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.