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| -rw-r--r-- | paper/rebuttal.txt | 46 |
1 files changed, 22 insertions, 24 deletions
diff --git a/paper/rebuttal.txt b/paper/rebuttal.txt index 25a9e62..1d56b36 100644 --- a/paper/rebuttal.txt +++ b/paper/rebuttal.txt @@ -2,19 +2,17 @@ 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.[...] If the authors incorporate -the constraints on the model parameters, it is not clear whether [Neghahba, -2012] will be applicable anymore since it assumes decomposable regularizers. -However, the authors would have (norm_1 + regularization induced by -constraints), which is not really clear whether is decomposable or not. +\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. " -ANS:TODO +This is a great point. In fact, the sign constraints are implicit since the +log-likelihood is undefined if these constraints are violated... " In the independent cascade model, nodes have one chance to infect their neighbors. However, the definition in section 2.2.1. seems to allow for multiple -attempts, since at any given time t+1, the probability depends on \theta_j -X_t +attempts " As the reviewer correctly points out, the standard ICC model does not allow for multiple infection attempts over time. The definition of section 2.2.1 also @@ -31,9 +29,9 @@ 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 [...]. -So 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. +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. " 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 @@ -53,16 +51,16 @@ comparison of running times can be be included. The inference in discrete time, one-time-susceptible contagion processes is less interesting and easier than the continuos version. " -This is an interesting point. Some things to note are: the generalized cascade -model class 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 +This is an interesting point. We note that the generalized cascade model class +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. " @@ -78,9 +76,9 @@ 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. +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? |