Reconstructing Undirected Graphs from Eigenspaces
Authors: Yohann De Castro, Thibault Espinasse, Paul Rochet
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments on simulated data (Section 5) and actual data (Section 6) assess the performances of our new estimation method. |
| Researcher Affiliation | Academia | Yohann De Castro EMAIL Laboratoire de Mathematiques d Orsay, Univ. Paris-Sud, CNRS, Universite Paris-Saclay, F-91405 Orsay, France; Thibault Espinasse EMAIL Institut Camille Jordan (CNRS UMR 5208), Universite Claude Bernard Lyon 1, F-69622 Villeurbanne, France; Paul Rochet EMAIL Laboratoire de Mathematiques Jean Leray (CNRS UMR 6629), Universite de Nantes, F-44322 Nantes, France |
| Pseudocode | Yes | Algorithm 1: Backward algorithm for support selection; Algorithm 2: Bagging backward algorithm |
| Open Source Code | No | On the current version, the bagging backward algorithm contains scalability issues for big graphs due to its space complexity. Leads to reduce the spatial complexity include using sparse matrix encoding although this was not implemented. These shall be investigated in future works. |
| Open Datasets | No | We now implement the bagging backward algorithm on real life data provided by Meteorage and Meteo France. The data contain the daily number of lightnings during a 3 year period in 16 regions of France localized on a 4 x 4 grid. |
| Dataset Splits | No | We generate a training sample by taking each observation with probability 1/2 independently, from the whole sample. The estimator of K in this subsample is denoted e K. We implement Algorithm 1 on e K, yielding a trajectory S1 ... Sl of nested supports whose sizes vary from |S1| = 20 (the full off-diagonal support) to |Sl| = 12 (the minimal size required for diagonal identifiability), along with the associated estimators e WSk, k = 1, ..., l. |
| Hardware Specification | Yes | The average computational time (obtained with the function timer of Scilab) on a processor Intel Xeon @2.6 GHz are shown |
| Software Dependencies | No | The average computational time (obtained with the function timer of Scilab) on a processor Intel Xeon @2.6 GHz are shown. While Scilab is mentioned, no version number is provided for it or any other software dependency for replication of the methodology. |
| Experiment Setup | Yes | Here, we consider the graph G1 represented in Figure 4, the kite graph on 5 vertices. We choose W as the (normalized) adjacency matrix of G1 then draw a sample of size n = 500 of centered Gaussian vectors X1, Xn of R5 with covariance matrix K = exp(W). ... a sample of size n = 10000 is drawn from a centered Gaussian vector of variance K = exp(W) ... M = 100 training samples drawn keeping observations with probability 1/2. For each m = 1, ..., M, we retain the threshold tm = Crit( b WS1m, b K) ... and the estimated support, that is, the smallest support b Sm in the trajectory such that Crit( b Wb Sm, b K) tm. ... we chose q = 2/M empirically. |