A scalable end-to-end Gaussian process adapter for irregularly sampled time series classification
We present a general framework for classification of sparse and irregularly-sampled time series. The properties of such time series can result in substantial uncertainty about the values of the underlying temporal processes, while making the data difficult to deal with using standard classification methods that assume fixeddimensional feature spaces. To address these challenges, we propose an uncertaintyaware classification framework based on a special computational layer we refer to as the Gaussian process adapter that can connect irregularly sampled time series data to any black-box classifier learnable using gradient descent. We show how to scale up the required computations based on combining the structured kernel interpolation framework and the Lanczos approximation method, and how to discriminatively train the Gaussian process adapter in combination with a number of classifiers end-to-end using backpropagation.
The paper builds a method of classification of irregularly sampled time series. GP regression is applied to the time series, and an efficient method is proposed to draw samples from the posterior functions, to propagate through the classifier. To do this, a regular set of points is defined on which all the samples will be interpolated (with uncertainty), the classifier is trained on the function values at those points, and the expected loss is computed by Monte Carlo over the GPR posteriors. 
Section 1 The standard of writing in this work is good, it was a pleasure to read the paper, and I understood nearly everything on the first pass. I'm still not entirely clear what the MEG method is, though, but I understand it uses Fourier features and a one-time estimate of the kernel parameters (i.e. it's not 'end-to-end').  Section 2 is standard GP background. Fine.   Section 3. line 96. Naming your "framework" is rather overkill, no? You're propagating uncertainty in the inputs through to a classifier model. I'm sure similar things have been done for e.g. missing data: you might view your problem as a missing data problem, with GP imputation, if so inclined.  It would be nice if you could outline what MEG does, and how it differs from your approach. My understanding is that the main difference between this paper and MEG is that you propagate samples through, and MEG just propagates the mean, is that right?  Section 4 is the most technical part of the paper. In section 4.1, the authors recap the SKI framework of Wilson and Nickish. In section 4.2, they show how do compute approximate square-root-matrix vector multiplication using the Lanczos method. I suspect that this procedure may be straightforward to those more versed in numerical linear algebra, but I think it's a neat cross-over with ML, and it does depend a little on combination with the SKI idea to get fast matrix-vector operations inside the Lanczos loop.  In section 5, the authors reiterate that they are doing end-to-end learning, and so will attempt to learn the GP parameters alongside the parameters of the classifier. This means backpropagating through the Lanczos operations.  Section 6 does not do a very good job of explaining the difference between this work and MEG. At this point, I'm left with the burning question: "is this worth it"?  Section 7.  Section 7.1 is well done: it attempt to answer the question about the accuracy of the sampling-approximation.  Figure 1 : caption should explain what the colors mean, very confusing otherwise.  In section 7.2, the method is demonstrated on a single dataset. Disappointingly, the irregular-sampling of the dataset is artificial i.e. data were sub-sampled irregularly. The experiment does attempt to address my main concern: "is it really worth training everything together", and table 1 purports that this is so.  The paper is is rather let down by a lack of scientific investigation as to _why_ this must be so. What were the different kernel parameters that were learned using the two methods? Are the GPs smoother under the end-to-end framework? Does the noise get interpreted differently? Maybe we could see a plot of the different imputed time series?!  The paper is also let down by failing to provide a motivating use-case. If it was difficult to find an irregularly sampled dataset, what's the point of the paper? For this reason, I've marked the paper down for impact.