
| # iterations   | time (s)   |       |
|----------------|------------|-------|
| ICDM           | 13         | 0.35  |
| KDD            | 13         | 0.50  |
| Pubmed         | 15         | 1.21  |
| Mushroom       | 35         | 0.012 |
| Retail         | 18         | 2.0   |
| Pumsb          | 36         | 0.10  |
| Pumsb star     | 37         | 0.94  |
| Connect        | 33         | 0.048 |
| T10I4D100K     | 34         | 2.0   |
| T40I10D100K    | 33         | 5.3   |

one global measure from these results, as in Gionis et al (2007), and compute an empirical p-value by comparing that measure obtained on the actual data with the result on the randomized versions. However, the plots given here do not force one to make such a choice, and they still give a good idea about which itemset sizes are significant in the datasets.

Figure 3 also shows averages and error bars for the results obtained on databases randomized using swaps, done using the code from Gionis **et al (2007)** and using five times the number of nonzero database entries (as recommended in Gionis et al (2007)). It can be noted that the error bars strongly overlap in most cases. The difference between the two randomization strategies is largest for the mushroom dataset. Interestingly, this is a dataset where **the transaction** sizes are fixed, such that the MaxEnt modeling approach may indeed **yield** qualitatively different results as compared to the swap randomization approach. Indeed, sampling from the MaxEnt model only conserves the transaction sizes in expectation. A way around this problem is sketched at the end of Sec. 5.1.

Computational cost compared to swap randomizations **The above shows**
that randomizing databases using swap randomizations leads to results similar to those obtained by sampling from a fitted MaxEnt model. However, the MaxEnt strategy is five to fifteen times more efficient in generating one randomized database (including the overhead for fitting the MaxEnt model), and about thirty times more efficient when several randomized databases need to be sampled. These computational results are summarized in Fig. 4.

## 7.2 The Maxent Model For Various Types Of Networks

Artificially generated power-law networks To assess the feasibility of using the MaxEnt modeling strategy for networks, we artificially generated powerlaw (weighted) degree distributions for networks of various sizes between n **= 10**