of the problem. Moreover, many modern unsupervised learning applications are essentially of an online nature - and sometimes decisions have to be made sequentially on top of that. For instance, consider a recommender systems that sequentially recommends items to users. In this context where sequential, active recommendations are made, it is important to leverage the latent structure underlying the individuals. While both the fields of unsupervised learning, and sequential, active learning, are thriving, research at the crossroad has been conducted mostly separately by each community - leading to procedures that can be improved. A second aim of this proposal will then be to bring together the fields of unsupervised learning and active learning, in order to propose new algorithms that are more efficient at leveraging sequentially the unknown latent structure. We will consider the same unsupervised learning problems as in the batch learning side of the proposal. We will focus on developing algorithms that fully take advantage of new advances in clustering, and of our own future work in batch learning.

Many models exist that describe the emission of greenhouse gases such as CO2 and N2O from soils. However, these global models need improvements to yield more accurate predictions. Indeed these models are ignoring important microscopic aspects of soils, in particular their high level of heterogeneity at the microbial habitat and pore scale, caused by soil structure which can lead to a spatial disconnection between soil carbon and nitrogen, oxygen and the microrganisms. Micro-scale processes that occur within the pores in soils affect phenomena at much larger spatial and temporal scales. New inputs and parameters are needed for the soil compartment in the global “circulation” models used by climatologists to predict future climate patterns. Most microbial degradation models developed in soil science use empirical functions, also called “reduction functions”. They take into account the different environmental factors that affect microbial functions such as biodegradation, denitrification or nitrification. Among these different factors, those linked to temperature and water content are conventionally used and accepted. However this type of approach cannot describe well the complex interactions that occur between processes. Therefore, such interactions need to be better represented in biogeochemical models for more reliable simulations. A recent alternative approach to the simulation of microbial degradation of organic matter is the "Bottom-Up" approach, based on an explicit description of the soil pore space at the small scale, that of the microbial habitats, and of the processes taking place therein. Innovative modeling tools have been developed at scales directly relevant to microorganisms. Emergence can be captured from the diversity of scenarios that can be run from these models and that would have been much more laborious to carry out experimentally. In parallel with the development of these 3D sophisticated models, technological advances have been made in the 3D visualization at the microscale. The Bottom-Up approach faces limitations due to the computational cost of describing the 3D heterogeneities of the soil at the µm scale to produce output at the centimeter column scale. Upscaling methods have been applied in the area of hydrology mainly to upscale water or solute transport properties taking into consideration the porous structure. However averaging methods used in soil physics or hydrology eliminate information that, in some situations like those involving microorganisms, appears essential. One of the challenges is to find a way to bring the micro-heterogeneities registered at the µ-scale to the soil profile using modeling and especially models of intermediate complexity between pore scale 3D models and existing field models. Revisiting upscaling methodology for soil microbial functions are essential to build more accurate soil models of microbial functions. Our previous MEPSOM project (ANR, 2009-2013) showed how soil physical characteristics control the decomposition of organic substrates. It has developed a suite of methods and models to visualize in 3D soil heterogeneity at scales relevant for microorganisms. The goal of this new project is now to go further by using the 3D models resulting from Mepsom to upscale heterogeneities identified at the scale of microhabitats to the soil profile scale. In Soilµ-3D project, MEPSOM’s 3D models will pass the baton to simpler models able to run at the field scale for a better prediction of organic matter decomposition, nitrous oxide emission and organic pollutants impacted by climate and environmental changes. The general question we intend to answer in the proposed research is whether information on the spatial heterogeneity of soils at the microscale can be used to predict the processes observed at the macroscale in soils.

