Non-negative Weighted DAG Structure Learning
Speaker: Samuel Rey Escudero
Location: 0.W100 Turing Room, Building 28
Time: 15:00 - 15:45
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Abstract:
In this talk, we discuss the problem of learning the topology of directed acyclic graphs (DAGs) from nodal observations that adhere to a linear structural equation model. While imposing acyclicity in an optimization problem is a notoriously difficult task, recent advances have framed combinatorial DAG structure learning as a continuous optimization problem, propelling the development of novel and efficient strategies to estimate DAG structures. Despite this success, existing methods must contend with the complexities of non-convex optimization and related issues stemming from acyclicity constraints. To overcome these limitations, we assume that the latent DAG contains only non-negative edge weights. Leveraging this additional structure, we argue that cycles can be effectively characterized (and prevented) using a more tractable acyclicity function based on the log-determinant of the adjacency matrix. Upon framing non-negative DAG learning as an optimization problem, our alternative characterization of acyclicity leads to more tractable gradients, enabling the use of well-known tools from constrained optimization. In particular, we propose a DAG recovery algorithm based on the method of multipliers and empirically observe consistent convergence to the ground-truth DAG. We argue that the proposed characterization of acyclicity can be applied beyond classical SEM, and we empirically validate the performance of our algorithm in several test cases, showing that it outperforms state-of-the-art alternatives.
Joint Recovery of Simplicial Complexes via Binary Linear Programming
Speaker: Varun Sarathchandran
Location: 0.W100 Turing Room, Building 28
Time: 15:45 - 16:05
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Abstract:
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet learning their structure is challenging due to the strong coupling across different simplicial levels imposed by the inclusion property. In this work, we propose a joint framework for simplicial complex learning that enforces the inclusion property through a linear constraint, enabling the formulation of the problem as a binary linear program. The objective function consists of a combination of smoothness measures across all considered simplicial levels, allowing for the incorporation of arbitrary smoothness criteria. This formulation enables the simultaneous estimation of edges and higher-order simplices within a single optimization problem. Experiments on simulated and real-world data demonstrate that the proposed joint approach outperforms hierarchical and greedy baselines, while more faithfully enforcing higher-order structural priors.
NodePro: An Instance-Level Profiling Framework for Graph-Structured Data
Speaker: Tianqi Zhao
Location: 0.W100 Turing Room, Building 28
Time: 16:05 - 16:25
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Abstract:
Graph machine learning models often achieve similar overall performance yet behave differently at the node level—failing on different subsets of nodes with varying reliability. Standard evaluation metrics such as accuracy obscure these fine-grained differences, making it difficult to diagnose when and where models fail. We introduce NodePro, a node profiling framework that enables fine-grained diagnosis of model behavior by assigning interpretable profile scores to individual nodes. These scores combine data-centric signals—such as feature dissimilarity, label uncertainty, and structural ambiguity—with model-centric measures of prediction confidence and consistency during training. By aligning model behavior with these profiles, NodePro reveals systematic differences between models, even when aggregate metrics are indistinguishable. We show that node profiles generalize to unseen nodes, supporting prediction reliability without ground-truth labels. Finally, we demonstrate the utility of NodePro in identifying semantically inconsistent or corrupted nodes in a structured knowledge graph, illustrating its effectiveness in real-world settings.