NIPS 2018
Sun Dec 2nd through Sat the 8th, 2018 at Palais des Congrès de Montréal
Paper ID: 5377 Inferring Latent Velocities from Weather Radar Data using Gaussian Processes

### Reviewer 1

The paper proposes a method to compute the MAP velocity vector fields from radar line-of-sight velocity measurements, using a Gaussian process prior over the velocity fields. The method is demonstrated with bird migration data from 146 US radar stations. The paper is a good read and it nicely combines previous methods (linear projections from GP, fast-kernel matrix multiplication, Laplace’s method) to solve a real-world task. The method is validated experimentally with real data, yielding both a numerical as well as a visual improvement against a naive implementation. The idea of using Laplace's method even for Gaussian posteriors, to enable fast computation, might be useful also in other places, too. It would be a strong additional point, if one could argue that the new formulation would give a new, important real-world insight that was not known before. As it is, we get nice images, but it is not clear what the real-world relevance of these is. Some remarks and questions: -) Eq (1): "a_ij" is not defined here (though it is mentioned above) -) Eq line 143: Is there a "\sigma^2" missing? It appears again in Eq (6). -) L 144-145: I would say that $k_\theta$ is stationary, "Cov(y,y)" is not. The reason for non-stationarity of the latter is rather the direction vectors, not the locations of the stations. -) L 150: $[z;y]$ is Matlab notation, but not formal maths. Change? -) L 159: "number of points" refers to the number of measurements, not the number of stations. The number of stations is rather small (a couple 100s). The real computational problem is with the many measurements from each station. Clarify? -) Eq (10): $[x_i \in \Omega]$ ==> Better write "1_[x_i \in \Omega]"? -) L 204: return"s" -) L 205: from "M"? -) L 226: Why not all 146 available stations? I have read the author response. By novel real-world insight I meant a statement like "Birds fly nicely but then become irritated by Chicago O'Hare. They start flying too low and crash against trees." or sth. similar. But it is also ok, to keep such results to biology journals and conference. Anyway, a good paper.