Stéphanie Allassonnière

Clément Chadebec, Louis J. Vincent, Stéphanie Allassonnière

In recent years, deep generative models have attracted increasing interest due to their capacity to model complex distributions. Among those models, variational autoencoders have gained popularity as they have proven both to be computationally efficient and yield impressive results in multiple fields. Following this breakthrough, extensive research has been done in order to improve the original publication, resulting in a variety of different VAE models in response to different tasks. In this paper we present Pythae, a versatile open-source Python library providing both a unified implementation and a dedicated framework allowing straightforward, reproducible and reliable use of generative autoencoder models. We then propose to use this library to perform a case study benchmark where we present and compare 19 generative autoencoder models representative of some of the main improvements on downstream tasks such as image reconstruction, generation, classification, clustering and interpolation. The open-source library can be found at https://github.com/clementchadebec/benchmark_VAE.

Clément Chadebec, Stéphanie Allassonnière

This paper introduces a new latent variable generative model able to handle high dimensional longitudinal data and relying on variational inference. The time dependency between the observations of an input sequence is modelled using normalizing flows over the associated latent variables. The proposed method can be used to generate either fully synthetic longitudinal sequences or trajectories that are conditioned on several data in a sequence and demonstrates good robustness properties to missing data. We test the model on 6 datasets of different complexity and show that it can achieve better likelihood estimates than some competitors as well as more reliable missing data imputation. A code is made available at \url{https://github.com/clementchadebec/variational_inference_for_longitudinal_data}.

Clément Chadebec, Stéphanie Allassonnière

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking into consideration those geometrical aspects can lead to better interpolations and an improved generation procedure. This new proposed sampling method consists in sampling from the uniform distribution deriving intrinsically from the learned Riemannian latent space and we show that using this scheme can make a vanilla VAE competitive and even better than more advanced versions on several benchmark datasets. Since generative models are known to be sensitive to the number of training samples we also stress the method's robustness in the low data regime.

Archibald Fraikin, Adrien Bennetot, Stéphanie Allassonnière

Multivariate time series present challenges to standard machine learning techniques, as they are often unlabeled, high dimensional, noisy, and contain missing data. To address this, we propose T-Rep, a self-supervised method to learn time series representations at a timestep granularity. T-Rep learns vector embeddings of time alongside its feature extractor, to extract temporal features such as trend, periodicity, or distribution shifts from the signal. These time-embeddings are leveraged in pretext tasks, to incorporate smooth and fine-grained temporal dependencies in the representations, as well as reinforce robustness to missing data. We evaluate T-Rep on downstream classification, forecasting, and anomaly detection tasks. It is compared to existing self-supervised algorithms for time series, which it outperforms in all three tasks. We test T-Rep in missing data regimes, where it proves more resilient than its counterparts. Finally, we provide latent space visualisation experiments, highlighting the interpretability of the learned representations.

Clément Chadebec, Stéphanie Allassonnière

We propose a new efficient way to sample from a Variational Autoencoder in the challenging low sample size setting. This method reveals particularly well suited to perform data augmentation in such a low data regime and is validated across various standard and real-life data sets. In particular, this scheme allows to greatly improve classification results on the OASIS database where balanced accuracy jumps from 80.7% for a classifier trained with the raw data to 88.6% when trained only with the synthetic data generated by our method. Such results were also observed on 3 standard data sets and with other classifiers. A code is available at https://github.com/clementchadebec/Data_Augmentation_with_VAE-DALI.

Agathe Senellart, Maëlys Solal, Stéphanie Allassonnière et al.

Variational autoencoders are widely used for unsupervised anomaly detection. Model selection however remains an open-question: to remain fully unsupervised, hyperparameters are often chosen to minimize the reconstruction error on normal samples. In this paper, we reveal a trade-off between reconstruction quality and anomaly detection among $β$-VAE models. Models with constrained latent space reach higher detection metrics but lower reconstruction quality. We also assess the performance variability across random seeds and show it is linked to the distance between normal and abnormal latent distributions. From this analysis, we justify and investigate two methods to mitigate the reconstructiondetection tradeoff: beta-scheduling and the Sparse VAE. The latter especially shows an improvement in detection while maintaining high reconstruction quality.

Agathe Senellart, Stéphanie Allassonnière

From medical diagnosis to autonomous vehicles, critical applications rely on the integration of multiple heterogeneous data modalities. Multimodal Variational Autoencoders offer versatile and scalable methods for generating unobserved modalities from observed ones. Recent models using mixturesof-experts aggregation suffer from theoretically grounded limitations that restrict their generation quality on complex datasets. In this article, we propose a novel interpretable model able to learn both joint and conditional distributions without introducing mixture aggregation. Our model follows a multistage training process: first modeling the joint distribution with variational inference and then modeling the conditional distributions with Normalizing Flows to better approximate true posteriors. Importantly, we also propose to extract and leverage the information shared between modalities to improve the conditional coherence of generated samples. Our method achieves state-of-the-art results on several benchmark datasets.

