

![0_image_0.png](0_image_0.png)

configuration according to the previous results. We compare Z∅ **also with anyTLSBP, a**
variant of our previous algorithm for truncating the loop series. We run anyTLSBP by selecting loops shorter than a given length, and the length is increased progressively. To provide a fair comparison between both methods, we run anyTLSBP for the same amount of cpu time as the one required to obtain Z∅.

Figure 7a shows the errors of different methods. Since variability in the errors is larger than before, we take the median for comparison. In order of increasing accuracy we get BP, TreeEP, anyTLSBP, CVM-Loop6, CVM-Loop4 and Z∅**. We note that larger clusters**
in CVM does not necessarily result in better performance.

Overall, we can see that results are roughly independent of the network size N **in almost**
all methods that we compare. The error of anyTLSBP starts being the smallest but soon increases because the proportion of loops captured decreases very fast. For N > 64, anyTLSBP performs worse than CVM. The Z∅ **correction, on the other hand, stays flat and** we can conclude that it scales reasonably well. Interestingly, although Z∅ **and TLSBP use**
different ways to truncate the loop series, both methods show similar scaling behavior for large graphs.

Figure 7b shows the cpu time for all the tested approaches averaged over all cases.

Concerning the approximate inference methods, in order of increasing cost, we have BP,
TreeEP, CVM-Loop4, Z∅ with anyTLSBP, and CVM-Loop6. Although the cpu time required to compute Z∅scales with O(N3Gext
), its curve shows the steepest growth. We discuss how to correct this caveat in Section 4. The cpu time of the junction tree method quickly