Estimating Diffusion Network Structures: Recovery Conditions, Sample Complexity & Soft-thresholding Algorithm
Authors: Hadi Daneshmand, Manuel Gomez-Rodriguez, Le Song, Bernhard Schoelkopf
ICML 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 8. Experiments In this section, we first illustrate some consequences of Th. 2 by applying our algorithm to several types of networks, parameters (n, p, d), and regularization parameter λn. Then, we compare our algorithm to two different stateof-the-art algorithms: NETRATE (Gomez-Rodriguez et al., 2011) and First-Edge (Abrahao et al., 2013). Experimental Setup We focus on synthetic networks that mimic the structure of real-world diffusion networks in particular, social networks. We consider two models of directed real-world social networks: the Forest Fire model (Barab asi & Albert, 1999) and the Kronecker Graph model (Leskovec et al., 2010), and use simple pairwise transmission models such as exponential, power-law or Rayleigh. We use networks with 128 nodes and, for each edge, we draw its associated transmission rate from a uniform distribution U(0.5, 1.5). We proceed as follows: we generate a network G and transmission rates A , simulate a set of cascades and, for each cascade, record the node infection times. Then, given the infection times, we infer a network ˆG. Finally, when we illustrate the consequences of Th. 2, we evaluate the accuracy of the inferred neighborhood of a node ˆ N (i) using probability of success P( ˆE = E ), estimated by running our method of 100 independent cascade sets. When we compare our algorithm to NETRATE and First-Edge, we use the F1 score, which is defined as 2PR/(P + R), where precision (P) is the fraction of edges in the inferred network ˆG present in the true network G , and recall (R) is the fraction of edges of the true network G present in the inferred network ˆG. |
| Researcher Affiliation | Academia | Hadi Daneshmand1 HADI.DANESHMAND@TUE.MPG.DE Manuel Gomez-Rodriguez1 MANUELGR@TUE.MPG.DE Le Song2 LSONG@CC.GATECH.EDU Bernhard Sch olkopf1 BS@TUE.MPG.DE 1MPI for Intelligent Systems and 2Georgia Institute of Technology |
| Pseudocode | Yes | Algorithm 1 ℓ1-regularized network inference |
| Open Source Code | No | The paper does not provide any explicit statements about releasing source code or links to a code repository. |
| Open Datasets | No | The paper uses 'synthetic networks' generated using models like 'Forest Fire model' and 'Kronecker Graph model'. It does not provide access information (link, DOI, citation) to a specific publicly available or open dataset used for training. |
| Dataset Splits | No | The paper does not provide specific training/validation/test dataset split percentages or sample counts. It describes generating synthetic data and then inferring a network. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory) used for running experiments are provided in the paper. |
| Software Dependencies | No | The paper does not specify any software names with version numbers that would be necessary to replicate the experiment. |
| Experiment Setup | Yes | We used an exponential transmission model and T = 5. Fig. 3(a) summarizes the results, where, for each node, we used cascades which contained at least one node in the super-neighborhood of the node under study. As predicted by Th. 2, very different p values lead to curves that line up with each other quite well. Regularization parameter λn Our main result indicates that the regularization parameter λn should be a constant factor of p log(p)/n. Fig. 3(b) shows the success probability of our algorithm against different scalings K of the regularization parameter λn = K p log(p)/n for different types of networks using 150 cascades and T = 5. |