Embedding Learning

Ben Dai, Xiaotong Shen and Junhui Wang

Journal of the American Statistical Association, 2022, vol. 117, issue 537, 307-319

Abstract: Numerical embedding has become one standard technique for processing and analyzing unstructured data that cannot be expressed in a predefined fashion. It stores the main characteristics of data by mapping it onto a numerical vector. An embedding is often unsupervised and constructed by transfer learning from large-scale unannotated data. Given an embedding, a downstream learning method, referred to as a two-stage method, is applicable to unstructured data. In this article, we introduce a novel framework of embedding learning to deliver a higher learning accuracy than the two-stage method while identifying an optimal learning-adaptive embedding. In particular, we propose a concept of U-minimal sufficient learning-adaptive embeddings, based on which we seek an optimal one to maximize the learning accuracy subject to an embedding constraint. Moreover, when specializing the general framework to classification, we derive a graph embedding classifier based on a hyperlink tensor representing multiple hypergraphs, directed or undirected, characterizing multi-way relations of unstructured data. Numerically, we design algorithms based on blockwise coordinate descent and projected gradient descent to implement linear and feed-forward neural network classifiers, respectively. Theoretically, we establish a learning theory to quantify the generalization error of the proposed method. Moreover, we show, in linear regression, that the one-hot encoder is more preferable among two-stage methods, yet its dimension restriction hinders its predictive performance. For a graph embedding classifier, the generalization error matches up to the standard fast rate or the parametric rate for linear or nonlinear classification. Finally, we demonstrate the utility of the classifiers on two benchmarks in grammatical classification and sentiment analysis. Supplementary materials for this article are available online.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2020.1775614 (text/html)
Access to full text is restricted to subscribers.

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:taf:jnlasa:v:117:y:2022:i:537:p:307-319

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2020.1775614

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().