Inferring Latent Velocities from Weather Radar Data using Gaussian Processes
Archived data from the US network of weather radars hold detailed information about bird migration over the last 25 years, including very high-resolution partial measurements of velocity. Historically, most of this spatial resolution is discarded and velocities are summarized at a very small number of locations due to modeling and algorithmic limitations. This paper presents a Gaussian process (GP) model to reconstruct high-resolution full velocity fields across the entire US. The GP faithfully models all aspects of the problem in a single joint framework, including spatially random velocities, partial velocity measurements, station-specific geometries, measurement noise, and an ambiguity known as aliasing. We develop fast inference algorithms based on the FFT; to do so, we employ a creative use of Laplace's method to sidestep the fact that the kernel of the joint process is non-stationary.
-- Paper Summary  The primary challenges posed by the problem considered in this paper arise from three main issues, namely 1) the data may be aliased, 2) only the radial velocity is measured (while the full velocity has to be inferred) and 3) the data is generally linked to a specific weather station. While some of these issues have been previously addressed, the paper delivers a solution which jointly tackles the three issues. This proposal builds upon the KISS-GP framework, while also developing an efficient way to carry out Laplace inference when incorporating a wrapped normal likelihood. While it was previously common practice to subsample the data, this approach can handle the full dataset (500k points) without compromising on speed. This is particularly important since the kernel is non-stationary, where standard inference techniques are not always applicable.    -- Originality + Significance  While applied papers do feature at NIPS, I believe that the theoretic contributions developed in this paper are only of minor significance to the general community, which tends to value significant algorithmic contributions above advances in applied areas. The generality of the proposed improvements to existing GP methods also lose their impact due to the paper’s focus on a single dataset.  While there is some emphasis on the Laplace method being used to carry out exact inference, the authors then claim that this is no longer possible when incorporating the wrapped normal likelihood. The novelty of the Laplace computation is also unclear to me. Similar work was carried out in relation to grid-structured inputs and conjugate gradient for Laplace in ‘Fast Kronecker Inference in Gaussian Processes with non-Gaussian likelihoods (Flaxman et al, 2015)’ and ‘Preconditioning Kernel Matrices (Cutajar et al, 2016)’, but these papers are not discussed or cited here.  The overall scope of this work is also limited to a particular problem and its associated data. While the conclusion indicates that there may in fact be other similar problems which are worth investigating (e.g. inferring wind velocity from precipitation or wind particles), it is not immediately clear whether the model developed in this paper can be similarly successful in these other instances.   -- Quality  The derivations put forward in the paper appear to be correct, drawing from results which were previously established in the literature on structured kernel interpolation for Gaussian processes. The superior performance of the method is not altogether surprising given the success of its intermediate components showcased in other papers. The impact of using pseudo-observations in order to fill up incomplete grids should however be elaborated by at least re-iterating the motivations given in the original KISS-GP paper.  The results obtained using the proposed method are very promising in comparison with other naïve GP approaches. The running time comparison is also very useful in validating the authors’ intuition that the increase in predictive performance does not incur a penalty in speed. There is however very little context for how successful the results are beyond the narrow GP setting. The “6 different methods” highlighted in L234 are only the proposed method and the naïve GP method with 5 different training set sizes. As alluded to before, the performance improvements enabled by this proposed method are expected given their success in other domains.  Although the temporal aspect of this problem is not considered in the paper (even though it is implied in the introductory comment that such analysis could answer questions “over more than two decades”), a brief investigation into INLA methods may also be warranted. Scalable deep GPs may also be useful for modelling non-stationarity behaviour.  Finally, while I understand that such data may not be readily available, I think it would be beneficial to have additional results for the model on similarly structured datasets having similar aliasing issues for example. I would expect similarly good results on other such spatio-temporal problems, but it would be best if this could also be supplemented with actual experiments.   -- Writing and Clarity  I cannot fault the writing of this paper – it is extremely well written with nary a typo to be found (I only spotted L62). The problem is adequately set up, and the individual components of the model design are well-motivated and described in an orderly manner. The paper is also sufficiently detailed to properly understand without having to rely on the supplementary material. The notation is easy to follow and interpret.   -- Overall Recommendation  I appreciate that having an end-to-end scalable model which takes partial measurements as input and successfully models actual wind velocities is useful for specific problems and datasets in this particular domain. This is evidenced by the model’s success compared to standard GP models.  Nevertheless, even though the problem is indeed interesting and the paper is in a state fit for publication, I do not think NIPS is the ideal venue unless a wider variety of problems or data settings are explored. Essentially, the minor theoretic contributions must be compensated for by a wider and more comprehensive set of experiments.  -------------  -- Post-rebuttal  I thank the authors for replying to my comments. After reading the rebuttal and other reviews, I have bumped up my score from 4 to 6 in order to better reflect its quality as an application track paper. Nonetheless, for other reasons mentioned in the full-review, I do not feel inclined to argue more strongly for its acceptance.