Robust Gaussian Covariance Estimation in Nearly-Matrix Multiplication Time

Authors: Jerry Li, Guanghao Ye

NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical In this paper, we demonstrate a novel algorithm which achieves the same statistical guarantees, but which runs in time e O(T(N, d) log κ). In particular our runtime has no dependence on ε. When Σ is reasonably conditioned, our runtime matches that of the fastest algorithm for covariance estimation without outliers, up to poly-logarithmic factors, showing that we can get robustness essentially for free.
Researcher Affiliation Collaboration Jerry Li Microsoft Research jerrl@microsoft.com Guanghao Ye University of Washington ghye@uw.edu
Pseudocode Yes Algorithm 1 Robust Covariance Estimation
Open Source Code No The paper does not contain any explicit statements or links indicating that the source code for the described methodology is publicly available.
Open Datasets No The paper uses a generative model for data, stating "we are given samples X1, . . . , XN drawn from a Gaussian N(0, Σ), but an ε-fraction of these points have been arbitrarily corrupted." This describes synthetic data generation for theoretical analysis, not a publicly available dataset with concrete access information.
Dataset Splits No The paper analyzes algorithms based on statistical guarantees and theoretical proofs rather than empirical evaluation with specific training, validation, or test dataset splits.
Hardware Specification No The paper discusses algorithmic runtime complexity abstractly (e.g., 'T(N, d) is the time it takes to multiply a d N matrix by its transpose') but does not provide any specific details about hardware used for running any computations or experiments.
Software Dependencies No The paper mentions using 'black-box nearly-linear time SDP solvers [AZLO15, AZLO16]' but does not provide specific version numbers for these or any other software dependencies required to replicate the work.
Experiment Setup No The paper is theoretical and describes algorithms and proofs without detailing an experimental setup, hyperparameters, or training configurations.