We propose a method to automatically compute the importance of features at every observation in time series, by simulating counterfactual trajectories given previous observations. We define the importance of each observation as the change in the model output caused by replacing the observation with a generated one. Our method can be applied to arbitrarily complex time series models. We compare the generated feature importance to existing methods like sensitivity analyses, feature occlusion, and other explanation baselines to show that our approach generates more precise explanations and is less sensitive to noise in the input signals.
--- Overall ---
This paper proposes a method for evaluating the influence of individual observations on the output of a time series prediction model by replacing each (discrete time) observation with its conditional expectation given the other observations. They evaluate this method qualitatively on synthetic, healthcare, and climate datasets. I reviewed this paper for NeurIPS and was happy to see that the authors have made substantial improvements to the presentation and evaluation of the method. With that said, I think that the methodological contribution is incremental (sampling from a conditional rather than marginal distribution), there is at least one major correctness issue that needs to be addressed, and the analysis of the experiments fails explain why the models perform differently.
--- Major comments ---
1. The Montecarlo approximation in Algorithm 1 does not approximate Imp(i,t). Specifically, because the averaging is done before the absolute value, Algorithm 1 approximates |F(X_{0:t}) - E[F(X_{0:-t},x_{-i,t},\hat{x}_{i,t}]|. This is also a valid measure of feature importance and it is not clear from the paper why we should prefer one over the other.
2. I think the paper needs to do a better job explaining why sampling from the conditional leads to better explanations than sampling from the marginal. The second paragraph makes an argument based on variance, but it is not clear that low variance translates to better explanations. In particular, using mean imputation has very low variance, but I would expect it to give poor explanations. I recommend using a toy example to make this point. For example, in a healthcare context, doctors are reacting to changes relative to a particular patient's baseline. A conditional model can capture this baseline but a marginal model cannot.
3. In general, I thought that the experiments were well done, but stops short of explaining *why* the methods perform differently. Put differently, I think it is really important to clearly explain why certain methods fail while others succeed. For example, the authors demonstrate the sensitivity analysis fails on the synthetic data, but never explain why. I am looking for a statement of the form: "Sensitivity analysis fails on this data because... FFC solves this weakness by doing... which is reflected in the experimental results."
4. In 4.2.1, it is very unsurprising to me that a model that samples from an approximation of the conditional has higher likelihood under the conditional than samples from the marginal, but why should we expect this to lead to better explanations?
5. I thought the idea of looking at feature importance just before clinician intervention was a very clever evaluation, but I wanted the qualitative evaluation to go one step further. That is, does bicarbonate being the most important feature just before administration norepinephrine and fluids make clinical sense? Is this picking up on a specific condition and if so what condition? A clinician could tell you what they are typically reacting to when they administer fluids or vasopressors and you can compare what they say to what the model says. I was surprised to see the top features all being lab measurements as opposed to vital signs. In particular, in a vacuum, I would expect systolic blood pressure to be the most important feature in both of these cases. Is it possible that the frequency of measurements affects which features are selected as important?
6. I thought GHG experiment was *much* better and clearer in this version of the paper. Well done.
7. I recommend moving the notation from the appendix to the main paper. I don't think a reader should have to reference another document to follow notation.
--- Minor comments ---
1. Pg. 3 "The magnitude of our...": I call the authors' definition of feature importance absolute not relative. I would expect a "relative importance" to be a ratio of some sort (e.g. relative risk). 
2. Pg. 5: Figure 8 --> Figure 3