Analysis of Variational Bayesian Factorizations for Sparse and Low-Rank Estimation
Authors: David Wipf
ICML 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To illustrate these effects, we conducted the following Monte Carlo experiment. First we generate a sparse vector x with x 0 = 20 nonzero elements randomly located with iid N(0, 1) nonzero elements. Next we generate a design matrix via Φ = Pn i=1 1 iη uiv i , where each vector ui R50 and vi R100 are distributed iid with N(0, 1) elements. We then normalized columns of Φ to have unit ℓ2 norm. The exponent parameter η is chosen from the interval [0, 2], the effect being that larger values of η will introduce larger correlations into the resulting columns of Φ, meaning that Φ Φ will have stronger offdiagonal elements. Finally we generate a data vector via y = Φx. We then run various VB sparse estimation algorithms and evaluate them using two metrics, normalized MSE D x ˆx 2 2 x 2 2 E and average # nonzeros ˆx 0 , where the empirical average is taken across 1000 independent trials. This process is repeated for values of η [0, 2], with results reported in Figure 1. |
| Researcher Affiliation | Industry | David Wipf DAVIDWIPF@GMAIL.COM Microsoft Research, Beijing |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any concrete access information for open-source code. |
| Open Datasets | No | The paper describes generating synthetic data for its experiments ('First we generate a sparse vector x...', 'Next we generate a design matrix via Φ...', 'Finally we generate a data vector via y = Φx.'), not using a publicly available dataset. |
| Dataset Splits | No | The paper uses generated synthetic data for Monte Carlo experiments and evaluates metrics across independent trials, but does not specify traditional training/validation/test splits of a fixed dataset. |
| Hardware Specification | No | The paper does not provide any specific hardware details used for running experiments. |
| Software Dependencies | No | The paper mentions methods like VB-GSM, VB-BG, and Lasso estimator, but does not specify any software libraries or frameworks with version numbers used for implementation. |
| Experiment Setup | Yes | First we generate a sparse vector x with x 0 = 20 nonzero elements randomly located with iid N(0, 1) nonzero elements. Next we generate a design matrix via Φ = Pn i=1 1 iη uiv i , where each vector ui R50 and vi R100 are distributed iid with N(0, 1) elements. We then normalized columns of Φ to have unit ℓ2 norm. The exponent parameter η is chosen from the interval [0, 2]... Finally we generate a data vector via y = Φx. We then run various VB sparse estimation algorithms and evaluate them using two metrics... This process is repeated for values of η [0, 2]... (we chose α = 10 4). |