Agathe Senellart, Clément Chadebec, Stéphanie Allassonnière

We propose a new multimodal variational autoencoder that enables to generate from the joint distribution and conditionally to any number of complex modalities. The unimodal posteriors are conditioned on the Deep Canonical Correlation Analysis embeddings which preserve the shared information across modalities leading to more coherent cross-modal generations. Furthermore, we use Normalizing Flows to enrich the unimodal posteriors and achieve more diverse data generation. Finally, we propose to use a Product of Experts for inferring one modality from several others which makes the model scalable to any number of modalities. We demonstrate that our method improves likelihood estimates, diversity of the generations and in particular coherence metrics in the conditional generations on several datasets.

Clément Chadebec, Elina Thibeau-Sutre, Ninon Burgos et al.

In this paper, we propose a new method to perform data augmentation in a reliable way in the High Dimensional Low Sample Size (HDLSS) setting using a geometry-based variational autoencoder. Our approach combines a proper latent space modeling of the VAE seen as a Riemannian manifold with a new generation scheme which produces more meaningful samples especially in the context of small data sets. The proposed method is tested through a wide experimental study where its robustness to data sets, classifiers and training samples size is stressed. It is also validated on a medical imaging classification task on the challenging ADNI database where a small number of 3D brain MRIs are considered and augmented using the proposed VAE framework. In each case, the proposed method allows for a significant and reliable gain in the classification metrics. For instance, balanced accuracy jumps from 66.3% to 74.3% for a state-of-the-art CNN classifier trained with 50 MRIs of cognitively normal (CN) and 50 Alzheimer disease (AD) patients and from 77.7% to 86.3% when trained with 243 CN and 210 AD while improving greatly sensitivity and specificity metrics.

Frédéric Logé, Rémi Besson, Stéphanie Allassonnière

A patient suffering from a rare disease in France has to wait an average of two years before being diagnosed. This medical wandering is highly detrimental both for the health system and for patients whose pathology may worsen. There exists an efficient network of Centres of Reference for Rare Diseases (CRMR), but patients are often referred to these structures too late. We are considering a probabilistic modelling of the patient pathway in order to create a simulator that will allow us to create an alert system that detects wandering patients and refers them to a CRMR while considering the potential additional costs associated with these decisions.

Clément Chadebec, Clément Mantoux, Stéphanie Allassonnière

Variational auto-encoders (VAEs) have proven to be a well suited tool for performing dimensionality reduction by extracting latent variables lying in a potentially much smaller dimensional space than the data. Their ability to capture meaningful information from the data can be easily apprehended when considering their capability to generate new realistic samples or perform potentially meaningful interpolations in a much smaller space. However, such generative models may perform poorly when trained on small data sets which are abundant in many real-life fields such as medicine. This may, among others, come from the lack of structure of the latent space, the geometry of which is often under-considered. We thus propose in this paper to see the latent space as a Riemannian manifold endowed with a parametrized metric learned at the same time as the encoder and decoder networks. This metric is then used in what we called the Riemannian Hamiltonian VAE which extends the Hamiltonian VAE introduced by arXiv:1805.11328 to better exploit the underlying geometry of the latent space. We argue that such latent space modelling provides useful information about its underlying structure leading to far more meaningful interpolations, more realistic data-generation and more reliable clustering.

Thomas Lartigue, Stanley Durrleman, Stéphanie Allassonnière

Conditional correlation networks, within Gaussian Graphical Models (GGM), are widely used to describe the direct interactions between the components of a random vector. In the case of an unlabelled Heterogeneous population, Expectation Maximisation (EM) algorithms for Mixtures of GGM have been proposed to estimate both each sub-population's graph and the class labels. However, we argue that, with most real data, class affiliation cannot be described with a Mixture of Gaussian, which mostly groups data points according to their geometrical proximity. In particular, there often exists external co-features whose values affect the features' average value, scattering across the feature space data points belonging to the same sub-population. Additionally, if the co-features' effect on the features is Heterogeneous, then the estimation of this effect cannot be separated from the sub-population identification. In this article, we propose a Mixture of Conditional GGM (CGGM) that subtracts the heterogeneous effects of the co-features to regroup the data points into sub-population corresponding clusters. We develop a penalised EM algorithm to estimate graph-sparse model parameters. We demonstrate on synthetic and real data how this method fulfils its goal and succeeds in identifying the sub-populations where the Mixtures of GGM are disrupted by the effect of the co-features.

