Online Learning of Eigenvectors

Authors: Dan Garber, Elad Hazan, Tengyu Ma

ICML 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical In this paper we present new algorithms that avoid both issues. On one hand they do not require any expensive matrix decompositions and on the other, they guarantee regret rates with a mild dependence on the dimension at most. We extend our results to also handle non-symmetric matrices. Our main result is an online algorithm that takes the so called oracle approach and is based on the Follow the Perturbed Leader meta-algorithm. We also consider a somewhat easier stochastic setting, in which we assume that the sequence of matrices is sampled from a fixed and unknown distribution. We present an algorithm that takes the so called iterative approach and is analogues to the Power algorithm for the offline setting, i.e. it computes a single matrix-vector product on each iteration.
Researcher Affiliation Academia Dan Garber DANGAR@TX.TECHNION.AC.IL Technion Israel Institute of Technology Elad Hazan EHAZAN@CS.PRINCETON.EDU Princeton University Tengyu Ma TENGYUL@CS.PRINCETON.EDU Princeton University
Pseudocode Yes Algorithm 1 Asymmetric to Symmetric Conversion Algorithm, Algorithm 2 Epoch Power Method, Algorithm 3 Follow the Perturbed Leader
Open Source Code No The paper does not contain any explicit statement about releasing source code for the described methodologies, nor does it provide a link to a code repository.
Open Datasets No The paper is theoretical and does not describe empirical experiments using specific datasets. Therefore, it does not provide information about public dataset availability or access.
Dataset Splits No The paper is theoretical and does not involve empirical experiments with data. Consequently, it does not specify training, validation, or test dataset splits.
Hardware Specification No The paper is theoretical and does not describe any hardware specifications used for running experiments.
Software Dependencies No The paper is theoretical and does not specify software dependencies with version numbers required for replication.
Experiment Setup No The paper is theoretical and does not describe a concrete experimental setup, including hyperparameters or system-level training settings.