Whole-body hemodynamics simulators, which model blood flow and pressure waveforms as functions of physiological parameters, are now essential tools for studying cardiovascular systems. However, solving the corresponding inverse problem of mapping observations (e.g., arterial pressure waveforms at specific locations in the arterial network) back to plausible physiological parameters remains challenging. Leveraging recent advances in simulation-based inference, we cast this problem as statistical inference by training an amortized neural posterior estimator on a newly built large dataset of cardiac simulations that we publicly release. To better align simulated data with real-world measurements, we incorporate stochastic elements modeling exogenous effects. The proposed framework can further integrate in-vivo data sources to refine its predictive capabilities on real-world data. In silico, we demonstrate that the proposed framework enables finely quantifying uncertainty associated with individual measurements, allowing trustworthy prediction of four biomarkers of clinical interest--namely Heart Rate, Cardiac Output, Systemic Vascular Resistance, and Left Ventricular Ejection Time--from arterial pressure waveforms and photoplethysmograms. Furthermore, we validate the framework in vivo, where our method accurately captures temporal trends in CO and SVR monitoring on the VitalDB dataset. Finally, the predictive error made by the model monotonically increases with the predicted uncertainty, thereby directly supporting the automatic rejection of unusable measurements.

This paper introduces Diffuse-TreeVAE, a deep generative model that integrates hierarchical clustering into the framework of Denoising Diffusion Probabilistic Models (DDPMs). The proposed approach generates new images by sampling from a root embedding of a learned latent tree VAE-based structure, it then propagates through hierarchical paths, and utilizes a second-stage DDPM to refine and generate distinct, high-quality images for each data cluster. The result is a model that not only improves image clarity but also ensures that the generated samples are representative of their respective clusters, addressing the limitations of previous VAE-based methods and advancing the state of clustering-based generative modeling.

We propose a novel method, scTree, for single-cell Tree Variational Autoencoders, extending a hierarchical clustering approach to single-cell RNA sequencing data. scTree corrects for batch effects while simultaneously learning a tree-structured data representation. This VAE-based method allows for a more in-depth understanding of complex cellular landscapes independently of the biasing effects of batches. We show empirically on seven datasets that scTree discovers the underlying clusters of the data and the hierarchical relations between them, as well as outperforms established baseline methods across these datasets. Additionally, we analyze the learned hierarchy to understand its biological relevance, thus underpinning the importance of integrating batch correction directly into the clustering procedure.

The field of deep generative modeling has grown rapidly and consistently over the years. With the availability of massive amounts of training data coupled with advances in scalable unsupervised learning paradigms, recent large-scale generative models show tremendous promise in synthesizing high-resolution images and text, as well as structured data such as videos and molecules. However, we argue that current large-scale generative AI models do not sufficiently address several fundamental issues that hinder their widespread adoption across domains. In this work, we aim to identify key unresolved challenges in modern generative AI paradigms that should be tackled to further enhance their capabilities, versatility, and reliability. By identifying these challenges, we aim to provide researchers with valuable insights for exploring fruitful research directions, thereby fostering the development of more robust and accessible generative AI solutions.

We propose Tree Variational Autoencoder (TreeVAE), a new generative hierarchical clustering model that learns a flexible tree-based posterior distribution over latent variables. TreeVAE hierarchically divides samples according to their intrinsic characteristics, shedding light on hidden structures in the data. It adapts its architecture to discover the optimal tree for encoding dependencies between latent variables. The proposed tree-based generative architecture enables lightweight conditional inference and improves generative performance by utilizing specialized leaf decoders. We show that TreeVAE uncovers underlying clusters in the data and finds meaningful hierarchical relations between the different groups on a variety of datasets, including real-world imaging data. We present empirically that Tree-VAE provides a more competitive log-likelihood lower bound than the sequential counterparts. Finally, due to its generative nature, TreeVAE is able to generate new samples from the discovered clusters via conditional sampling.

We propose a novel anomaly detection method for echocardiogram videos. The introduced method takes advantage of the periodic nature of the heart cycle to learn three variants of a variational latent trajectory model (TVAE). While the first two variants (TVAE-C and TVAE-R) model strict periodic movements of the heart, the third (TVAE-S) is more general and allows shifts in the spatial representation throughout the video. All models are trained on the healthy samples of a novel in-house dataset of infant echocardiogram videos consisting of multiple chamber views to learn a normative prior of the healthy population. During inference, maximum a posteriori (MAP) based anomaly detection is performed to detect out-of-distribution samples in our dataset. The proposed method reliably identifies severe congenital heart defects, such as Ebstein's Anomaly or Shone-complex. Moreover, it achieves superior performance over MAP-based anomaly detection with standard variational autoencoders when detecting pulmonary hypertension and right ventricular dilation. Finally, we demonstrate that the proposed method enables interpretable explanations of its output through heatmaps highlighting the regions corresponding to anomalous heart structures.

