Testing Unfaithful Gaussian Graphical Models
Authors: De Wen Soh, Sekhar C Tatikonda
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper we provide a characterization of faithful relations and then provide an algorithm to test faithfulness based only on knowledge of other conditional relations of the form Xi Xj | XS. Our algorithm is the first algorithm, to the best of our knowledge, that is able to distinguish between faithful and unfaithful conditional independence relations without any restrictions on the topology or assumptions on spatial mixing of the Gaussian graphical model. |
| Researcher Affiliation | Academia | De Wen Soh Department of Electrical Engineering Yale University 17 Hillhouse Ave, New Haven, CT 06511 dewen.soh@yale.edu Sekhar Tatikonda Department of Electrical Engineering Yale University 17 Hillhouse Ave, New Haven, CT 06511 sekhar.tatikonda@yale.edu |
| Pseudocode | Yes | Algorithm 1 (Testing Faithfulness) Input covariance matrix Σ. 1. Define new graph G = { W, E}, where W = W \ S and E = {(i, j) : i, j W \ S, Xi Xj | XS, i = j}. 2. Generate set U to be the set of all nodes in W that are connected to u by a path in G, including u. (A breadth-first search could be used.) 3. If v U, there exists a path from u to v in G, output Xu Xv | XS as unfaithful. 4. If v / U, let V = W \ U. Output Xu Xv | XS as faithful. Algorithm 2 (Edge Learning) Input covariance matrix Σ. For each node pair (i, j), 1. Let F = {S W \ {i, j} : |S| = K, Xi Xj | XS, and it is faithful}. 2. If F = φ, output (i, j) / E. If F = φ, output (i, j) E. 3. Output E. |
| Open Source Code | No | The paper does not provide any statement or link indicating that the source code for the methodology is openly available. |
| Open Datasets | No | The paper uses illustrative examples with specific covariance matrices (e.g., in Example 1 and Example 3), which are not described as publicly available datasets or provided with access information. |
| Dataset Splits | No | The paper does not provide any information regarding training, validation, or test dataset splits, as it focuses on theoretical algorithms illustrated with examples rather than empirical evaluation on partitioned datasets. |
| Hardware Specification | No | The paper does not include any specific hardware details used for running experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers required to replicate the work. |
| Experiment Setup | No | The paper does not provide specific experimental setup details, such as hyperparameters or system-level training settings, as it is a theoretical paper illustrated with examples rather than full-scale experiments. |