Conditional Matrix Flows for Gaussian Graphical Models
Authors: Marcello Massimo Negri, Fabricio Arend Torres, Volker Roth
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we showcase the effectiveness of the proposed CMF first on artificial data and then on a real application. In particular, we study the evolution of the variational posterior as a function of λ and q. We then perform model selection on λ through marginal likelihood maximization. We further illustrate the effect of training through simulated annealing and show that we recover the frequentist solution path through the MAP. Lastly, we show that the proposed method can be readily applied to real data in higher-dimensional settings. Results show that sub-l1 pseudo-norms provide sparser solutions and contrast the well-known overshrinking effect of Lasso relaxation. |
| Researcher Affiliation | Academia | Marcello Massimo Negri University of Basel marcellomassimo.negri@unibas.ch Fabricio Arend Torres University of Basel fabricio.arendtorres@unibas.ch Volker Roth University of Basel volker.roth@unibas.ch |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | We open-source the implementation of the conditional bijective layers.1 ... 1Flow Conductor: (Conditional) Normalizing Flows and bijective Layers for Pytorch https://github.com/Fabricio Arend Torres/Flow Conductor |
| Open Datasets | Yes | We consider a colorectal cancer dataset [Sheffer et al., 2009], which contains measurements of 7 clinical variables together with 312 gene measurements from biopsies for 260 cancer patients. |
| Dataset Splits | Yes | In the Appendix A.4 in Figure 7, we show the (approximate) marginal log-likelihood as a function of λ and the resulting optimal λ CMF = 3.52 that maximizes it. We compare the result with the frequentist estimate obtained through MLE with 5-fold cross validation λ GLasso = 3.36. |
| Hardware Specification | Yes | This result was obtained on a Intel(R) Xeon(R) CPU E5-1660 v3 @ 3.00GHz. On the ohter hand, on the consumer-grade GPU NVIDIA TITAN X (12GB VRAM) sampling is extremely efficient: each second we can generate 2000 independent samples from the approximate posterior. |
| Software Dependencies | No | The paper mentions software like PyTorch, nflows, and scikit-learn, but does not provide specific version numbers for these dependencies. |
| Experiment Setup | Yes | We trained our model for 10 000 epochs through simulated annealing with an initial temperature of T0 = 5 to Tn = 0.01 and performed 100 geometric cooling steps with Ti = T0ai/n for a = Tn/T0. ... The proposed CMF is trained for 5000 epochs to a final temperature T = 1... For the BGL we run the Gibbs sampler for 4000 iterations with a burn-in of 1000 and keep every fourth sample. |