Laura Iacovissi

Laura Iacovissi, Nan Lu, Robert C. Williamson

Corruption is notoriously widespread in data collection. Despite extensive research, the existing literature predominantly focuses on specific settings and learning scenarios, lacking a unified view of corruption modelization and mitigation. In this work, we develop a general theory of corruption, which incorporates all modifications to a supervised learning problem, including changes in model class and loss. Focusing on changes to the underlying probability distributions via Markov kernels, our approach leads to three novel opportunities. First, it enables the construction of a novel, provably exhaustive corruption framework, distinguishing among different corruption types. This serves to unify existing models and establish a consistent nomenclature. Second, it facilitates a systematic analysis of corruption's consequences on learning tasks, by comparing Bayes risks in the clean and corrupted scenarios. Notably, while label corruptions affect only the loss function, attribute corruptions additionally influence the hypothesis class. Third, building upon these results, we investigate mitigations for various corruption types. We expand existing loss-correction methods for label corruption to handle dependent corruption types. Our findings highlight the necessity to generalize the classical corruption-corrected learning framework to a new paradigm with weaker requirements to encompass more corruption types. We provide such a paradigm as well as loss correction formulas in the attribute and joint corruption cases.

Laura Iacovissi, Caterina De Bacco

Community detection and hierarchy extraction are usually thought of as separate inference tasks on networks. Considering only one of the two when studying real-world data can be an oversimplification. In this work, we present a generative model based on an interplay between community and hierarchical structures. It assumes that each node has a preference in the interaction mechanism and nodes with the same preference are more likely to interact, while heterogeneous interactions are still allowed. The sparsity of the network is exploited for implementing a more efficient algorithm. We demonstrate our method on synthetic and real-world data and compare performance with two standard approaches for community detection and ranking extraction. We find that the algorithm accurately retrieves the overall node's preference in different scenarios, and we show that it can distinguish small subsets of nodes that behave differently than the majority. As a consequence, the model can recognize whether a network has an overall preferred interaction mechanism. This is relevant in situations where there is no clear "a priori" information about what structure explains the observed network datasets well. Our model allows practitioners to learn this automatically from the data.