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 .

Variational Autoencoders (VAE) are popular generative models used to sample from complex data distributions. Despite their empirical success in various machine learning tasks, significant gaps remain in understanding their theoretical properties, particularly regarding convergence guarantees. This paper aims to bridge that gap by providing non-asymptotic convergence guarantees for VAE trained using both Stochastic Gradient Descent and Adam algorithms. We derive a convergence rate of $\mathcal{O}(\log n / \sqrt{n})$, where $n$ is the number of iterations of the optimization algorithm, with explicit dependencies on the batch size, the number of variational samples, and other key hyperparameters. Our theoretical analysis applies to both Linear VAE and Deep Gaussian VAE, as well as several VAE variants, including $\beta$-VAE and IWAE. Additionally, we empirically illustrate the impact of hyperparameters on convergence, offering new insights into the theoretical understanding of VAE training.

Score-based Generative Models (SGMs) have achieved impressive performance in data generation across a wide range of applications and benefit from strong theoretical guarantees. Recently, methods inspired by statistical mechanics, in particular, Hamiltonian dynamics, have introduced Critically-damped Langevin Diffusions (CLDs), which define diffusion processes on extended spaces by coupling the data with auxiliary variables. These approaches, along with their associated score-matching and sampling procedures, have been shown to outperform standard diffusion-based samplers numerically. In this paper, we analyze a generalized dynamic that extends classical CLDs by introducing an additional hyperparameter controlling the noise applied to the data coordinate, thereby better exploiting the extended space. We further derive a novel upper bound on the sampling error of CLD-based generative models in the Wasserstein metric. This additional hyperparameter influences the smoothness of sample paths, and our discretization error analysis provides practical guidance for its tuning, leading to improved sampling performance.

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such problems. Amongst such priors, score-based generative models (SGM) have recently been successfully applied to several different inverse problems. In this study, we exploit the particular structure of the prior defined by the SGM to define a sequence of intermediate linear inverse problems. As the noise level decreases, the posteriors of these inverse problems get closer to the target posterior of the original inverse problem. To sample from this sequence of posteriors, we propose the use of Sequential Monte Carlo (SMC) methods. The proposed algorithm, \algo, is shown to be theoretically grounded and we provide numerical simulations showing that it outperforms competing baselines when dealing with ill-posed inverse problems in a Bayesian setting.

Stochastic Gradient Descent (SGD) with adaptive steps is widely used to train deep neural networks and generative models. Most theoretical results assume that it is possible to obtain unbiased gradient estimators, which is not the case in several recent deep learning and reinforcement learning applications that use Monte Carlo methods. This paper provides a comprehensive non-asymptotic analysis of SGD with biased gradients and adaptive steps for non-convex smooth functions. Our study incorporates time-dependent bias and emphasizes the importance of controlling the bias of the gradient estimator. In particular, we establish that Adagrad, RMSProp, and AMSGRAD, an exponential moving average variant of Adam, with biased gradients, converge to critical points for smooth non-convex functions at a rate similar to existing results in the literature for the unbiased case. Finally, we provide experimental results using Variational Autoenconders (VAE) and applications to several learning frameworks that illustrate our convergence results and show how the effect of bias can be reduced by appropriate hyperparameter tuning.

We consider the problem of state estimation in general state-space models using variational inference. For a generic variational family defined using the same backward decomposition as the actual joint smoothing distribution, we establish under mixing assumptions that the variational approximation of expectations of additive state functionals induces an error which grows at most linearly in the number of observations. This guarantee is consistent with the known upper bounds for the approximation of smoothing distributions using standard Monte Carlo methods. We illustrate our theoretical result with state-of-the art variational solutions based both on the backward parameterization and on alternatives using forward decompositions. This numerical study proposes guidelines for variational inference based on neural networks in state-space models.

Non-linear state-space models, also known as general hidden Markov models (HMM), are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences. Learning in HMM, either via Maximum Likelihood Estimation (MLE) or Markov Score Climbing (MSC) requires the estimation of the- smoothing expectation of some additive functionals. Controlling the bias and the variance of this estimation is crucial to establish the convergence of learning algorithms. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs (PPG) sampler, which can be viewed as a PaRIS (Olsson, Westerborn 2017) algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. We then establish, in the learning context, and under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

Vector Quantized-Variational AutoEncoders (VQ-VAE) are generative models based on discrete latent representations of the data, where inputs are mapped to a finite set of learned embeddings. To generate new samples, an autoregressive prior distribution over the discrete states must be trained separately. This prior is generally very complex and leads to slow generation. In this work, we propose a new model to train the prior and the encoder/decoder networks simultaneously. We build a diffusion bridge between a continuous coded vector and a non-informative prior distribution. The latent discrete states are then given as random functions of these continuous vectors. We show that our model is competitive with the autoregressive prior on the mini-Imagenet and CIFAR dataset and is efficient in both optimization and sampling. Our framework also extends the standard VQ-VAE and enables end-to-end training.

