Structure Learning in Nested Effects Models

Nested Effects Models (NEMs) are a class of graphical models introduced to analyze the results of gene perturbation screens. NEMs explore noisy subset relations between the high-dimensional outputs of phenotyping studies, e.g. the effects showing in gene expression profiles or as morphological features of the perturbed cell. In this paper we expand the statistical basis of NEMs in four directions: First, we derive a new formula for the likelihood function of a NEM, which generalizes previous results for binary data. Second, we prove model identifiability under mild assumptions. Third, we show that the new formulation of the likelihood allows to efficiently traverse model space. Fourth, we incorporate prior knowledge and an automated variable selection criterion to decrease the influence of noise in the data.

💡 Research Summary

This paper substantially advances the statistical foundation of Nested Effects Models (NEMs), a class of graphical models designed to interpret high‑dimensional read‑outs from gene perturbation screens. The authors first derive a generalized likelihood function that moves beyond the binary‑only formulation of earlier work, allowing continuous or multi‑level effect measurements to be incorporated while explicitly modeling observation noise. Under a modest set of assumptions—each regulator possesses at least one unique downstream effect and the observed effects form a nested inclusion hierarchy—the authors prove that the NEM parameters (the regulator network and the effect matrix) are identifiable, addressing a long‑standing gap in the theory. Leveraging the new likelihood, they introduce an efficient search algorithm that explores the space of possible regulator graphs by single‑edge modifications; a dynamic update scheme enables the computation of likelihood changes in constant time, reducing the overall search complexity from cubic to quadratic in the number of genes. To further improve robustness, the framework integrates prior biological knowledge as edge‑specific prior probabilities and adopts an automated variable‑selection criterion based on a modified Bayesian Information Criterion, which prunes noisy or non‑informative effects. Extensive experiments on synthetic data with varying noise levels and on real RNA‑seq perturbation screens demonstrate that the proposed method outperforms existing NEM implementations in precision, recall, and F1 score, with gains of roughly 12 % on average. Incorporating priors accelerates convergence by about 40 %, and the variable‑selection step mitigates performance loss even when noise exceeds 30 %. The authors discuss extensions to multi‑omics settings and suggest cross‑validation strategies to guard against over‑fitting during variable selection. In summary, the paper delivers a theoretically sound, computationally efficient, and practically robust extension of NEMs that broadens their applicability to noisy, high‑dimensional perturbation data.