Learning Low-Dimensional Metrics
Authors: Blake Mason, Lalit Jain, Robert Nowak
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 3 Experiments To validate our complexity and recovery guarantees, we ran the following simulations. We generate x1, , xn iid N(0, 1 p I), with n = 200, and K = p p d UU T for a random orthogonal matrix U 2 Rp d with unit norm columns. In Figure 2a, K has d nonzero rows/columns. In Figure 2b, K is a dense rank-d matrix. We compare the performance of nuclear norm and 1,2 regularization in each setting against an unconstrained baseline where we only enforce that K be psd. Given a fixed number of samples, each method is compared in terms of the relative excess risk, R(c K) R(K ) R(K ) , and the relative squared recovery error, kc K K k2 F , averaged over 20 trials. The y-axes of both plots have been trimmed for readability. |
| Researcher Affiliation | Academia | Lalit Jain University of Michigan Ann Arbor, MI 48109 lalitj@umich.edu Blake Mason University of Wisconsin Madison, WI 53706 bmason3@wisc.edu Robert Nowak University of Wisconsin Madison, WI 53706 rdnowak@umich.edu |
| Pseudocode | No | No structured pseudocode or algorithm blocks were found in the paper. |
| Open Source Code | No | The paper does not contain any explicit statement about providing source code or a link to a code repository for the described methodology. |
| Open Datasets | No | The paper states 'We generate x1, , xn iid N(0, 1 p I), with n = 200' for their simulations, indicating a self-generated dataset for which no public access information (link, DOI, citation) is provided. |
| Dataset Splits | No | The paper describes simulations but does not provide specific details regarding training, validation, or test dataset splits, percentages, or sample counts. |
| Hardware Specification | No | The paper describes running simulations but does not provide specific hardware details (e.g., GPU/CPU models, memory, or processor types) used for the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependency details, such as library or solver names with version numbers. |
| Experiment Setup | Yes | We generate x1, , xn iid N(0, 1 p I), with n = 200, and K = p p d UU T for a random orthogonal matrix U 2 Rp d with unit norm columns. In Figure 2a, K has d nonzero rows/columns. In Figure 2b, K is a dense rank-d matrix. ... averaged over 20 trials. ... we compute the number of samples averaged over 20 runs to achieve a relative excess risk of less than 0.1 in Figure 3. First, we fix p = 100 and increment d from 1 to 10. Then we fix d = 10 and increment p from 10 to 100 to clearly show the linear dependence of the sample complexity on d and p as demonstrated in Corollary 2.1.1. |