Paper ID: | 6770 |
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Title: | Distribution Learning of a Random Spatial Field with a Location-Unaware Mobile Sensor |

As the title suggests, this paper uses learning-theoretic tools to study a problem of estimating a (Lipschitz) spatial field using sensors which are location-unaware. The main contributions are the formulation of the sensing problem, a proposed algorithm, an analysis of its sample complexity, and some proof-of concept experiments. This work may be a solid start towards an interesting (new) class of problems which are amenable to probabilistic/learning-theoretic techniques. While in the future this may involve new "contributions to statistical learning theory," the present study does not really develop new techniques. Overall, the problem is interesting but the paper could be strengthened significantly in several directions as noted by the reviewers. In particular some more specific motivating examples would help ground the paper -- the authors mention "spatial sensing... in smart cities or IoT or climatology" but do not elaborate. This would help the readers better evaluate the appropriateness of various mathematical assumptions. The goal of the authors is to present a more abstract formulation, but designing practical schemes may only be possible under more restrictive assumptions. The (asymptotic) analysis of the algorithm seems to be the first step towards a more complete story which could provide results for the finite sample setting. The authors allude to this in their response, and reviewers felt that the current manuscript would have been much stronger with such results. As it stands, the $N$ chosen for experiments is quite small (as the authors have it, "shy of infinity") so it is unclear to what degree the experiments are reflective of the theoretical contributions.