Alternating Estimation for Structured High-Dimensional Multi-Response Models
Authors: Sheng Chen, Arindam Banerjee
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we present some experimental results to support our theoretical analysis. Specifically we focus on the sparse structure of θ captured by L1 norm. Throughout the experiment, we fix problem dimension p = 500, sparsity level of θ s = 20, and number of iterations for Alt Est T = 5. Entries of design X is generated by i.i.d. standard Gaussians, and θ = [1, . . . , 1 | {z } 10 , 1, . . . , 1 | {z } 10 , 0, . . . , 0 | {z } 480 ]T . Σ is given as a block diagonal matrix with blocks Σ = h 1 a a 1 i replicated along diagonal, and number of responses m is assumed to be even. All plots are obtained by averaging 100 trials. |
| Researcher Affiliation | Academia | Sheng Chen Arindam Banerjee Dept. of Computer Science & Engineering University of Minnesota, Twin Cities {shengc,banerjee}@cs.umn.edu |
| Pseudocode | Yes | Algorithm 1 Alternating Estimation with Resampling |
| Open Source Code | No | The paper does not provide an explicit statement or link for the open-source code of the described methodology. |
| Open Datasets | No | Entries of design X is generated by i.i.d. standard Gaussians, and θ = [1, . . . , 1 | {z } 10 , 1, . . . , 1 | {z } 10 , 0, . . . , 0 | {z } 480 ]T . Σ is given as a block diagonal matrix with blocks Σ = h 1 a a 1 i replicated along diagonal, and number of responses m is assumed to be even. This indicates synthetic data generation, not the use of a publicly available dataset with access information. |
| Dataset Splits | No | The paper mentions resampling of datasets D2t-1 and D2t for theoretical analysis within the alternating estimation algorithm, but it does not provide specific train/validation/test dataset splits (e.g., percentages or sample counts) for model reproduction. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details with version numbers required to replicate the experiments. |
| Experiment Setup | Yes | In this section, we present some experimental results to support our theoretical analysis. Specifically we focus on the sparse structure of θ captured by L1 norm. Throughout the experiment, we fix problem dimension p = 500, sparsity level of θ s = 20, and number of iterations for Alt Est T = 5. Entries of design X is generated by i.i.d. standard Gaussians, and θ = [1, . . . , 1 | {z } 10 , 1, . . . , 1 | {z } 10 , 0, . . . , 0 | {z } 480 ]T . Σ is given as a block diagonal matrix with blocks Σ = h 1 a a 1 i replicated along diagonal, and number of responses m is assumed to be even. All plots are obtained by averaging 100 trials. In the first set of experiments, we set a = 0.8, m = 10 and investigate the error of ˆθt as n varies from 40 to 90. For the second experiment, we fix the product mn 500, and let m = 2, 4, . . . , 10. In the third experiment, we test Alt Est under different covariance matrices Σ by varying a from 0.5 to 0.9. m is set to 10 and sample size n is 90. |