Separability Analysis for Causal Discovery in Mixture of DAGs
Authors: Burak Varici, Dmitriy Katz, Dennis Wei, Prasanna Sattigeri, Ali Tajer
TMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate the performance of Algorithm 1 for estimating the skeleton of the mixture graph and partially orienting the recovered edges using synthetic data. To generate G1 and G2, we use Erd os-Rényi model with G(n, p) with density p = 2/n for n {6, 8} for each of the component DAGs. We repeat sampling graphs from Erd os-Rényi model until both G1 and G2 have tree structures. ... We repeat this experimental procedure for 500 randomly generated G1 and G2 tree pairs and report the average results. We investigate the effects of the choice of CI test and varying mixing rate of two component distributions in Appendix C. Figure 4 illustrates the precision and recall rates for recovering the skeleton EM with varying numbers of samples for n = 6 and n = 8. Figure 5: Orientation recovery rates |
| Researcher Affiliation | Collaboration | Burak Varıcı EMAIL Electrical, Computer, and Systems Engineering Rensselaer Polytechnic Institute Dmitriy Katz-Rogozhnikov EMAIL IBM Research AI Dennis Wei EMAIL IBM Research AI Prasanna Sattigeri EMAIL IBM Research AI Ali Tajer EMAIL Electrical, Computer, and Systems Engineering Rensselaer Polytechnic Institute |
| Pseudocode | Yes | Algorithm 1 1: Input: Samples from mixture distribution p M, ˆ 2: Stage 1: Skeleton of GM = (V, EM) 3: Form complete undirected graph: EM {(i j) : i V, j V} 4: for all i, j V do |
| Open Source Code | No | The paper does not provide any explicit statement about releasing code, nor does it include a link to a code repository. The OpenReview link provided is for paper review, not code. |
| Open Datasets | No | To generate G1 and G2, we use Erd os-Rényi model with G(n, p) with density p = 2/n for n {6, 8} for each of the component DAGs. We repeat sampling graphs from Erd os-Rényi model until both G1 and G2 have tree structures. |
| Dataset Splits | No | The paper uses synthetic data generated using an Erd os-Rényi model and linear SEM. It specifies the number of samples generated for each component DAG (s {1e3, 3e3, 1e4, 3e4, 5e4, 1e5}) but does not define training, validation, or test splits of a fixed dataset. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU, GPU models, memory) used to run the experiments. |
| Software Dependencies | No | The paper mentions using a 'partial correlation test as a conditional independence test routine' but does not specify any software names with version numbers for this or other components used in the implementation. |
| Experiment Setup | Yes | To generate G1 and G2, we use Erd os-Rényi model with G(n, p) with density p = 2/n for n {6, 8} for each of the component DAGs. ... For the causal relationships, we follow linear structural equation models (SEM) with additive Gaussian noise for both component DAGs. Edge weights are sampled uniformly in [0.25, 2], and shared directed edges between two graphs are assigned the same weights. The mean of the Gaussian noise for each node is sampled uniformly in [ 2, 2] with a standard deviation of 1 and set to be equal in both graphs. ... The threshold for the p-value of the CI test is set to α = 0.1. For each case, we run the algorithm with s {1e3, 3e3, 1e4, 3e4, 5e4, 1e5} number of samples from each component DAG. We repeat this experimental procedure for 500 randomly generated G1 and G2 tree pairs and report the average results. |