Latent Agents in Networks: Estimation and Targeting.

Latent Agents in Networks: Estimation and Targeting In "Latent Agents in Networks: Estimation and Targeting," Baris Ata, Alexandre Belloni, and Ozan Candogan address the problem of estimating network effects in a setting in which data only on a subset of agents is available. In this setting, the observable agents influence each other's outcomes both directly and indirectly through their influence on the latent agents. Even in sparse networks, the combination of direct and indirect network effects yields a nonsparse influence structure that makes estimation challenging. The authors overcome this challenge and provide an estimation algorithm that performs well in high-dimensional settings. They also establish convergence rates for their proposed estimator and show that their performance guarantees are valid for a large class of networks. Finally, the authors demonstrate the application of their algorithm to a targeted advertising problem, in which it can be used to obtain asymptotically optimal advertising decisions despite the presence of latent agents. We consider a platform that serves (observable) agents, who belong to a larger network that also includes additional agents who are not served by the platform. We refer to the latter group of agents as latent agents. Associated with each agent are the agent's covariate and outcome. The platform has access to past covariates and outcomes of the observable agents, but no data for the latent agents is available to the platform. Crucially, the agents influence each other's outcome through a certain influence structure. In particular, observable agents influence each other both directly and indirectly through the influence they exert on the latent agents. The platform doesn't know the inference structure of either the observable or the latent parts of the network. We investigate how the platform can estimate the dependence of the observable agents' outcomes on their covariates, taking the presence of the latent agents into account. First, we show that a certain matrix succinctly captures the relationship between the outcomes and the covariates. We provide an algorithm that estimates this matrix using historical data of covariates and outcomes for the observable agents under a suitable approximate sparsity condition. We also establish convergence rates for the proposed estimator despite the high dimensionality that allows more agents than observations. Second, we show that the approximate sparsity condition holds under the standard conditions used in the literature. Hence, our results apply to a large class of networks. Finally, we illustrate the applications to a targeted advertising problem. We show that, by using the available historical data with our estimator, it is possible to obtain asymptotically optimal advertising decisions despite the presence of latent agents. Funding: O. Candogan acknowledges NSF award 2216912 for "Institute for Data, Econometrics, Algorithms and Learning". Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2485. [ABSTRACT FROM AUTHOR]