Stephen Y. Zhang

Stephen Y Zhang

Network inference, the task of reconstructing interactions in a complex system from experimental observables, is a central yet extremely challenging problem in systems biology. While much progress has been made in the last two decades, network inference remains an open problem. For systems observed at steady state, limited insights are available since temporal information is unavailable and thus causal information is lost. Two common avenues for gaining causal insights into system behaviour are to leverage temporal dynamics in the form of trajectories, and to apply interventions such as knock-out perturbations. We propose an approach for leveraging both dynamical and perturbational single cell data to jointly learn cellular trajectories and power network inference. Our approach is motivated by min-entropy estimation for stochastic dynamics and can infer directed and signed networks from time-stamped single cell snapshots.

Noah El Rimawi-Fine, Adam Stecklov, Lucas Nelson et al.

Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and stochastic in nature, and admit only partial, noisy state measurements. This poses a significant challenge for addressing the problems of modeling the underlying dynamics and inferring the network structure of these systems. Existing methods are typically tailored either for structure learning or modeling dynamics at the population level, but are limited in their ability to address both problems together. In this work, we address both problems simultaneously: we present StructureFlow, a novel and principled simulation-free approach for jointly learning the structure and stochastic population dynamics of physical systems. We showcase the utility of StructureFlow for the tasks of structure learning from interventions and dynamical (trajectory) inference of conditional population dynamics. We empirically evaluate our approach on high-dimensional synthetic systems, a set of biologically plausible simulated systems, and an experimental single-cell dataset. We show that StructureFlow can learn the structure of underlying systems while simultaneously modeling their conditional population dynamics -- a key step toward the mechanistic understanding of systems behavior.

Stephen Y. Zhang

Non-negative matrix and tensor factorisations are a classical tool for finding low-dimensional representations of high-dimensional datasets. In applications such as imaging, datasets can be regarded as distributions supported on a space with metric structure. In such a setting, a loss function based on the Wasserstein distance of optimal transportation theory is a natural choice since it incorporates the underlying geometry of the data. We introduce a general mathematical framework for computing non-negative factorisations of both matrices and tensors with respect to an optimal transport loss. We derive an efficient computational method for its solution using a convex dual formulation, and demonstrate the applicability of this approach with several numerical illustrations with both matrix and tensor-valued data.