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1. Efficient interaction selection for clustered data via stagewise generalized estimating equations

   https://doi.org/10.1002/sim.8574  

   Vaughan, Gregory; Aseltine, Robert; Chen, Kun; Yan, Jun (July 2020, Statistics in Medicine)

   Abstract Model selection in the presence of interaction terms is challenging as the final model must maintain a hierarchy between main effects and interaction terms. This work presents two stagewise estimation approaches to appropriately select models with interaction terms that can utilize generalized estimating equations to model clustered data. The first proposed technique is a hierarchical lasso stagewise estimating equations approach, which is shown to directly correspond to the hierarchical lasso penalized regression. The second is a stagewise active set approach, which enforces the variable hierarchy by conforming the selection to a properly growing active set in each stagewise estimation step. The effectiveness in interaction selection and the superior computational efficiency of the proposed techniques are assessed in simulation studies. The new methods are applied to a study of hospitalization rates attributed to suicide attempts among 15 to 19 year old at the school district level in Connecticut. 

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2. Neural Sculpting: Uncovering hierarchically modular task structure in neural networks through pruning and network analysis

   Shreyas Malakarjun Patil, Loizos Michael (December 2023, Advances in neural information processing systems)

   Natural target functions and tasks typically exhibit hierarchical modularity – they can be broken down into simpler sub-functions that are organized in a hierarchy. Such sub-functions have two important features: they have a distinct set of inputs (input-separability) and they are reused as inputs higher in the hierarchy (reusability). Previous studies have established that hierarchically modular neural networks, which are inherently sparse, offer benefits such as learning efficiency, generalization, multi-task learning, and transfer. However, identifying the underlying sub-functions and their hierarchical structure for a given task can be challenging. The high-level question in this work is: if we learn a task using a sufficiently deep neural network, how can we uncover the underlying hierarchy of sub-functions in that task? As a starting point, we examine the domain of Boolean functions, where it is easier to determine whether a task is hierarchically modular. We propose an approach based on iterative unit and edge pruning (during training), combined with network analysis for module detection and hierarchy inference. Finally, we demonstrate that this method can uncover the hierarchical modularity of a wide range of Boolean functions and two vision tasks based on the MNIST digits dataset. 

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3. Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones

   Bai, J; Ying, R; Ren, H; Leskovec, J (December 2021, Advances in neural information processing systems)

   Hierarchical relations are prevalent and indispensable for organizing human knowledge captured by a knowledge graph (KG). The key property of hierarchical relations is that they induce a partial ordering over the entities, which needs to be modeled in order to allow for hierarchical reasoning. However, current KG embeddings can model only a single global hierarchy (single global partial ordering) and fail to model multiple heterogeneous hierarchies that exist in a single KG. Here we present ConE (Cone Embedding), a KG embedding model that is able to simultaneously model multiple hierarchical as well as non-hierarchical relations in a knowledge graph. ConE embeds entities into hyperbolic cones and models relations as transformations between the cones. In particular, ConE uses cone containment constraints in different subspaces of the hyperbolic embedding space to capture multiple heterogeneous hierarchies. Experiments on standard knowledge graph benchmarks show that ConE obtains state-of-the-art performance on hierarchical reasoning tasks as well as knowledge graph completion task on hierarchical graphs. In particular, our approach yields new state-of-the-art Hits@1 of 45.3% on WN18RR and 16.1% on DDB14 (0.231 MRR). As for hierarchical reasoning task, our approach outperforms previous best results by an average of 20% across the three datasets. 

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4. Hierarchies of Violence, Victimhood, and Remedy in the Pursuit of Women’s Rights After War

   https://doi.org/10.1093/isagsq/ksaf051  

   Berry, Marie; Lake, Milli; Raja, Sinduja; Zarook, Soraya (June 2025, Global Studies Quarterly)

   Abstract Recent postwar recovery efforts have paved the way for reforms that advance women's participation in politics, inclusion in the economy, and access to justice. In this article, we show how a singular emphasis on gender reforms after war that are inattentive to other societal cleavages can leave various forms of marginalization in the shadows. Subnational interviews on the reverberations of gender reforms in five postwar countries expose three hierarchies that structure access to rights for war-affected communities. We reveal which violence is privileged, whose violence is privileged, and which responses are privileged from the perspectives of differently situated war-affected women, showing how patterns of access to new rights can reinforce exclusionary dynamics. Importantly, because international and domestic actors tend to privilege top-down, state-based responses to wartime violence (what we term hierarchies of remedy), hierarchies of violence and victimhood frequently also reflect state actors’ priorities. Speaking to debates on legal and policy reform, we acknowledge that attention to women's rights after war offers an urgently needed corrective to earlier gender inequalities. Yet, a singular focus on gender reforms that ignores other conflict-related cleavages, particularly those that are amplified by the distribution of political power within the state apparatus, can risk obstructing access for marginalized women, sometimes reproducing grievances that contributed to violence in the first place. For policymakers, we suggest that striving for more equal access to new rights after war will help foster a more inclusive—and therefore more stable and durable—peace. 

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5. Structural hierarchy confers error tolerance in biological materials

   https://doi.org/10.1073/pnas.1813801116  

   Michel, Jonathan A.; Yunker, Peter J. (February 2019, Proceedings of the National Academy of Sciences)

   Structural hierarchy, in which materials possess distinct features on multiple length scales, is ubiquitous in nature. Diverse biological materials, such as bone, cellulose, and muscle, have as many as 10 hierarchical levels. Structural hierarchy confers many mechanical advantages, including improved toughness and economy of material. However, it also presents a problem: Each hierarchical level adds a new source of assembly errors and substantially increases the information required for proper assembly. This seems to conflict with the prevalence of naturally occurring hierarchical structures, suggesting that a common mechanical source of hierarchical robustness may exist. However, our ability to identify such a unifying phenomenon is limited by the lack of a general mechanical framework for structures exhibiting organization on disparate length scales. Here, we use simulations to substantiate a generalized model for the tensile stiffness of hierarchical filamentous networks with a nested, dilute triangular lattice structure. Following seminal work by Maxwell and others on criteria for stiff frames, we extend the concept of connectivity in network mechanics and find a similar dependence of material stiffness upon each hierarchical level. Using this model, we find that stiffness becomes less sensitive to errors in assembly with additional levels of hierarchy; although surprising, we show that this result is analytically predictable from first principles and thus potentially model independent. More broadly, this work helps account for the success of hierarchical, filamentous materials in biology and materials design and offers a heuristic for ensuring that desired material properties are achieved within the required tolerance. 

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