Thomas Lartigue, Stanley Durrleman, Stéphanie Allassonnière

The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step has been replaced by Monte Carlo (MC), Markov Chain Monte Carlo or tempered approximations, etc. Most of the well-studied approximations belong to the stochastic class. By comparison, the literature is lacking when it comes to deterministic approximations. In this paper, we introduce a theoretical framework, with state-of-the-art convergence guarantees, for any deterministic approximation of the E step. We analyse theoretically and empirically several approximations that fit into this framework. First, for intractable E-steps, we introduce a deterministic version of MC-EM using Riemann sums. A straightforward method, not requiring any hyper-parameter fine-tuning, useful when the low dimensionality does not warrant a MC-EM. Then, we consider the tempered approximation, borrowed from the Simulated Annealing literature and used to escape local extrema. We prove that the tempered EM verifies the convergence guarantees for a wider range of temperature profiles than previously considered. We showcase empirically how new non-trivial profiles can more successfully escape adversarial initialisations. Finally, we combine the Riemann and tempered approximations into a method that accomplishes both their purposes.

Thomas Lartigue, Simona Bottani, Stephanie Baron et al.

Gaussian Graphical Models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: nodewise edge selection and penalised likelihood maximisation. We demonstrate on synthetic data that, when the sample size is small, the two methods produce graphs with either too few or too many edges when compared to the real one. As a result, we propose a composite procedure that explores a family of graphs with an nodewise numerical scheme and selects a candidate among them with an overall likelihood criterion. We demonstrate that, when the number of observations is small, this selection method yields graphs closer to the truth and corresponding to distributions with better KL divergence with regards to the real distribution than the other two. Finally, we show the interest of our algorithm on two concrete cases: first on brain imaging data, then on biological nephrology data. In both cases our results are more in line with current knowledge in each field.

Rémi Besson, Erwan Le Pennec, Stéphanie Allassonnière

In this work we study the problem of inferring a discrete probability distribution using both expert knowledge and empirical data. This is an important issue for many applications where the scarcity of data prevents a purely empirical approach. In this context, it is common to rely first on an initial domain knowledge a priori before proceeding to an online data acquisition. We are particularly interested in the intermediate regime where we do not have enough data to do without the initial expert a priori of the experts, but enough to correct it if necessary. We present here a novel way to tackle this issue with a method providing an objective way to choose the weight to be given to experts compared to data. We show, both empirically and theoretically, that our proposed estimator is always more efficient than the best of the two models (expert or data) within a constant.

Igor Koval, Stéphanie Allassonnière, Stanley Durrleman

The ability to predict the progression of biomarkers, notably in NDD, is limited by the size of the longitudinal data sets, in terms of number of patients, number of visits per patients and total follow-up time. To this end, we introduce a data augmentation technique that is able to reproduce the variability seen in a longitudinal training data set and simulate continuous biomarkers trajectories for any number of virtual patients. Thanks to this simulation framework, we propose to transform the training set into a simulated data set with more patients, more time-points per patient and longer follow-up duration. We illustrate this approach on the prediction of the MMSE of MCI subjects of the ADNI data set. We show that it allows to reach predictions with errors comparable to the noise in the data, estimated in test/retest studies, achieving a improvement of 37% of the mean absolute error compared to the same non-augmented model.

Rémi Besson, Erwan Le Pennec, Stéphanie Allassonnière et al.

In this work, we present our various contributions to the objective of building a decision support tool for the diagnosis of rare diseases. Our goal is to achieve a state of knowledge where the uncertainty about the patient's disease is below a predetermined threshold. We aim to reach such states while minimizing the average number of medical tests to perform. In doing so, we take into account the need, in many medical applications, to avoid, as much as possible, any misdiagnosis. To solve this optimization task, we investigate several reinforcement learning algorithm and make them operable in our high-dimensional and sparse-reward setting. We also present a way to combine expert knowledge, expressed as conditional probabilities, with real clinical data. This is crucial because the scarcity of data in the field of rare diseases prevents any approach based solely on clinical data. Finally we show that it is possible to integrate the ontological information about symptoms while remaining in our probabilistic reasoning. It enables our decision support tool to process information given at different level of precision by the user.

Igor Koval, Jean-Baptiste Schiratti, Alexandre Routier et al.

We introduce a mixed-effects model to learn spatiotempo-ral patterns on a network by considering longitudinal measures distributed on a fixed graph. The data come from repeated observations of subjects at different time points which take the form of measurement maps distributed on a graph such as an image or a mesh. The model learns a typical group-average trajectory characterizing the propagation of measurement changes across the graph nodes. The subject-specific trajectories are defined via spatial and temporal transformations of the group-average scenario, thus estimating the variability of spatiotemporal patterns within the group. To estimate population and individual model parameters, we adapted a stochastic version of the Expectation-Maximization algorithm, the MCMC-SAEM. The model is used to describe the propagation of cortical atrophy during the course of Alzheimer's Disease. Model parameters show the variability of this average pattern of atrophy in terms of trajectories across brain regions, age at disease onset and pace of propagation. We show that the personalization of this model yields accurate prediction of maps of cortical thickness in patients.