mlsanityData to 7 Oct 2026

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

arXiv 2210.02002 ↗First posted 5 Oct 2022math.ST stat.ME stat.THcited by 31

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Abstract (arXiv)

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

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Oct 2022.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 6; 2025: 10; 2026: 12.

31 papers.

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  1. 2023Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimensioncited by 15
  2. 2024Tensor-view Topological Graph Neural Networkcited by 12
  3. 2023Neural networks for geospatial datacited by 11
  4. 2023UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregationcited by 8
  5. 2024Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learningcited by 7
  6. 2024Factor Augmented Tensor-on-Tensor Neural Networkscited by 7
  7. 2025Representation Retrieval Learning for Heterogeneous Data Integrationcited by 5
  8. 2024Representation-Enhanced Neural Knowledge Integration with Application to Large-Scale Medical Ontology Learningcited by 4
  9. 2024Deep Transfer Learning: Model Framework and Error Analysiscited by 4
  10. 2025Inference for Deep Neural Network Estimators in Generalized Nonparametric Modelscited by 3
  11. 2026Optimally taming biases in black-box models for efficient semiparametric estimationcited by 3
  12. 2025Factor Informed Double Deep Learning For Average Treatment Effect Estimationcited by 2
19 more
  1. 2025A general framework for deep learningcited by 2
  2. 2024Factor Adjusted Spectral Clustering for Mixture Modelscited by 1
  3. 2025Semi-supervised Clustering Through Representation Learning of Large-scale EHR Datacited by 1
  4. 2025Supervised Dynamic Dimension Reduction with Deep Neural Networkcited by 1
  5. 2025CINDES: Classification induced neural density estimator and simulatorcited by 1
  6. 2026Optimal use of a black-box learner in semiparametric estimationcited by 1
  7. 2025Generalized Factor Neural Network Model for High-dimensional Regressioncited by 0
  8. 2025Boosting Statistic Learning with Synthetic Data from Pretrained Large Modelscited by 0
  9. 2025Feature Augmentations for High-Dimensional Learningcited by 0
  10. 2026NeuroMAS: Multi-Agent Systems as Neural Networks with Joint Reinforcement Learningcited by 0
  11. 2026Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selectioncited by 0
  12. 2026Factor Augmented High-Dimensional SGDcited by 0
  13. 2026Rate-optimal neural boundary detection from unlabeled noisy imagescited by 0
  14. 2026Mitigating the Curse of Dimensionality in Uniform Convergence of Deep Neural Networks via Smooth Activationscited by 0
  15. 2026MediEncoder: Nonlinear Representation Learning for High-Dimensional Causal Mediation Analysiscited by 0
  16. 2026Deep Multitask Learning for Mixed-Type Outcomes with Shared Sparsitycited by 0
  17. 2026Minimax Theory of Likelihood-Based Deep Learning for Speckle Regressioncited by 0
  18. 2026Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAScited by 0
  19. 2026FAST-DeepONet: Factor-Augmented Branch Representations for High-Dimensional PDE Inputs in the Small-Sample Regimecited by 0