Nonparametric Modeling of Higher-Order Interactions via Hypergraphons
Authors: Krishnakumar Balasubramanian
JMLR 2021 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Simulation results are provided to corroborate the theory. ... We now provide simulation results depicting the performance of our algorithm for the case when the random graphs are generated from the following two simple hypergraphons: Case 1: f(u, v, w) = uvw Case 2: f(u, v, w) = 1 1 + e{ (c1u2+c2v2+c3w2)} ... Our error metric is the normalized L2 reconstruction error... For our experiments, we use the the GPS dataset (Zheng et al., 2010) and the Movie Lens dataset (Harper and Konstan, 2015). |
| Researcher Affiliation | Academia | Krishnakumar Balasubramanian EMAIL Department of Statistics University of California Davis, CA 95616 USA |
| Pseudocode | Yes | Algorithm 1 Alternating Minimization for hypergraphon Input: A, k. Let Eia be the number of hyperedges containing both i and a member of a according to the current ˆz. j2 ˆz( 1)(a) j3, ,jm [n] Aij2 jm (4) Update ˆz as ˆz(i) = argmax a 1 κa Eia where κa is defined in Equation 5. until Convergence Compute ˆQa = 1 ηa P j ˆz( 1)(a) Aj Output: ˆQa and ˆz. |
| Open Source Code | No | The theoretical analysis of this algorithm is more involved than the standard graph based stochastic block model case. We plan to report the theoretical results in the context of community detection in hypergraphs in the near future. The paper does not provide concrete access to source code for the methodology described. |
| Open Datasets | Yes | For our experiments, we use the the GPS dataset (Zheng et al., 2010) and the Movie Lens dataset (Harper and Konstan, 2015). |
| Dataset Splits | Yes | For the sake of experiments, we randomly pick 70%, 80% and 90% and treat them as observed data. |
| Hardware Specification | No | In this section, we compare the wall-clock times of random-initialization method for the above experiments. The paper does not provide specific hardware details (like CPU/GPU models) used for running its experiments. |
| Software Dependencies | No | The paper does not explicitly state any software dependencies with version numbers. |
| Experiment Setup | Yes | The value of ρn was set to 1 and 0.7 in Figure 1 and 2 respectively... The value of k was fixed at 0.6 n3 and 0.5 n3 in Figure 1 and 2 respectively... We experimented with both random initialization and spectral initialization... We considered n = 20... We use hypergraphs samples from both case 1 and 2 hypergraphons and increase k from 0.1 n3 to 0.9 n3 in steps of 0.1. |