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# CS代写|计算机网络代写Computer Networking代考|CSEE4119 Event Simulation Methodology

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## CS代写|计算机网络代写Computer Networking代考|Event Simulation Methodology

A suitable method for evaluating the efficacy of our approach is to simulate correlated events
on graphs and see if we can correctly detect correlations. Specifically, we adopt similar methodologies as those used in the analogous point pattern problem (Diggle and Cox, 1983) to generate pairs of events with positive and negative correlations on graphs. The DBLP network is used as the test bed. We investigate correlations with respect to different vicinity levels $h=1,2,3$. Positively correlated event pairs are generated in a linked pair fashion: We randomly select 5000 nodes from the graph as event $a$, and each node $v \in V_a$ has an associated event $b$ node whose distance to $v$ is described by a Gaussian distribution with mean zero and variance equal to $h$ (distances go beyond $h$ are set to $h$ ). When the distance is decided, we randomly pick a node at that distance from $v$ as the associated event $b$ node. This represents strong positive correlations since wherever we observe an event $a$, there is always a nearby event $b$. For negative correlation, again we first generate 5000 event $a$ nodes randomly, after which we employ Batch_BFS to retrieve the nodes in the $h$-vicinity of $V_a$, that is, $V_a^h$. Then, we randomly color 5000 nodes in $V \backslash V_a^h$ as having event $b$. In this way, every node of $b$ is kept at least $h+1$ hops away from all nodes of $a$ and the two events exhibit a strong negative correlation. For each vicinity level, we generate 100 positive event pairs and 100 negative event pairs from the simulation processes, respectively. We use recall as the evaluation metric which is defined as the number of correctly detected event pairs divided by the total number of event pairs (100). We report results obtained from one-tailed tests with significance level $\alpha=0.05$. In our experiments, we empirically set the sample size of reference nodes $n=900$.

## CS代写|计算机网络代写Computer Networking代考|Performance Comparison

We investigate the performance of three reference node sampling algorithms, namely, Batch_BFS, Importance sampling, and Whole-graph sampling, under different vicinity levels and different noise levels. Noises are introduced as follows. Regarding positive correlation, we introduce a sequence of independent Bernoulli trails, one for each linked pair of event nodes, in which with probability $p$ the pair is broken and the node of $b$ is relocated outside $V_a^h$. For negative correlation, given an event pair each node in $V_b$ has probability $p$ to be relocated and attached with one node in $V_a$. The probability $p$ controls to what extent noises are introduced and can be regarded as noise level.
We show the experimental results in Figures $2.15$ and $2.16$, for positive correlation and negative correlation, respectively. As can be seen, overall the performance curves start from $100 \%$ and fall off as the noise level increases. This indicates that the proposed statistical testing approach is efficacious for measuring TESC. Among the three reference node sampling algorithms, Batch_BFS achieves relatively better performance. Importance sampling, though not as good as Batch_BFS, can also achieve acceptable recall, especially for $h=1,2$. We shall show in Section 2.4.4.6 that Importance sampling is more efficient than Batch_BFS in many cases. Whole-graph sampling also shows good recall in most cases, as expected. However, its running time can vary drastically and therefore it can only be applied in limited scenarios. An interesting phenomenon is that positive correlations for higher vicinity levels (e.g., 3) are harder to break than those for lower levels, while for negative correlations it is the reverse: Lower level ones are harder to break. Note that the noise level ranges in figures of Figures $2.15$ and $2.16$ are not the same. This is intuitive. Consider the size of $V_a^h$. When $h$ increases, $\left|V_a^h\right|$ usually increases exponentially. For example, among our synthetic events in DBLP graph, the typical size of $V_a^1$ is $60 \mathrm{k}$, while that of $V_a^3$ is $700 \mathrm{k}\left(7 / 10\right.$ of the whole graph), for $\left|V_a\right|=5000$. Hence, it is much harder for event $b$ to “escape” event $a$ for the higher vicinity levels. On the contrary, for $h=1$ it is easier to find a node whose 1-vicinity does not even overlap with $V_a^1$. Hence, low vicinity level positive correlations and high vicinity level negative correlations are hard to maintain and consequently more interesting than those in other cases. In the following experiment on real events, we will focus on these interesting cases.

## CS代写|计算机网络代写Computer Networking代写;|Performance Comparison

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