3,042 research outputs found
The skew energy of random oriented graphs
Given a graph , let be an oriented graph of with the
orientation and skew-adjacency matrix . The skew energy
of the oriented graph , denoted by , is
defined as the sum of the absolute values of all the eigenvalues of
. In this paper, we study the skew energy of random oriented
graphs and formulate an exact estimate of the skew energy for almost all
oriented graphs by generalizing Wigner's semicircle law. Moreover, we consider
the skew energy of random regular oriented graphs , and get an
exact estimate of the skew energy for almost all regular oriented graphs.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1011.6646 by
other author
Rainbow -connectivity of random bipartite graphs
A path in an edge-colored graph is called a rainbow path if no two edges
of the path are colored the same. The minimum number of colors required to
color the edges of such that every pair of vertices are connected by at
least internally vertex-disjoint rainbow paths is called the rainbow
-connectivity of the graph , denoted by . For the random graph
, He and Liang got a sharp threshold function for the property
. In this paper, we extend this result to the case of
random bipartite graph .Comment: 15 pages. arXiv admin note: text overlap with arXiv:1012.1942 by
other author
False Discovery Rate Controlled Heterogeneous Treatment Effect Detection for Online Controlled Experiments
Online controlled experiments (a.k.a. A/B testing) have been used as the
mantra for data-driven decision making on feature changing and product shipping
in many Internet companies. However, it is still a great challenge to
systematically measure how every code or feature change impacts millions of
users with great heterogeneity (e.g. countries, ages, devices). The most
commonly used A/B testing framework in many companies is based on Average
Treatment Effect (ATE), which cannot detect the heterogeneity of treatment
effect on users with different characteristics. In this paper, we propose
statistical methods that can systematically and accurately identify
Heterogeneous Treatment Effect (HTE) of any user cohort of interest (e.g.
mobile device type, country), and determine which factors (e.g. age, gender) of
users contribute to the heterogeneity of the treatment effect in an A/B test.
By applying these methods on both simulation data and real-world
experimentation data, we show how they work robustly with controlled low False
Discover Rate (FDR), and at the same time, provides us with useful insights
about the heterogeneity of identified user groups. We have deployed a toolkit
based on these methods, and have used it to measure the Heterogeneous Treatment
Effect of many A/B tests at Snap
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