High Dimensional Structured Superposition Models
Authors: Qilong Gu, Arindam Banerjee
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we confirm the theoretical results in this paper with some simple experiments. We show our experimental results under different settings. In our experiments we focus on MCA when k = 2. The design matrix X are generated from Gaussian distribution such that every entry of X subjects to N(0, 1). The noise ω is generated from Gaussian distribution such that every entry of ω subjects to N(0, 1). We implement our algorithm 1 in MATLAB. We use synthetic data in all our experiments, and let the true signal θ1 = (1, . . . , 1 | {z } s1 , 0 . . . , 0), Qθ2 = (1, . . . , 1 | {z } s2 , 0 . . . , 0). We generate our data in different ways for our three experiments. Figure 2: (a) Effect of parameter ρ on estimation error when noise ω = 0. We choose the parameter ρ to be 0, 1/ 2, and a random sample. (b) Effect of dimension p on fraction of successful recovery in noiseless case. Dimension p varies in {20, 40, 50, 150} |
| Researcher Affiliation | Academia | Qilong Gu Dept of Computer Science & Engineering University of Minnesota, Twin Cities guxxx396@cs.umn.edu Arindam Banerjee Dept of Computer Science & Engineering University of Minnesota, Twin Cities banerjee@cs.umn.edu |
| Pseudocode | No | The paper presents the estimator as a mathematical optimization problem (2) but does not provide it in a pseudocode or algorithm block format. |
| Open Source Code | No | The paper does not include any statements or links indicating that open-source code for the methodology is provided. |
| Open Datasets | No | We use synthetic data in all our experiments, and let the true signal θ1 = (1, . . . , 1 | {z } s1 , 0 . . . , 0), Qθ2 = (1, . . . , 1 | {z } s2 , 0 . . . , 0). |
| Dataset Splits | No | The paper mentions using synthetic data and varying sample sizes, but it does not specify any train/validation/test dataset splits. For example, it says 'The number of samples n varied between 1 and 1000.' and 'for each n, we generate 100 pairs of X and w.' |
| Hardware Specification | No | The paper does not explicitly describe the specific hardware used to run its experiments, such as CPU or GPU models. |
| Software Dependencies | No | The paper states 'We implement our algorithm 1 in MATLAB.' but does not provide a version number for MATLAB or list any other software dependencies with specific versions. |
| Experiment Setup | Yes | We choose dimension p = 1000, and let s1 = s2 = 1. The number of samples n varied between 1 and 1000. ... We choose three different matrices Q... We increase n from 1 to 40, and the plot we get is figure 2(b). In this experiment, we choose different dimension p with p = 20, p = 40, p = 80, and p = 160. We let s1 = s2 = 1. |