Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Optimal Linear Estimation under Unknown Nonlinear Transform
Authors: Xinyang Yi, Zhaoran Wang, Constantine Caramanis, Han Liu
NeurIPS 2015 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We now turn to the numerical results that support our theory. For the three models introduced in 2, we apply Algorithm 1 and Algorithm 2 to do parameter estimation in the classic and high dimensional regimes. Our simulations are based on synthetic data. For classic recovery, β is randomly chosen from Sp 1; for sparse recovery, we set β j = s 1/21(j S) for all j [p], where S is a random index subset of [p] with size s. In Figure 1, as predicted by Theorem 3.5, we observe that the same p/n leads to nearly identical estimation error. Figure 2 demonstrates similar results for the predicted rate s log p/n of sparse recovery and thus validates Theorem 3.6. |
| Researcher Affiliation | Academia | Xinyang Yi The University of Texas at Austin EMAIL Zhaoran Wang Princeton University EMAIL Constantine Caramanis The University of Texas at Austin EMAIL Han Liu Princeton University EMAIL |
| Pseudocode | Yes | Algorithm 1 Low dimensional recovery Algorithm 2 Sparse recovery |
| Open Source Code | No | The paper does not provide any explicit statements or links indicating the availability of open-source code for the described methodology. |
| Open Datasets | No | Our simulations are based on synthetic data. |
| Dataset Splits | No | The paper mentions generating synthetic data for simulations but does not specify any dataset splits (e.g., training, validation, test percentages or sample counts) used for reproducibility. |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., GPU/CPU models, memory) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies or version numbers needed to replicate the experiments. |
| Experiment Setup | Yes | Suppose ρ=C φ(f)+(1 µ2 0) p log p/n with a sufficiently large constant C, where φ(f) and µ0 are specified in (3.2) and (3.5). Meanwhile, assume the sparsity parameter bs in Algorithm 2 is set to be bs=C max 1/(κ 1/2 1)2 ,1 s . For n nmin with nmin defined in (3.10), we have... In Figure 1... p = 10 p = 20 p = 40 In Figure 2... p = 100, s = 5 p = 100, s = 10 p = 200, s = 5 p = 200, s = 10 |