Spurious correlations are everywhere. While humans often do not perceive them, neural networks are notorious for learning unwanted associations, also known as biases, instead of the underlying decision rule. As a result, practitioners are often unaware of the biased decision-making of their classifiers. Such a biased model based on spurious correlations might not generalize to unobserved data, leading to unintended, adverse consequences. We propose Signal is Harder (SiH), a variational-autoencoder-based method that simultaneously trains a biased and unbiased classifier using a novel, disentangling reweighting scheme inspired by the focal loss. Using the unbiased classifier, SiH matches or improves upon the performance of state-of-the-art debiasing methods. To improve the interpretability of our technique, we propose a perturbation scheme in the latent space for visualizing the bias that helps practitioners become aware of the sources of spurious correlations.

Partitioning a set of elements into subsets of a priori unknown sizes is essential in many applications. These subset sizes are rarely explicitly learned - be it the cluster sizes in clustering applications or the number of shared versus independent generative latent factors in weakly-supervised learning. Probability distributions over correct combinations of subset sizes are non-differentiable due to hard constraints, which prohibit gradient-based optimization. In this work, we propose the differentiable hypergeometric distribution. The hypergeometric distribution models the probability of different group sizes based on their relative importance. We introduce reparameterizable gradients to learn the importance between groups and highlight the advantage of explicitly learning the size of subsets in two typical applications: weakly-supervised learning and clustering. In both applications, we outperform previous approaches, which rely on suboptimal heuristics to model the unknown size of groups. Many machine learning approaches rely on differentiable sampling procedures, from which the reparameterization trick for Gaussian distributions is best known (Kingma & Welling, 2014; Rezende et al., 2014). The non-differentiable nature of discrete distributions has long hindered their use in machine learning pipelines with end-to-end gradient-based optimization. Only the concrete distribution (Maddison et al., 2017) or Gumbel-Softmax trick (Jang et al., 2016) boosted the use of categorical distributions in stochastic networks. Unlike the high-variance gradients of score-based methods such as REINFORCE (Williams, 1992), these works enable reparameterized and lowvariance gradients with respect to the categorical weights. Despite enormous progress in recent years, the extension to more complex probability distributions is still missing or comes with a trade-off regarding differentiability or computational speed (Huijben et al., 2021). The hypergeometric distribution plays a vital role in various areas of science, such as social and computer science and biology. The range of applications goes from modeling gene mutations and recommender systems to analyzing social networks (Becchetti et al., 2011; Casiraghi et al., 2016; Lodato et al., 2015). The hypergeometric distribution describes sampling without replacement and, therefore, models the number of samples per group given a limited number of total samples. Hence, it is essential wherever the choice of a single group element influences the probability of the remaining elements being drawn. Previous work mainly uses the hypergeometric distribution implicitly to model assumptions or as a tool to prove theorems.

Survival analysis has gained significant attention in the medical domain and has many far-reaching applications. Although a variety of machine learning methods have been introduced for tackling time-to-event prediction in unstructured data with complex dependencies, clustering of survival data remains an under-explored problem. The latter is particularly helpful in discovering patient subpopulations whose survival is regulated by different generative mechanisms, a critical problem in precision medicine. To this end, we introduce a novel probabilistic approach to cluster survival data in a variational deep clustering setting. Our proposed method employs a deep generative model to uncover the underlying distribution of both the explanatory variables and the potentially censored survival times. We compare our model to the related work on survival clustering in comprehensive experiments on a range of synthetic, semi-synthetic, and real-world datasets. Our proposed method performs better at identifying clusters and is competitive at predicting survival times in terms of the concordance index and relative absolute error. To further demonstrate the usefulness of our approach, we show that our method identifies meaningful clusters from an observational cohort of hemodialysis patients that are consistent with previous clinical findings.

Generating visualizations and interpretations from high-dimensional data is a common problem in many fields. Two key approaches for tackling this problem are clustering and representation learning. There are very performant deep clustering models on the one hand and interpretable representation learning techniques, often relying on latent topological structures such as self-organizing maps, on the other hand. However, current methods do not yet successfully combine these two approaches. We present a new deep architecture for probabilistic clustering, VarPSOM, and its extension to time series data, VarTPSOM. We show that they achieve superior clustering performance compared to current deep clustering methods on static MNIST/Fashion-MNIST data as well as medical time series, while inducing an interpretable representation. Moreover, on the medical time series, VarTPSOM successfully predicts future trajectories in the original data space.