Figure 5: Comparison of GenStat architecture to selected graph generative models. This proof uses two properties of LDP: composability and immunity to post-processing [2]. Figure 6 illustrates the PGM of Randomized algorithms. The GGM parameters are a function of the perturbed graph statistics as learning input. The implementation can be easily extended to directed graphs. A statistics-based GGM that takes the degree sequence as sufficient statistics [5].

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MIPS is a challenging problem as modern datasets often have high dimensionality and large cardinality. Initially, tree-based methods [Ram and Gray, 2012, Koenigstein et al., 2012] were proposed for MIPS, which use the idea of branch and bound similar to k-d tree [Friedman and Tukey, 1974].

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We still need to demonstrate that the properties in P AC-Bayes analysis hold for both the margin operator and the robust margin operator. Then we complete the proof of Lemma 6.1. The proof of Lemma 7.1 and 7.2 is similar. We provide the proof of Lemma 7.2 below. Lemma 7.1 follows the proof of Lemma 7.2 by replacing the robust margin operator by the margin Since the above bound holds for any x in the domain X, we can get the following a.s.: R The second inequality is the tail bound above.

While the object detection task requires a huge number of annotated samples to guarantee its performance, placing bounding boxes for every object in each sample is time-consuming and costs alot.