Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translation

In optimal transport (OT), a Monge map is known as a mapping that transports a source distribution to a target distribution in the most cost-efficient way. Recently, multiple neural estimators for Monge maps have been developed and applied in diverse unpaired domain translation tasks, e.g. in single-cell biology and computer vision. However, the classic OT framework enforces mass conservation, which makes it prone to outliers and limits its applicability in real-world scenarios. The latter can be particularly harmful in OT domain translation tasks, where the relative position of a sample within a distribution is explicitly taken into account. While unbalanced OT tackles this challenge in the discrete setting, its integration into neural Monge map estimators has received limited attention. We propose a theoretically grounded method to incorporate unbalancedness into any Monge map estimator. We improve existing estimators to model cell trajectories over time and to predict cellular responses to perturbations. Moreover, our approach seamlessly integrates with the OT flow matching (OT-FM) framework. While we show that OT-FM performs competitively in image translation, we further improve performance by incorporating unbalancedness (UOT-FM), which better preserves relevant features. We hence establish UOT-FM as a principled method for unpaired image translation.

Generative Entropic Neural Optimal Transport To Map Within and Across Spaces

Learning measure-to-measure mappings is a crucial task in machine learning, featured prominently in generative modeling. Recent years have witnessed a surge of techniques that draw inspiration from optimal transport (OT) theory. Combined with neural network models, these methods collectively known as \textit{Neural OT} use optimal transport as an inductive bias: such mappings should be optimal w.r.t. a given cost function, in the sense that they are able to move points in a thrifty way, within (by minimizing displacements) or across spaces (by being isometric). This principle, while intuitive, is often confronted with several practical challenges that require adapting the OT toolbox: cost functions other than the squared-Euclidean cost can be challenging to handle, the deterministic formulation of Monge maps leaves little flexibility, mapping across incomparable spaces raises multiple challenges, while the mass conservation constraint inherent to OT can provide too much credit to outliers. While each of these mismatches between practice and theory has been addressed independently in various works, we propose in this work an elegant framework to unify them, called \textit{generative entropic neural optimal transport} (GENOT). GENOT can accommodate any cost function; handles randomness using conditional generative models; can map points across incomparable spaces, and can be used as an \textit{unbalanced} solver. We evaluate our approach through experiments conducted on various synthetic datasets and demonstrate its practicality in single-cell biology. In this domain, GENOT proves to be valuable for tasks such as modeling cell development, predicting cellular responses to drugs, and translating between different data modalities of cells.

MAGNet: Motif-Agnostic Generation of Molecules from Shapes

Recent advances in machine learning for molecules exhibit great potential for facilitating drug discovery from in silico predictions. Most models for molecule generation rely on the decomposition of molecules into frequently occurring substructures (motifs), from which they generate novel compounds. While motif representations greatly aid in learning molecular distributions, such methods struggle to represent substructures beyond their known motif set. To alleviate this issue and increase flexibility across datasets, we propose MAGNet, a graph-based model that generates abstract shapes before allocating atom and bond types. To this end, we introduce a novel factorisation of the molecules' data distribution that accounts for the molecules' global context and facilitates learning adequate assignments of atoms and bonds onto shapes. While the abstraction to shapes introduces greater complexity for distribution learning, we show the competitive performance of MAGNet on standard benchmarks. Importantly, we demonstrate that MAGNet's improved expressivity leads to molecules with more topologically distinct structures and, at the same time, diverse atom and bond assignments.

Uncertainty Quantification for Atlas-Level Cell Type Transfer

Single-cell reference atlases are large-scale, cell-level maps that capture cellular heterogeneity within an organ using single cell genomics. Given their size and cellular diversity, these atlases serve as high-quality training data for the transfer of cell type labels to new datasets. Such label transfer, however, must be robust to domain shifts in gene expression due to measurement technique, lab specifics and more general batch effects. This requires methods that provide uncertainty estimates on the cell type predictions to ensure correct interpretation. Here, for the first time, we introduce uncertainty quantification methods for cell type classification on single-cell reference atlases. We benchmark four model classes and show that currently used models lack calibration, robustness, and actionable uncertainty scores. Furthermore, we demonstrate how models that quantify uncertainty are better suited to detect unseen cell types in the setting of atlas-level cell type transfer.

