Learning Unfaithful $K$-separable Gaussian Graphical Models
Authors: De Wen Soh, Sekhar Tatikonda
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We propose an algorithm to test the faithfulness of a conditional independence relation of the form Xu Xv | XS, where Xu, Xv and XS are the random variables associated with the nodes u, v and the node set S. This algorithm uses other conditional independence relations of the form Xi Xj | XS, where i, j / S to determine this. The faithfulness test does not require any assumption on the population version of covariance matrix Σ and can be applied to any Gaussian graphical model. To the best of our knowledge, this is the first algorithm that uses local information of a matrix to test for the faithfulness of a conditional independence relation. We also provide sample complexity bounds for this algorithm. We propose a structure learning algorithm for weakly K-separable Gaussian graphical models. [...] We propose a precision matrix learning algorithm for strongly K-separable Gaussian graphical models. This algorithm not only learns the structure of the graph, it learns the entries of the precision matrix (edge weights) as well. [...] In this section, we will examine some examples where our algorithm can perform structural estimation while others that rely on sparsity cannot. |
| Researcher Affiliation | Academia | De Wen Soh EMAIL Institute of High Performance Computing 1 Fusionopolis Way, #16-16 Connexis Singapore, 138632 Sekhar Tatikonda EMAIL Department of Electrical Engineering Yale University New Haven, CT 06511, USA |
| Pseudocode | Yes | Algorithm 1: Testing Faithfulness of Relation Xu Xv | XS Algorithm 2: Learning topology of weakly K-separable GGM Algorithm 3: Learning the precision matrix of strongly K-separable GGM |
| Open Source Code | No | The paper does not provide any explicit statements about releasing code, nor does it provide links to a code repository or mention code in supplementary materials. |
| Open Datasets | No | The paper uses synthetic examples, such as '4-dimensional Gaussian distribution' and '6-dimensional Gaussian distribution', but does not mention or provide access information for any publicly available or open datasets. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments on datasets, therefore, it does not specify any dataset splits. |
| Hardware Specification | No | The paper is theoretical and focuses on algorithm design and theoretical guarantees. It does not describe any experiments that would require specific hardware, thus no hardware specifications are provided. |
| Software Dependencies | No | The paper is theoretical and focuses on algorithm design. It does not mention any specific software dependencies with version numbers that would be required to reproduce experiments. |
| Experiment Setup | No | The paper focuses on theoretical algorithms and their properties, rather than empirical experiments. Therefore, it does not provide details on experimental setup, hyperparameters, or training configurations. |