How to sample undirected graph/network data? - Cross Validated most recent 30 from stats.stackexchange.com 2019-07-18T04:43:35Z https://stats.stackexchange.com/feeds/question/315651 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://stats.stackexchange.com/q/315651 0 How to sample undirected graph/network data? Haohan Wang https://stats.stackexchange.com/users/42004 2017-11-25T21:18:13Z 2017-11-25T21:18:13Z <p>I recently want to test my network estimation algorithms and need to sample some data from undirected graphs. </p> <p>The natural way I think of was:</p> <ol> <li>Generate a sparse symmetric Precision matrix $P$. </li> <li>Calculate SVD: $P=USV^T$</li> <li>adding a constant $\hat{S}=S+c$ to make sure min$(\hat{S})\geq 0$. (So $c$ can be determined very with constant time since it will be 0 if min$(S)\geq 0$ and will be $|$min$(S)$$|$ otherwise.) </li> <li>$\Sigma=(U\hat{S}V^T)^{-1}$ and sample data with $\Sigma$ as covariance. </li> </ol> <p>However, I found that $U\hat{S}V^T$ is always quite dense, which is not ideal. </p> <p>Alternatively, it seems a better way is to use $\hat{P}=P+\lambda I$ for the minimum positive $\lambda$ for $\hat{P}$ to be p.s.d. But how should I find the optimal $\lambda$?</p> <p>Actually, I am not sure I understand why these two methods are different. Can someone please also explain that?</p>