Sparsity in Continuous-Depth Neural Networks

Neural Ordinary Differential Equations (NODEs) have proven successful in learning dynamical systems in terms of accurately recovering the observed trajectories. While different types of sparsity have been proposed to improve robustness, the generalization properties of NODEs for dynamical systems beyond the observed data are underexplored. We systematically study the influence of weight and feature sparsity on forecasting as well as on identifying the underlying dynamical laws. Besides assessing existing methods, we propose a regularization technique to sparsify "input-output connections" and extract relevant features during training. Moreover, we curate real-world datasets consisting of human motion capture and human hematopoiesis single-cell RNA-seq data to realistically analyze different levels of out-of-distribution (OOD) generalization in forecasting and dynamics identification respectively. Our extensive empirical evaluation on these challenging benchmarks suggests that weight sparsity improves generalization in the presence of noise or irregular sampling. However, it does not prevent learning spurious feature dependencies in the inferred dynamics, rendering them impractical for predictions under interventions, or for inferring the true underlying dynamics. Instead, feature sparsity can indeed help with recovering sparse ground-truth dynamics compared to unregularized NODEs.

FedNorm: Modality-Based Normalization in Federated Learning for Multi-Modal Liver Segmentation

Given the high incidence and effective treatment options for liver diseases, they are of great socioeconomic importance. One of the most common methods for analyzing CT and MRI images for diagnosis and follow-up treatment is liver segmentation. Recent advances in deep learning have demonstrated encouraging results for automatic liver segmentation. Despite this, their success depends primarily on the availability of an annotated database, which is often not available because of privacy concerns. Federated Learning has been recently proposed as a solution to alleviate these challenges by training a shared global model on distributed clients without access to their local databases. Nevertheless, Federated Learning does not perform well when it is trained on a high degree of heterogeneity of image data due to multi-modal imaging, such as CT and MRI, and multiple scanner types. To this end, we propose Fednorm and its extension \fednormp, two Federated Learning algorithms that use a modality-based normalization technique. Specifically, Fednorm normalizes the features on a client-level, while Fednorm+ employs the modality information of single slices in the feature normalization. Our methods were validated using 428 patients from six publicly available databases and compared to state-of-the-art Federated Learning algorithms and baseline models in heterogeneous settings (multi-institutional, multi-modal data). The experimental results demonstrate that our methods show an overall acceptable performance, achieve Dice per patient scores up to 0.961, consistently outperform locally trained models, and are on par or slightly better than centralized models.

Predicting single-cell perturbation responses for unseen drugs

Single-cell transcriptomics enabled the study of cellular heterogeneity in response to perturbations at the resolution of individual cells. However, scaling high-throughput screens (HTSs) to measure cellular responses for many drugs remains a challenge due to technical limitations and, more importantly, the cost of such multiplexed experiments. Thus, transferring information from routinely performed bulk RNA-seq HTS is required to enrich single-cell data meaningfully. We introduce a new encoder-decoder architecture to study the perturbational effects of unseen drugs. We combine the model with a transfer learning scheme and demonstrate how training on existing bulk RNA-seq HTS datasets can improve generalisation performance. Better generalisation reduces the need for extensive and costly screens at single-cell resolution. We envision that our proposed method will facilitate more efficient experiment designs through its ability to generate in-silico hypotheses, ultimately accelerating targeted drug discovery.

Mitosis Detection in Intestinal Crypt Images with Hough Forest and Conditional Random Fields

Intestinal enteroendocrine cells secrete hormones that are vital for the regulation of glucose metabolism but their differentiation from intestinal stem cells is not fully understood. Asymmetric stem cell divisions have been linked to intestinal stem cell homeostasis and secretory fate commitment. We monitored cell divisions using 4D live cell imaging of cultured intestinal crypts to characterize division modes by means of measurable features such as orientation or shape. A statistical analysis of these measurements requires annotation of mitosis events, which is currently a tedious and time-consuming task that has to be performed manually. To assist data processing, we developed a learning based method to automatically detect mitosis events. The method contains a dual-phase framework for joint detection of dividing cells (mothers) and their progeny (daughters). In the first phase we detect mother and daughters independently using Hough Forest whilst in the second phase we associate mother and daughters by modelling their joint probability as Conditional Random Field (CRF). The method has been evaluated on 32 movies and has achieved an AUC of 72%, which can be used in conjunction with manual correction and dramatically speed up the processing pipeline.