arXiv subjects

Laura Iacovissi

Publications and source records attributed to Laura Iacovissi.

3 recordsLinked to original sources

arXiv2026

Comparing Corrupted Constrained Learning Problems

A key result in statistics is the data processing inequality, originally proved by Blackwell (1951) and later refined by DeGroot (1962) in terms of statistical uncertainty. It states that the Bayes risk of a statistical experiment obtained by stochastically modifying another experiment cannot be lower than the Bayes risk of the original experiment, regardless of the loss function or prior chosen. In machine learning, this result underlies applications such as the information bottleneck principle and some feature learning techniques. However, machine learning problems are constrained learning problems: the model class used does not include all measurable functions. We present a simple counterexample showing that the classical data processing inequality fails to hold in such a setting. Hence, we formulate a generalized data processing inequality, requiring the constrained Bayes risk of a joint distribution (with respect to a loss function and a constrained hypothesis class) to lower bound the constrained Bayes risk on the stochastically modified distribution, regardless of the choice of distribution. We show this inequality to be equivalent to a set containment condition on a specific function set induced by the loss and model class, called the superprediction set. Finally, we derive sufficient conditions for this containment.

cs.LG↗

arXiv2026

Corruptions of Supervised Learning Problems: Typology and Mitigations

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 this 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.

cs.LG↗

arXiv2022

The interplay between ranking and communities in networks

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.

cs.SI↗