Alice Martin, Guillaume Quispe, Charles Ollion, Sylvain Le Corff, Florian Strub, Olivier Pietquin. Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2022.

We introduce a new general identifiable framework for principled disentanglement referred to as Structured Nonlinear Independent Component Analysis (SNICA). Our contribution is to extend the identifiability theory of deep generative models for a very broad class of structured models. While previous works have shown identifiability for specific classes of time-series models, our theorems extend this to more general temporal structures as well as to models with more complex structures such as spatial dependencies. In particular, we establish the major result that identifiability for this framework holds even in the presence of noise of unknown distribution. Finally, as an example of our framework's flexibility, we introduce the first nonlinear ICA model for time-series that combines the following very useful properties: it accounts for both nonstationarity and autocorrelation in a fully unsupervised setting; performs dimensionality reduction; models hidden states; and enables principled estimation and inference by variational maximum-likelihood.

Sampling from a complex distribution $\pi$ and approximating its intractable normalizing constant $\mathrm{Z}$ are challenging problems. In this paper, a novel family of importance samplers (IS) and Markov chain Monte Carlo (MCMC) samplers is derived. Given an invertible map $\mathrm{T}$, these schemes combine (with weights) elements from the forward and backward Orbits through points sampled from a proposal distribution $\rho$. The map $\mathrm{T}$ does not leave the target $\pi$ invariant, hence the name NEO, standing for Non-Equilibrium Orbits. NEO-IS provides unbiased estimators of the normalizing constant and self-normalized IS estimators of expectations under $\pi$ while NEO-MCMC combines multiple NEO-IS estimates of the normalizing constant and an iterated sampling-importance resampling mechanism to sample from $\pi$. For $\mathrm{T}$ chosen as a discrete-time integrator of a conformal Hamiltonian system, NEO-IS achieves state-of-the art performance on difficult benchmarks and NEO-MCMC is able to explore highly multimodal targets. Additionally, we provide detailed theoretical results for both methods. In particular, we show that NEO-MCMC is uniformly geometrically ergodic and establish explicit mixing time estimates under mild conditions.

This paper considers hidden Markov models where the observations are given as the sum of a latent state which lies in a general state space and some independent noise with unknown distribution. It is shown that these fully nonparametric translation models are identifiable with respect to both the distribution of the latent variables and the distribution of the noise, under mostly a light tail assumption on the latent variables. Two nonparametric estimation methods are proposed and we prove that the corresponding estimators are consistent for the weak convergence topology. These results are illustrated with numerical experiments.

In this paper, we consider the filtering and smoothing recursions in nonparametric finite state space hidden Markov models (HMMs) when the parameters of the model are unknown and replaced by estimators. We provide an explicit and time uniform control of the filtering and smoothing errors in total variation norm as a function of the parameter estimation errors. We prove that the risk for the filtering and smoothing errors may be uniformly upper bounded by the L1-risk of the estimators. It has been proved very recently that statistical inference for finite state space nonparametric HMMs is possible. We study how the recent spectral methods developed in the parametric setting may be extended to the nonparametric framework and we give explicit upper bounds for the L2-risk of the nonparametric spectral estimators. In the case where the observation space is compact, this provides explicit rates for the filtering and smoothing errors in total variation norm. The performance of the spectral method is assessed with simulated data for both the estimation of the (nonparametric) conditional distribution of the observations and the estimation of the marginal smoothing distributions.

Mobile device localization in wireless sensor networks is a challenging task. It has already been addressed when the WiFi propagation maps of the access points are modeled deterministically or estimated using an offline human training calibration. However, these techniques do not take into account the environmental dynamics. In this paper, the maps are assumed to be made of an average indoor propagation model combined with a perturbation field which represents the influence of the environment. This perturbation field is embedded with a distribution describing the prior knowledge about the environmental influence. The device is localized with Sequential Monte Carlo methods and relies on the estimation of the propagation maps. This inference task is performed online, using the observations sequentially, with a new online Expectation Maximization based algorithm. The performance of the algorithm is illustrated with Monte Carlo experiments using both simulated data and a true data set.

This paper addresses the problem of mobile device localization in wireless sensor networks. The mobile is assumed to receive the signals transmitted byWiFi access points. The localization procedure is performed online (i.e. using the observations acquired by the mobile) and relies on the estimation of the propagation maps of the signal associated with each access point. This intermediate estimation step uses a new online Expectation Maximization based algorithm and Sequential Monte Carlo methods.