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the most efficient PageRank solvers, and we use it throughout the pre- ceding chapters to compute PageRank vectors for the other sensitivity analyses. Three conclusions from this thesis are: α matters, but don’t pick it; everything is just PageRank, so make it fast; and don’t ignore sensitivity, it could help. In all of the experiments, we pick a value of α. Just as illustrated in the introduction (chapter 1), changing α produces a different PageRank vector. Nothing in this thesis solves this problem. We offer an alternative, however. Don’t pick α. Pick a distribution for a random α instead. Choosing an appropriate distribution does not change the sensitivity be- cause changing the distribution affects the new random PageRank vector, too. Sometimes—like in web search—there is a natural distribution to use. Otherwise, consider a uniform distribution. Even though the distribution may not be perfect, the distribution produces a useful sensitivity measure: the standard deviation. For both sensitivity analyses, the derivative and the standard deviation, the key computational technique was PageRank itself! Using both models reduces to solving a few PageRank problems and then deriving the results from these PageRank vectors. The inner-outer iteration even solves PageRank using PageRank, albeit with a smaller value of α. These results seem like a fluke. But they show the remarkable flexibility of PageRank as a function of α. The devil’s advocate will argue that such results are expected from an exploration of sensitivity analysis. This objection is unfounded. Consider the conversion from the derivative into PageRank problems. It is surprising that this conversion is possible because it depends crucially on the structure of the PageRank problem. Investing the effort in a speedy PageRank solver enables these, and other, experiments. The sensitivity measures helped the spam classification task. Nothing in the design of these measures is tuned to spam identification. This suggests that using the sensitivity vectors in other applications may produce similar improvement. Thus, do not ignore sensitivity. 7.1 discussion Will this thesis matter? Predicting the future is a difficult problem best avoided in this case. Instead, let us critically address a few points raised by this thesis. • IsPageRankresearchstilluseful? • Is picking a distribution for α really helpful? • Whyusesuchstricttolerancesinyourcomputations? • WhatabouttiesinthePageRankvector? We address each question in order. 7.1 ⋅ discussion 145PDF Image | ALGORITHMS FOR PAGERANK SENSITIVITY DISSERTATION
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