Search for: All records

There is an emerging interest in generating robust algorithmic recourse that would remain valid if the model is updated or changed even slightly. Towards finding robust algorithmic recourse (or counterfactual explanations), existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., ||Params(M)−Params(m)||<Δ. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure – that we call Stability – to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential “naturally-occurring” model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine estimators of our proposed measure and derive a fundamental lower bound on the sample size required to have a precise estimate. We explore methods of using stability measures to generate robust counterfactuals that are close, realistic, and remain valid after potential model changes. This work also has interesting connections with model multiplicity, also known as the Rashomon effect. 

We consider a group of agents that estimate their locations in an environment through sensor measurements and aim to transmit a message signal to a client via collaborative beamforming. Assuming that the localization error of each agent follows a Gaussian distribution, we study the problem of forming a reliable communication link between the agents and the client that achieves a desired signal-to-noise ratio (SNR) at the client with minimum variability. In particular, we develop a greedy subset selection algorithm that chooses only a subset of the agents to transmit the signal so that the variance of the received SNR is minimized while the expected SNR exceeds a desired threshold. We show the optimality of the proposed algorithm when the agents’ localization errors satisfy certain sufficient conditions that are characterized in terms of the carrier frequency.