English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper introduces a Factor Augmented Sparse Throughput (FAST) model thatutilizes both latent factors and sparse idiosyncratic components fornonparametric regression. The FAST model bridges factor models on one end andsparse nonparametric models on the other end. It encompasses structurednonparametric models such as factor augmented additive models and sparselow-dimensional nonparametric interaction models and covers the cases where thecovariates do not admit factor structures. Via diversified projections asestimation of latent factor space, we employ truncated deep ReLU networks tononparametric factor regression without regularization and to a more generalFAST model using nonconvex regularization, resulting in factor augmentedregression using neural network (FAR-NN) and FAST-NN estimators respectively.We show that FAR-NN and FAST-NN estimators adapt to the unknown low-dimensionalstructure using hierarchical composition models in nonasymptotic minimax rates.We also study statistical learning for the factor augmented sparse additivemodel using a more specific neural network architecture. Our results areapplicable to the weak dependent cases without factor structures. In provingthe main technical result for FAST-NN, we establish a new deep ReLU networkapproximation result that contributes to the foundation of neural networktheory. Our theory and methods are further supported by simulation studies andan application to macroeconomic data.

Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression