A Junction Tree Framework for Undirected Graphical Model Selection
Authors: Divyanshu Vats, Robert D. Nowak
JMLR 2014 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Section 8 presents numerical simulations to highlight the advantages of using junction trees for UGMS in practice. We applied our methods to the data set in Choi et al. (2011) of n = 216 monthly stock returns of p = 85 companies in the S&P 100. The gene expression data we study is the Lymph node status data which contains n = 148 expression values from p = 587 genes (Li and Toh, 2010). |
| Researcher Affiliation | Academia | Divyanshu Vats EMAIL Department of Electrical and Computer Engineering Rice University Houston, TX 77005, USA. Robert D. Nowak EMAIL Department of Electrical and Computer Engineering University of Wisconsin Madison Madison, WI 53706, USA. |
| Pseudocode | Yes | Algorithm 1: Constructing region graphs. Algorithm 2: UGMS over regions in a region graph. Algorithm 3: Junction Tree Framework for UGMS. Algorithm 4: PC-Algorithm for UGMS: PC(κ, Xn, H, L). |
| Open Source Code | Yes | All the data and code used in our numerical simulations can be found at http://www.ima.umn.edu/~dvats/Junction Tree UGMS.html. |
| Open Datasets | Yes | We applied our methods to the data set in Choi et al. (2011) of n = 216 monthly stock returns of p = 85 companies in the S&P 100. The gene expression data we study is the Lymph node status data which contains n = 148 expression values from p = 587 genes (Li and Toh, 2010). |
| Dataset Splits | Yes | The thresholds for the conditional independence test are computed using 5-fold cross-validation. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running experiments. It mentions numerical simulations but no concrete specifications like GPU/CPU models or memory. |
| Software Dependencies | No | The paper mentions using algorithms like graphical Lasso, neighborhood selection using Lasso, and the PC-Algorithm. It also refers to EBIC and adaptive Lasso. However, it does not provide specific version numbers for any software libraries, packages, or programming languages used in the implementation. |
| Experiment Setup | Yes | We assume that Θii = 1 for all i = 1, . . . , p. For CH1, ρ1 = 0.15 and ρ2 = 0.245. For CH2, ρ1 = 0.075 and ρ2 = 0.245. We use EBIC with γ = 0.5 to choose regularization parameters when estimating graphs using Jg L and JPC. When applying PC and JPC, we choose κ as 1, 2, 1, and 3 for Chain, Cycle, Hub, and Neighborhood graphs, respectively. When computing H, we choose κ as 0, 1, 0, and 2 for Chain, Cycle, Hub, and Neighborhood graphs, respectively. Whenever |R| is small (less than 8 in our simulations), we independently test whether each edge is in G using hypothesis testing. |