High-dimensional Robust Mean Estimation via Gradient Descent
Authors: Yu Cheng, Ilias Diakonikolas, Rong Ge, Mahdi Soltanolkotabi
ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomialtime algorithms for this problem with dimensionindependent error guarantees for a range of natural distribution families. In this work, we show that a natural non-convex formulation of the problem can be solved directly by gradient descent. Our approach leverages a novel structural lemma, roughly showing that any approximate stationary point of our non-convex objective gives a near-optimal solution to the underlying robust estimation task. |
| Researcher Affiliation | Academia | 1University of Illinois at Chicago, Chicago, IL, USA 2University of Wisconsin-Madison, Madison, WI, USA 3Duke University, Durham, NC, USA 4University of Southern California, Los Angeles, CA, USA. |
| Pseudocode | Yes | Algorithm 1 Robust Mean Estimation via PGD |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | Let S be an ϵ-corrupted set of N = eΩ(d/ϵ2) samples from a d-dimensional Gaussian N(µ , I) with unknown mean µ . The paper does not specify a publicly available dataset by name, citation, or provide access information for the data used in its theoretical framework. |
| Dataset Splits | No | The paper uses terms like 'train', 'validation', and 'test' in the JSON schema, which refer to dataset splits in empirical studies. This paper is theoretical and does not describe any practical dataset splits or experimental validation procedures. |
| Hardware Specification | No | The paper does not contain any specific details about the hardware used, such as GPU or CPU models. This is consistent with its theoretical nature, which does not involve empirical experiments requiring hardware specifications. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers. This is consistent with its theoretical nature, which does not involve empirical experiments requiring specific software configurations. |
| Experiment Setup | No | The paper describes algorithms and proofs but does not provide specific experimental setup details such as hyperparameters, learning rates, or training schedules. This is consistent with its theoretical focus. |