Statistical inference for the population landscape via moment‐adjusted stochastic gradients

Tengyuan Liang and Weijie J. Su

Journal of the Royal Statistical Society Series B, 2019, vol. 81, issue 2, 431-456

Abstract: Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint informs us only how well the solution is approximated numerically but overlooks the sampling nature of the data. In contrast, recognizing the randomness in the data, statisticians are keen to provide uncertainty quantification, or confidence, for the solution obtained by using iterative optimization methods. The paper makes progress along this direction by introducing moment‐adjusted stochastic gradient descent: a new stochastic optimization method for statistical inference. We establish non‐asymptotic theory that characterizes the statistical distribution for certain iterative methods with optimization guarantees. On the statistical front, the theory allows for model misspecification, with very mild conditions on the data. For optimization, the theory is flexible for both convex and non‐convex cases. Remarkably, the moment adjusting idea motivated from ‘error standardization’ in statistics achieves a similar effect to acceleration in first‐order optimization methods that are used to fit generalized linear models. We also demonstrate this acceleration effect in the non‐convex setting through numerical experiments.

Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://doi.org/10.1111/rssb.12313

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:81:y:2019:i:2:p:431-456

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().