Soft Tensor Regression
Authors: Georgia Papadogeorgou, Zhengwu Zhang, David B. Dunson
JMLR 2021 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To illustrate the performance of Softer and compare it against alternatives, we simulated data under various scenarios. In one set of simulations (Section 5.1), we considered a tensor predictor of dimension 32 32, corresponding coefficient tensors ranging from close to low-rank to full-rank, and with different degrees of sparsity, and sample size equal to 400. ... We use the soft tensor regression framework in a study of the relationship between brain structural connectomics and human traits for participants in the Human Connectome Project (HCP; Van Essen et al. (2013)). |
| Researcher Affiliation | Academia | Georgia Papadogeorgou EMAIL Department of Statistics University of Florida Gainesville, FL 32611-8545, USA Zhengwu Zhang zhengwu EMAIL Department of Statistics and Operations Research University of North Carolina at Chapel Hill Chapel Hill, NC 27599-3260, USA David B. Dunson EMAIL Department of Statistical Science Duke University Durham, NC 27708-0251, USA |
| Pseudocode | No | We approximate the posterior distribution of B using Markov chain Monte Carlo (MCMC). An MCMC scheme where most parameters are updated using Gibbs sampling is shown in Appendix C. ... Appendix C. Alternative Sampling from the Posterior Distribution The full set of parameters is θ = {µ, δ, τ 2, β(d) k, j, γ(d) k,jk, σ2 k, ζ(d), w(d) k,jk, λ(d) k , τ 2 γ, for all d, k, jk, j}. We use the notation | and | , y to denote conditioning on the data and all parameters, and the data and all parameters but y, accordingly. Then, our MCMC updates are: (µ, δ)| N(µ , Σ ), for Σ = (Σ 1 0 + e CT e C/τ 2) 1, and µ = Σ e CT RB/τ 2, where e C is the N (p+1) matrix with ith row equal to (1, Ci), and RB = (Y1 X1, B F , . . . , YN XN, B F )T is the vector of residuals of the outcome on the tensor predictor. τ 2| IG(aτ + N/2, bτ + PN i=1(Yi µ CT i δ Xi, B F )). σ2 k| gi G(p , a , b ), for p = aσ D QK k=1 pk/2, a = 2bσ, and b = P d, j(β(d) k, j γ(d) k,jk)2/ζ(d). The text describes MCMC updates but does not present them in a structured pseudocode or algorithm block. |
| Open Source Code | No | No explicit statement or link for open-source code is provided in the paper. |
| Open Datasets | Yes | We use the soft tensor regression framework in a study of the relationship between brain structural connectomics and human traits for participants in the Human Connectome Project (HCP; Van Essen et al. (2013)). |
| Dataset Splits | Yes | For each approach, we estimate the out-of-sample prediction error by performing 15-fold cross validation, fitting the method on 90% of the data and predicting the outcome on the remaining 10%. |
| Hardware Specification | No | No specific hardware details (like GPU models, CPU models, or memory) are provided for running the experiments. The paper only mentions using Stan and R. |
| Software Dependencies | No | The paper mentions 'HMC implemented in Stan (Carpenter et al., 2017) and on the R interface (Stan Development Team, 2018)' but does not provide specific version numbers for these software components. |
| Experiment Setup | Yes | Using Stan, we employ the No-U-Turn sampler (NUTS) algorithm (Hoffman and Gelman, 2014) which automatically tunes the HMC parameters to achieve a target acceptance rate (the default step size adaptation parameters were used). If MCMC convergence is slow, one could increase the NUTS parameter δ in RStan from 0.8, which is the default, to a value closer to 1. ... For continuous outcomes, the methods predictive performance was evaluated by calculating the percentage of the marginal variance explained by the model defined as 1 (CV MSE)/(marginal variance). For binary outcomes, we used the model s estimated linear predictor to estimate the optimal cutofffor classification based on Youden s index (Youden, 1950) and calculated the average percentage of correctly classified observations in the heldout data. |