Tournament revelation problem 1CDreport the heaviest edgeBCeliminate Breport the heaviest edgeADeliminate Areport the heaviest edgeCD Tournament revelation problem 123ACDreport the heaviest edgeBCeliminate Breport the heaviest edgeAD Tournament revelation problem 123ACDreport the heaviest edgeBCeliminate Breport the heaviest edge Tournament revelation problem 123456ABCDreport the heaviest edgeBC Tournament revelation problem 123456ABCDreport the heaviest edge OBJECTIVE: minimize total time spent generating reports What is bad data ?g = TRUTHh = DATA (empirical density)| h-g |1 = 2max |h(A)-g(A)|AY(F)Y(F) = Yatracos class of F Aij= in G1 ADVERSARY eliminates u2 or v2 G2. Obstacles to quality:DATA+weak class of densitiesbad dataFdist1(g,F)? Measure of quality:L1 distance from the truthWhy L1? |f-g|1 = |f(x)-g(x)| dx1) small L1 all events estimated with small additive error2) scale invariantg=TRUTH f=OUTPUT Satyaki MahalanabisDaniel tefankoviUniversity of RochesterDensity estimation in linear time(+approximating L1-distances)ĭensity estimationDATA+f1f2f3f4f5f6density F = a family of densitiesĭensity estimation - example + N(,1)0.418974, 0.848565, 1.73705, 1.59579, -1.18767, -1.05573, -1.36625F = a family of normal densities with =1
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