Regularization-Free Estimation in Trace Regression with Symmetric Positive Semidefinite Matrices
Authors: Martin Slawski, Ping Li, Matthias Hein
NeurIPS 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we empirically study properties of the estimator bΣ. In particular, its performance relative to regularization-based methods is explored. We also present an application to spiked covariance estimation for the CBCL face image data set and stock prices from NASDAQ. |
| Researcher Affiliation | Academia | Martin Slawski Ping Li Department of Statistics & Biostatistics Department of Computer Science Rutgers University Piscataway, NJ 08854, USA {martin.slawski@rutgers.edu, pingli@stat.rutgers.edu} Matthias Hein Department of Computer Science Department of Mathematics Saarland University Saarbr ucken, Germany hein@cs.uni-saarland.de |
| Pseudocode | No | The paper does not contain any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements or links to open-source code for the methodology described. |
| Open Datasets | Yes | The CBCL facial image data set [1] ... http://cbcl.mit.edu/software-datasets/Face Data2.html. ... NASDAQ, starting from the beginning of the year 2000 to the end of the year 2014 (in total N = 3773 days, retrieved from finance.yahoo.com). |
| Dataset Splits | No | The paper mentions tuning regularization parameters using a 'separate validation data set' but does not specify the explicit split percentages or sample counts for training, validation, and test sets across its main experiments using the CBCL or NASDAQ datasets, where data is generated rather than split. |
| Hardware Specification | No | The paper does not provide any specific details regarding the hardware used to run the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers. |
| Experiment Setup | Yes | Setup. We consider rank-one Wishart measurement matrices Xi = ziz i , zi i.i.d. N(0, I), i = 1, . . . , n, fix m = 50 and let n {0.24, 0.26, . . ., 0.36, 0.4, . . ., 0.56} m2 and r {1, 2, . . ., 10} vary. Each configuration of (n, r) is run with 50 replications. In each of these, we generate data yi = tr(XiΣ ) + σεi, σ = 0.1, i = 1, . . . , n, where Σ is generated randomly as rank r Wishart matrices and the {εi}n i=1 are i.i.d. N(0, 1). ... Regarding the choice of the regularization parameter λ, we consider the grid λ {0.01, 0.05, 0.1, 0.3, 0.5, 1, 2, 4, 8, 16}... For λ, we consider the grid nσ p 2/π {0.2, 0.3, . . ., 1, 1.25}. ... n = C(mr), where C ranges from 0.25 to 12. ... For each choice of n and β, the reported results are averages over 20 replications. |