The Landscape of Non-convex Empirical Risk with Degenerate Population Risk
Authors: Shuang Li, Gongguo Tang, Michael B. Wakin
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We first conduct numerical experiments on the two examples introduced in Section 1, i.e., the rank-1 matrix sensing and phase retrieval problems. In both problems, we fix N = 2 and set x = [1 1] . Then, we generate the population risk and empirical risk based on the formulation introduced in these two examples. The contour plots of the population risk and a realization of empirical risk with M = 3 and M = 10 are given in Figure 4 for rank-1 matrix sensing and Figure 5 for phase retrieval. Next, we conduct another experiment on general-rank matrix sensing with k = 2, r = 3, N = 8, and a variety of M. We set U as the first r columns of an N N identity matrix and create X = U U . The population and empirical risks are then generated according to the model introduced in Section 3.1. As shown in Figure 6, the distance (averaged over 100 trials) between the local minima of the population and empirical risk decreases as we increase M. |
| Researcher Affiliation | Academia | Shuang Li, Gongguo Tang, and Michael B. Wakin Department of Electrical Engineering Colorado School of Mines Golden, CO 80401 {shuangli,gtang,mwakin}@mines.edu |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statements regarding the release of open-source code or links to a code repository. |
| Open Datasets | No | The paper describes generating measurements and random matrices/vectors based on Gaussian distributions (e.g., 'Gaussian sensing matrix', 'Gaussian random vector') for numerical simulations, but does not specify or provide access information for any publicly available or open datasets. |
| Dataset Splits | No | The paper describes conducting numerical simulations with M samples but does not provide specific details on how data was split into training, validation, or test sets. |
| Hardware Specification | No | The paper does not provide any specific hardware details (e.g., CPU, GPU models, or memory specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide any specific software names with version numbers for reproducibility. |
| Experiment Setup | Yes | In both problems, we fix N = 2 and set x = [1 1] . Then, we generate the population risk and empirical risk based on the formulation introduced in these two examples. The contour plots of the population risk and a realization of empirical risk with M = 3 and M = 10 are given in Figure 4 for rank-1 matrix sensing and Figure 5 for phase retrieval. Next, we conduct another experiment on general-rank matrix sensing with k = 2, r = 3, N = 8, and a variety of M. |