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Longitudinal biomedical data are often characterized by a sparse time grid and individual‐specific development patterns. Specifically, in epidemiological cohort studies and clinical registries we are facing the question of what can be learned from the data in an early phase of the study, when only a baseline characterization and one follow‐up measurement are available. Inspired by recent advances that allow to combine deep learning with dynamic modeling, we investigate whether such approaches can be useful for uncovering complex structure, in particular for an extreme small data setting with only two observations time points for each individual. Irregular spacing in time could then be used to gain more information on individual dynamics by leveraging similarity of individuals. We provide a brief overview of how variational autoencoders (VAEs), as a deep learning approach, can be linked to ordinary differential equations (ODEs) for dynamic modeling, and then specifically investigate the feasibility of such an approach that infers individual‐specific latent trajectories by including regularity assumptions and individuals' similarity. We also provide a description of this deep learning approach as a filtering task to give a statistical perspective. Using simulated data, we show to what extent the approach can recover individual trajectories from ODE systems with two and four unknown parameters and infer groups of individuals with similar trajectories, and where it breaks down. The results show that such dynamic deep learning approaches can be useful even in extreme small data settings, but need to be carefully adapted. [ABSTRACT FROM AUTHOR]

Differentiable programming has recently received much interest as a paradigm that facilitates taking gradients of computer programs. While the corresponding flexible gradient-based optimization approaches so far have been used predominantly for deep learning or enriching the latter with modeling components, we want to demonstrate that they can also be useful for statistical modeling per se, for example, for quick prototyping when classical maximum likelihood approaches are challenging or not feasible. In an application from a COVID-19 setting, we use differentiable programming to quickly build and optimize a flexible prediction model adapted to the data quality challenges at hand. Specifically, we develop a regression model, inspired by delay differential equations, that can bridge temporal gaps of observations in the central German registry of COVID-19 intensive care cases for predicting future demand. With this exemplary modeling challenge, we illustrate how differentiable programming can enable simple gradient-based optimization of the model by automatic differentiation. This allowed us to quickly prototype a model under time pressure that outperforms simpler benchmark models. We thus exemplify the potential of differentiable programming also outside deep learning applications to provide more options for flexible applied statistical modeling. [ABSTRACT FROM AUTHOR]

Background: Time-series forecasting models play a central role in guiding intensive care coronavirus disease 2019 (COVID-19) bed capacity in a pandemic. A key predictor of future intensive care unit (ICU) COVID-19 bed occupancy is the number of new severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections in the general population, which in turn is highly associated with week-to-week variability, reporting delays, regional differences, number of unknown cases, time-dependent infection rates, vaccinations, SARS-CoV‑2 virus variants, and nonpharmaceutical containment measures. Furthermore, current and also future COVID ICU occupancy is significantly influenced by ICU discharge and mortality rates., Methods: Both the number of new SARS-CoV‑2 infections in the general population and intensive care COVID-19 bed occupancy rates are recorded in Germany. These data are statistically analyzed on a daily basis using epidemic SEIR (susceptible, exposed, infection, recovered) models using ordinary differential equations and multiple regression models., Results: Forecast results of the immediate trend (20-day forecast) of ICU occupancy by COVID-19 patients are made available to decision makers at various levels throughout the country., Conclusion: The forecasts are compared with the development of available ICU bed capacities in order to identify capacity limitations at an early stage and to enable short-term solutions to be made, such as supraregional transfers., (© 2022. The Author(s).)

Recent extensions of single-cell studies to multiple data modalities raise new questions regarding experimental design. For example, the challenge of sparsity in single-omics data might be partly resolved by compensating for missing information across modalities. In particular, deep learning approaches, such as deep generative models (DGMs), can potentially uncover complex patterns via a joint embedding. Yet, this also raises the question of sample size requirements for identifying such patterns from single-cell multi-omics data. Here, we empirically examine the quality of DGM-based integrations for varying sample sizes. We first review the existing literature and give a short overview of deep learning methods for multi-omics integration. Next, we consider eight popular tools in more detail and examine their robustness to different cell numbers, covering two of the most common multi-omics types currently favored. Specifically, we use data featuring simultaneous gene expression measurements at the RNA level and protein abundance measurements for cell surface proteins (CITE-seq), as well as data where chromatin accessibility and RNA expression are measured in thousands of cells (10x Multiome). We examine the ability of the methods to learn joint embeddings based on biological and technical metrics. Finally, we provide recommendations for the design of multi-omics experiments and discuss potential future developments., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Brombacher, Hackenberg, Kreutz, Binder and Treppner.)

Motivation: Following many successful applications to image data, deep learning is now also increasingly considered for omics data. In particular, generative deep learning not only provides competitive prediction performance, but also allows for uncovering structure by generating synthetic samples. However, exploration and visualization is not as straightforward as with image applications., Results: We demonstrate how log-linear models, fitted to the generated, synthetic data can be used to extract patterns from omics data, learned by deep generative techniques. Specifically, interactions between latent representations learned by the approaches and generated synthetic data are used to determine sets of joint patterns. Distances of patterns with respect to the distribution of latent representations are then visualized in low-dimensional coordinate systems, e.g. for monitoring training progress. This is illustrated with simulated data and subsequently with cortical single-cell gene expression data. Using different kinds of deep generative techniques, specifically variational autoencoders and deep Boltzmann machines, the proposed approach highlights how the techniques uncover underlying structure. It facilitates the real-world use of such generative deep learning techniques to gain biological insights from omics data., Availability and Implementation: The code for the approach as well as an accompanying Jupyter notebook, which illustrates the application of our approach, is available via the GitHub repository: https://github.com/ssehztirom/Exploring-generative-deep-learning-for-omics-data-by-using-log-linear-models., Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author(s) 2020. Published by Oxford University Press.)