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A Distribution Dependent Analysis of Meta-Learning

  • Author / Creator
    Konobeev, Mikhail
  • A key problem in the theory of meta-learning is to understand how the task distributions influence transfer risk, the expected error of a meta-learner on a new task drawn from the unknown task distribution. In this work, focusing on fixed design linear regression with Gaussian noise and a Gaussian task (or parameter) distribution, we give distribution-dependent lower bounds on the transfer risk of any algorithm, while we also show that a novel, weighted version of the so-called biased regularized regression method is able to match these lower bounds up to a fixed constant factor. Notably, the weighting is derived from the covariance of the Gaussian task distribution. Altogether, our results provide a precise characterization of the difficulty of meta-learning in this Gaussian setting. While this problem setting may appear simple, we show that it is rich enough to unify the “parameter sharing” and “representation learning” streams of meta-learning; in particular, representation learning is obtained as the special case when the covariance matrix of the task distribution is unknown. For this case we propose to adopt the EM method, which is shown to enjoy efficient updates in our case. The work is completed by an empirical study of EM. In particular, our experimental results show that the EM algorithm can attain the lower bound as the number of tasks grows, while the algorithm is also successful in competing with its alternatives when used in a representation learning context.

  • Subjects / Keywords
  • Graduation date
    Spring 2022
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-dd15-va56
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.