Certifiable Robustness for Nearest Neighbor Classifiers

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.

A Prioritized Trajectory Planning Algorithm for Connected and Automated Vehicle Mandatory Lane Changes

We introduce a prioritized system-optimal algorithm for mandatory lane change (MLC) behavior of connected and automated vehicles (CAV) from a dedicated lane. Our approach applies a cooperative lane change that prioritizes the decisions of lane changing vehicles which are closer to the end of the diverging zone (DZ), and optimizes the predicted total system travel time. Our experiments on synthetic data show that the proposed algorithm improves the traffic network efficiency by attaining higher speeds in the dedicated lane and earlier MLC positions while ensuring a low computational time. Our approach outperforms the traditional gap acceptance model.