diff options
| -rw-r--r-- | paper/rebuttal.txt | 81 |
1 files changed, 30 insertions, 51 deletions
diff --git a/paper/rebuttal.txt b/paper/rebuttal.txt index 8ac4e91..91a3cf5 100644 --- a/paper/rebuttal.txt +++ b/paper/rebuttal.txt @@ -1,10 +1,18 @@ +We would like to thank the reviewers for carefully reading our paper and their +insightful remarks. It seems that most of the major points raised by the +reviewers are due to ambiguity in our presentation, which can easily be +addressed by including a couple of paragraphs of clarifying text. If +appropriate, we would be happy to include these clarifications in the +manuscript and have a reviewer shepherd our paper to ensure we indeed address +all the comments raised. + R2: " -The set of parameters \theta always lies in some constrained space. For example, -in the independent cascade model, \theta_{i,j} < 0; in the voter model, -\sum_{i,j} \theta = 1 and \theta_{i,i} \neq 0.[...] authors would have (norm_1 + -regularization induced by constraints), which is not really clear whether is -decomposable or not. +The set of parameters \theta always lies in some constrained space. For +example, in the independent cascade model, \theta_{i,j} < 0; in the voter +model, \sum_{i,j} \theta = 1 and \theta_{i,i} \neq 0.[...] authors would have +(norm_1 + regularization induced by constraints), which is not really clear +whether is decomposable or not. " This is a great point and we should have been more explicit about this. Overall @@ -48,17 +56,10 @@ time step, defining X_t as the set of nodes active at the previous time step only, and saying that only nodes which have not been infected before are susceptible to be infected. -" -in a continuous-time model there are not necessarily steps and property 1 is not -necessarily satisfied -" -This is a good point and the distinction can be made. - R3: " multiple sources don't make much of a difference in their model, because [...] -if two cascades originate at sources that are more than a constant distance away -from each other, it's the same as two consecutive, independent cascades. +it's the same as two consecutive, independent cascades. " This is an interesting point. However, in the problem we study the graph is unknown to us. Suppose that two cascades start at the same time at two very @@ -66,13 +67,6 @@ different points in the graph. Despite the fact that the infected nodes from each cascade will not overlap, we cannot in practice attribute an infected node to either cascade because we don't know which source is closer to it. -" -Running time is not discussed here. -" -This is a valid point. The MLE algorithm from Netrap.-Sangh. has similar running -time to the penalized MLE algorithm. Their greedy algorithm runs considerably -faster at the price of a slower convergence rate in practice. A precise -comparison of running times can be be included. " The inference in discrete time, one-time-susceptible contagion @@ -83,40 +77,25 @@ is sufficiently flexible to include multiple-time-susceptible contagion processes (such as the linear voter model). Furthermore, it is not immediately clear that discrete-time processes cannot approximate some continuous time processes efficiently. For example, we can discretize the continuous time -process with exponential transmission likelihood by considering intervals of -time of length dt, binning infections to these intervals, and considering that -nodes remain infected until the final observation time. By exploiting the -memoryless property of the exponential distribution, we recover its -discrete-time analog, the geometric distribution. When dt<<1, the problem is -still decomposable and fits into the Generalized Linear Cascade model framework. +process of Gomez-Rodriguez et al. 2011 with exponential transmission likelihood +by considering intervals of time of length dt, binning infections to these +intervals, and considering that nodes remain infected until the final +observation time. By the exponential distribution's memorylessness, it can be +shown that when dt<<1, the problem is still decomposable and fits into the +Generalized Linear Cascade model framework. -" -the unrealistic assumption of one time infection chance. -" -It is true that the standard discrete-time independent cascade model -studied by Netrapalli-Sanghavi assumes one time infection chance but this -restriction is not made at the Generalized Linear Cascade level and is specific -only to the example of section 2.2.1 +We agree that it should be made clear in the definition of cascade models that +we mean discrete-time cascades, and that running time comparison of different +algorithms should be added. Indeed, the MLE from NS has the same running time +as the penalized MLE, but both are slower than the more naive greedy algorithm. -R4: -" -what would be the guaranteed/expected performance given some number of -cascades? -" -This is an interesting point. For the experiment section, we could calculate the -theoretical guarantees for the synthetic graphs and observe whether or not the -theoretical bounds are pessimistic in practice. - -" -Where is the explanation about Figure 1(f)? What is p_init? -" -This is a typo. It should read "n" the number of cascades. -" -The authors need to show at least one common metric for all types for graphs -" -This is an interesting point: A graph plotting the same metric for all -considered networks can replace one of the 6 figures. +R4: +Reviewer 4 raised the point of showing expected performance given some +number of cascades, which could be added to the existing simulations. +Figure 1(f) does have a typo, it should read "n" the number of cascades. +Finally, we agree that showing "at least one common metric for all +types of graph" should be added to the experimental section. Misc. " |