Functional Directed Acyclic Graphs
Authors: Kuang-Yao Lee, Lexin Li, Bing Li
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the efficacy of our method through both simulations and an application to a time-course proteomic dataset. Keywords: Graphical model, faithfulness, functional regression, linear operator, reproducing kernel Hilbert space, uniform consistency. 6. Numerical studies We first evaluate the empirical performance of the proposed method through two simulation examples, then illustrate with an analysis of a time-course proteomic dataset. 6.1 Simulations 6.2 Proteomic application |
| Researcher Affiliation | Academia | Kuang-Yao Lee EMAIL Department of Statistics, Operations, and Data Science Temple University Philadelphia, PA 19122, USA Lexin Li EMAIL Department of Biostatistics and Epidemiology University of California at Berkeley Berkeley, CA 94720, USA Bing Li EMAIL Department of Statistics Pennsylvannia State University University Park, PA 16802, USA |
| Pseudocode | Yes | Algorithm 1 Evaluation of Xi Xj | XS for a given triplet (i, j, S) H0. Algorithm 2 Step 1 of the PC-algorithm |
| Open Source Code | No | The paper mentions the existence of supplementary material for 'technical proofs and additional numerical results' in the Appendix, but it does not provide any explicit statements about releasing source code for the methodology described in the paper, nor does it include a link to a code repository. |
| Open Datasets | Yes | We illustrate our method with a DREAM breast cancer proteomic dataset (https://www.synapse.org/#!Synapse:syn1720047/wiki/56213). |
| Dataset Splits | No | For the proteomic dataset, the paper states: 'the data consists of n = 48 subjects, each with p = 20 protein levels measured at m = 11 time points.' This describes the dataset's overall structure and size but does not specify any explicit training, validation, or test splits. The simulation section describes how data was generated but does not mention splitting strategies for evaluation. |
| Hardware Specification | Yes | On a 2 x E5-2630 v4 workstation, the average running time of our method is 6.31 seconds, and that of SEM is 18.64 seconds. |
| Software Dependencies | No | The paper discusses various methods and tools used for comparison (e.g., linear-PC, rank-PC, CAM, SEM, Qiao et al. (2019)) and describes mathematical operations, but it does not specify version numbers for any software libraries, frameworks, or programming languages used in the implementation of their proposed methodology. |
| Experiment Setup | Yes | Algorithm 1 Evaluation of Xi Xj | XS for a given triplet (i, j, S) H0. ... 2: Compute the coordinate [Xk i ] using (6), for i V, k = 1, . . . , n, where the ridge parameter is set as ϵk T = 0.01 σmax[b1:r(Tk)b1:r(Tk)T], k = 1, . . . , n, with σmax( ) denoting the largest eigenvalue. 3: ... the parameter d is set as d = [n1/5]. Then obtain Ca i , C1:d i , and CS. 4: Compute the coordinates of ˆΣ d,ϵ Xi Xj|XS and ˆR d,ϵ,δ Xi Xj|XS using (8) and (9), where the tuning parameters are set at ϵ = 0.1 σmax(CSCT S ), and δ = 0.5 max{σmax[Mi,i|S(ϵ)], σmax[Mj,j|S(ϵ)]}. 5: Evaluate Xi Xj | XS using (10), where we take ρCCO = c 1 (n |S| 3) 1/2, and ρPCO = Φ 1(1 c/2) (n |S| 3) 1/2, with Φ( ) being the normal cumulative distribution function, 0 < c < 1 being a constant and set as c = 0.05. |