Bayesian Spanning Tree: Estimating the Backbone of the Dependence Graph
Authors: Leo L. Duan, David B. Dunson
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In both theory and experiments, we show that this model does not require the population graph to be a spanning tree or the covariance to satisfy assumptions beyond positive-definiteness. The model accurately recovers the backbone of the population graph at a rate competitive with existing approaches but with better robustness. We show combinatorial properties of the spanning tree, which may be of independent interest, and develop an efficient Gibbs sampler for Bayesian inference. Analyzing electroencephalography data using a hidden Markov model with each latent state modeled by a spanning tree, we show that results are much more interpretable compared with popular alternatives. Keywords: Graph-constrained Model, Incidence Matrix, Laplacian, Matrix Tree Theorem, Traveling Salesperson Problem. |
| Researcher Affiliation | Academia | Leo L. Duan EMAIL Department of Statistics, University of Florida David B. Dunson EMAIL Department of Statistical Science, Duke University |
| Pseudocode | Yes | Algorithm 1: Finding the conditional posterior mode  Initialize U = {1}, ET = and U = {1, . . . , p} \ U; while |U| < p do Find (j, k) = arg max (l,l ) (U, U) ql,l , and (j, k) into ET . Move l from U to U. end |
| Open Source Code | No | No explicit statement or link to their own implementation code is provided. The paper mentions using 'scikit-learn package' for data generation and examples, but not for releasing their own method's code. |
| Open Datasets | Yes | Next, we move to the case of a graph formed near two manifolds. We use the two-moon example provided in the scikit-learn package. As shown in Figure 8, each point has only one or a few points in the neighborhood, therefore, the posterior distribution of T is highly concentrated near the posterior mode. |
| Dataset Splits | No | The paper mentions, 'To validate our trained model, we use a previously reserved set of EEG data collected from another 20 subjects (hence 40 time series),' which indicates a validation set, but it does not specify exact split percentages, sample counts, or a detailed splitting methodology for reproducibility. |
| Hardware Specification | Yes | In terms of the computational time, for a graph containing p = 200 nodes, sampling a 1, 000 steps takes about 2 minutes using Python on a quad-core laptop. |
| Software Dependencies | No | The paper mentions using 'Python' and the 'scikit-learn package' but does not provide specific version numbers for either, which is required for reproducible software dependencies. |
| Experiment Setup | Yes | We choose α = 5 as a balanced choice between shrinkage and tail-robustness; details can found in Armagan et al. (2013). We use an informative exponential prior τ Exp(1/µτ) with the prior mean set to µτ = min(j,k:j =k) yj yk 2/n, as an empirical estimate of the smallest scale among vectors ( yj yk) s. For the first step, we use an adaptation period at the beginning of the MCMC algorithm to tune δ > 0, so that the acceptance rate of this step is around 0.3. We set K = 20 for as an upper bound. We run our MCMC algorithm for 20, 000 iterations, and discard the initial 10, 000 as a burn-in. We average the last 5, 000 iterations to compute the likelihood... |