Frank-Wolfe-based Algorithms for Approximating Tyler's M-estimator
Authors: Lior Danon, Dan Garber
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In order to give some demonstration for the empirical performance of our Frank-Wolfe-based algorithms, we conducted two types of experiments that closely follow those in [28] (Chapter 3) with some minor changes, which consider a Gaussian distribution with outlier contamination, and a heavy-tailed multivariate t-distribution. [...] In Figure 1 we report the distance in spectral norm (in log scale) of the iterates of the different methods form Q , and in Figure 2 we report the approximation error f(Qt) f(Q ) of the iterates (also in log scale). |
| Researcher Affiliation | Academia | Lior Danon Technion Israel Institute of Technology Haifa, Israel 3200003 liordanon@campus.technion.ac.il Dan Garber Technion Israel Institute of Technology Haifa, Israel 3200003 dangar@technion.ac.il |
| Pseudocode | Yes | Algorithm 1 Frank-Wolfe variants for approximating Tyler s M-estimator |
| Open Source Code | No | The paper states in the internal checklist that code is included or details allow reproduction, but does not provide an explicit statement or link in the main text for open-source code of their methodology. |
| Open Datasets | No | The paper describes a data generation process ('Gaussian distribution with outliers contamination' and 'heavy-tailed multivariate t-distribution') and references [28] for the experiments, but does not explicitly state that a public dataset was used with concrete access information. |
| Dataset Splits | No | The paper does not explicitly provide training, validation, or test dataset splits. It describes data generation and then directly evaluates performance metrics. |
| Hardware Specification | No | The paper explicitly states 'Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [N/A]' in its checklist. |
| Software Dependencies | No | The paper mentions using 'Python s SCIPY.SPARSE.LINALG.EIGSH procedure' but does not provide specific version numbers for Python, SciPy, or any other software dependencies. |
| Experiment Setup | Yes | In both experiments we set p = 50, n = 2500, and we take the true unknown covariance to be a Toeplitz matrix with the elements Qi,j = 0.85|i j|. [...] All methods are initialized from the sample covariance (normalized to have trace equals p) [...] For all experiments we compute Tyler s estimator to high accuracy by running 250 iterations of the Fixed-point method and we denote the resulting matrix by Q . |