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(section 4.2). We also present an empirically measured distribution of α values for around 2,000,000 people (section 4.5) and show that the standard deviation vector aids a spam classification task (section 4.8.4). This chapter contains rigorous error analysis and convergence theory for all of the algorithmic techniques (section 4.7). pagerank solvers Third, the problem of computing a PageRank vector for a particular value of α can be formulated as computing a sequence of PageRank vectors with a β smaller than α. To wit, PageRank with 0 < β < α solves PageRank at any desired α. The resulting inner-outer iteration for PageRank is discussed in chapter 5. Sensitivity does not arise directly in these ideas. Rather, the interplay of α and β in an efficient computation depends on many ideas related to the structure of the PageRank function itself, which inevitably leads to some sen- sitivity interpretations. The inner-outer computation is also one of 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 161PDF Image | Instagram Cheat Sheet
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