eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-03-19
6:1
6:20
10.4230/LIPIcs.ICDT.2022.6
article
Certifiable Robustness for Nearest Neighbor Classifiers
Fan, Austen Z.
1
https://orcid.org/0000-0001-7714-2195
Koutris, Paraschos
1
https://orcid.org/0000-0001-6309-1702
Department of Computer Sciences, University of Wisconsin-Madison, WI, USA
ML models are typically trained using large datasets of high quality. However, training datasets often contain inconsistent or incomplete data. To tackle this issue, one solution is to develop algorithms that can check whether a prediction of a model is certifiably robust. Given a learning algorithm that produces a classifier and given an example at test time, a classification outcome is certifiably robust if it is predicted by every model trained across all possible worlds (repairs) of the uncertain (inconsistent) dataset. This notion of robustness falls naturally under the framework of certain answers. In this paper, we study the complexity of certifying robustness for a simple but widely deployed classification algorithm, k-Nearest Neighbors (k-NN). Our main focus is on inconsistent datasets when the integrity constraints are functional dependencies (FDs). For this setting, we establish a dichotomy in the complexity of certifying robustness w.r.t. the set of FDs: the problem either admits a polynomial time algorithm, or it is coNP-hard. Additionally, we exhibit a similar dichotomy for the counting version of the problem, where the goal is to count the number of possible worlds that predict a certain label. As a byproduct of our study, we also establish the complexity of a problem related to finding an optimal subset repair that may be of independent interest.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol220-icdt2022/LIPIcs.ICDT.2022.6/LIPIcs.ICDT.2022.6.pdf
Inconsistent databases
k-NN classification
certifiable robustness