Optimal Estimator for Unlabeled Linear Regression
Authors: Hang Zhang, Ping Li
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments are also provided to corroborate the theoretical claims. 5. Simulations This section presents the numerical results. Since our estimator cannot guarantee the correct permutation matrix Π under the single observation model, our simulations focus on the multiple observations model, i.e., m > 1. |
| Researcher Affiliation | Industry | Hang Zhang, Ping Li Cognitive Computing Lab Baidu Research 10900 NE 8th ST. Bellevue, WA 98004, USA {zhanghanghitomi, pingli98}@gmail.com |
| Pseudocode | Yes | Algorithm 1 The one-step estimator proposed in this paper. Input: observation Y and sensing matrix X. Output: pair ( !Π, !B), which is written as !Π = argmaxΠ Pn !B = (X) !Π where X = (X X) 1X is the pseudo-inverse of X and Pn is the set of all possible permutation matrices. |
| Open Source Code | No | The paper does not provide any statement or link indicating the availability of open-source code for the described methodology. |
| Open Datasets | No | The paper describes generating synthetic data for simulations: 'We closely follow the experiment setting in Zhang et al. (2019b). We set the i-th column B :,i (1 i min(m, p)) to be the i-th canonical basis, which has 1 on the i-th entry and 0 elsewhere.' It does not refer to a publicly available dataset for training. |
| Dataset Splits | No | The paper describes simulation experiments but does not provide explicit train/validation/test dataset splits or cross-validation details. |
| Hardware Specification | No | The paper does not provide any specific hardware details (e.g., GPU/CPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers. |
| Experiment Setup | Yes | For each n, we choose p {0.1n, 0.2n} and h {n/10, n/4}. That is, when n = 500, we have p {50, 100} and h {50, 125}; and when n = 1000, we have p {100, 200} and h {100, 250}. For each chosen set of parameters (n, p, m, h) and SNR value, we simulate the data 1000 times and report the success rate of exact recovery of Π using our proposed estimator in Algorithm 1. |