BACKGROUND: The gut microbiome plays a crucial role in human health, making it a cornerstone of modern biomedical research. To study its structure and dynamics, machine learning models are increasingly used to identify key microbial patterns associated with disease and environmental factors, but their performance is often limited by the intrinsic complexity of microbiome data and the small size of available cohorts. In this context, data augmentation has emerged as a promising strategy to overcome these challenges by generating artificial microbiome profiles. RESULTS: We introduce TaxaPLN, a data augmentation method based on PLN-Tree generative models, which leverages the taxonomy and a data-driven sampler to generate realistic synthetic microbiome compositions. Additionally, we propose a conditional extension based on feature-wise linear modulation, enabling covariate-aware generation. Experiments on diverse curated microbiome datasets show that TaxaPLN preserves ecological properties and generally improves or maintains predictive performances, outperforming state-of-the-art baselines on most tasks. Furthermore, the conditional variant of TaxaPLN establishes a new benchmark for metadata-aware microbiome augmentation. CONCLUSION: TaxaPLN provides a model-based framework for augmenting microbiome datasets while preserving their ecological and clinical relevance. By integrating taxonomic structure and host metadata, it enhances predictive modeling across diverse real-world settings. To facilitate reproducible and scalable microbiome analysis using our method, TaxaPLN is released as an open-source Python package available on PyPI (plntree), with MIT-licensed source code hosted at https://github.com/AlexandreChaussard/PLNTree-package .

This paper addresses nonparametric estimation of nonlinear multivariate Hawkes processes, where the interaction functions are assumed to lie in a reproducing kernel Hilbert space (RKHS). Motivated by applications in neuroscience, the model allows complex interaction functions, in order to express exciting and inhibiting effects, but also a combination of both (which is particularly interesting to model the refractory period of neurons), and considers in return that conditional intensities are rectified by the ReLU function. The latter feature incurs several methodological challenges, for which workarounds are proposed in this paper. In particular, it is shown that a representer theorem can be obtained for approximated versions of the log-likelihood and the least-squares criteria. Based on it, we propose an estimation method, that relies on two common approximations (of the ReLU function and of the integral operator). We provide a bound that controls the impact of these approximations. Numerical results on synthetic data confirm this fact as well as the good asymptotic behavior of the proposed estimator. It also shows that our method achieves a better performance compared to related nonparametric estimation techniques and suits neuronal applications.

We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle and minimax points of view, and provide new lower bounds when the intensity belongs to a Sobolev ball. By developing the Goldenshluger-Lepski methodology in the case of deconvolution for Poisson processes, we propose an optimal data-driven selection of the kernel bandwidth. Our method is illustrated on the spatial distribution of replication origins and sequence motifs along the human genome.