ANSWER is a French-Chinese collaborative project which focuses on the modelling and the simulation of eutrophic lake ecosystems to study the impact of anthropogenic environmental changes on the proliferation of cyanobacteria. Worldwide the current environmental situation is preoccupying: the water needs for humans increase while the quality of the available resources is deteriorating due to pollution of various kinds and to hydric stress. In particular, the eutrophication of lentic ecosystems due to excessive inputs of nutrients (phosphorus and nitrogen) has become a major problem because it promotes cyanobacteria blooms, which disrupt the functioning and the uses of the ecosystems. For 40 years, some measures of reduction of nutrient inputs, especially of phosphorus, have been applied in developed countries to fight against these blooms whereas a reverse tendency of increase of the nutrient loading is observed in other countries. At the same time, the temperature and the atmospheric CO2 concentration have been increasing with significant consequences on the dynamics of phytoplankton communities in lakes. All these local and global changes finally lead to significant modifications of the C/N/P ratio in ecosystems (i.e. the modification of the availability of the three major elements: C, N & P). The project ANSWER will evaluate the consequences that these variations can have on the dynamics of cyanobacterial blooms, by using modelling approaches and numerical simulations which will be based on existing and specific experiments and field data. To represent the complexity of the functioning of lentic ecosystems, the use of 3D dynamical models, obtained by coupling hydrodynamic and ecological models, is essential. Because the development, the calibration and the simulation of such models require a wide range of skills, researchers of various fields (computer science, applied mathematics, modelling, physical limnology and microbial ecology) will work together to develop an integrative platform for lake ecosystems modelling, which will include tools of data management and knowledge representation, models and statistical methods for model calibration and validation. The models will be used for: (1) the simulation of the short-term (weeks) impact of sudden changes of C/N/P ratio (due to weather events) on the initiation of blooms and the evolution of their spatial distribution; (2) comparative simulations of the dynamics and the composition of phytoplankton communities during an annual cycle following the observed trends for the C/N/P ratio in France and in China; (3) the test and optimization of control strategies whose combined impact with climate changes results in a modification of the C/N/P ratio. The processes of recycling of organic matter by bacteria in the water column and of release of nutrients from the sediments will be studied experimentally to improve the model ability. Indeed, although these processes are considered as essential for the dynamics of cyanobacteria, they are often ignored or poorly represented in existing models. One of the difficulties of the implementation of these modelling approaches often comes from the lack of data, or from their poor quality, which makes the validation and the calibration of the models difficult. Thanks to the diversity of the French and Chinese teams gathered in our consortium, we will have access to a rich database composed of good quality data acquired on diversified ecosystems (the large shallow Lake Taihu in China, the long and deep Villerest reservoir and the small and shallow urban Lake Champs-sur-Marne in France). The broad skills of our consortium, ranging from microbial ecology and limnology to modelling, will allow us to take into account in the construction, the validation and the analysis of the models, all the key processes involved in the ecosystem functioning.

The objectives of the FooSIN project are to establish and work within the recently proposed and endorsed GO FAIR Food Systems Implementation Network (IN) to 1) accelerate the implementation of FAIR principles in the agri-food community, and 2) position France as a leader in this evolution and make French actions and productions more visible at an international level. The Food Systems IN, co-led by Inra and Wageningen University and Research, gathers 22 major actors of the agriculture and nutrition domains worldwide, who commit to FAIR principles and collectively work for their wider and quicker adoption. As members of the Food Systems IN, we propose concrete actions towards the French community of people involved in data production and management for agriculture and food. We will organize a Bring-Your-Own-Data workshop (a.k.a datathon), seek for adapted training materials, and recommend tools and methodologies to FAIRify data and semantic resources, with the aim to leverage the FAIR awareness and skills, and the adoption of efficient tooling by our community. We will also propose original tools and services for data FAIRification to be adopted and disseminated by the Food Systems IN at the international level. These services and tools may also be transfered to other fields among the INs of the GO FAIR network.

We are interested in the long-time behavior of infinite-dimensional branching processes and in the applications of these limiting results. Such stochastic processes are particle systems where particles move independently according to a Markov process. When a branching event occurs, a particle is replaced by a random number of new particles. Times of branching events, numbers of offspring and offspring locations may depend on the ancestor position. We focus on models with non-local branching: the offspring's location at birth is chosen through a Markov kernel. Examples are cell division or evolution model. More precisely, we will study 1) growth-fragmentation processes: size of cells grow exponentially and cells divide into two new cells at random times depending on their sizes 2) models for the evolution of phenotype: individuals possess a trait that they pass on to their descendants up to a small variation. Non-local branching involves non-self-adjoint operators making their study much more difficult than classical branching diffusions. We propose to develop new approaches to prove law of large numbers type results, leveraging ideas from functional analysis, partial differential equation study and probability theory and then derive from those results new statistical estimators. The project is structured around 3 challenges: The first challenge is based on the partial differential equations (PDE) theory. Our aim is to develop new tools, close to Krein-Rutman theorem or entropy methods, to study the long time behavior of linear but non-local evolutionary PDE. The second challenge is based on the probability theory. Its aim is to establish new law of large number results and central limit theorems for those particle systems. Finally, the last challenge is focused on the applications. Our aim is to compare our theoretical results with concrete applications. In particular, we will develop new statistical tools to estimate the various parameters of our models.