# Statistical Guarantees for Regularized Neural Networks

@article{Taheri2020StatisticalGF, title={Statistical Guarantees for Regularized Neural Networks}, author={Mahsa Taheri and Fang Xie and Johannes Lederer}, journal={Neural networks : the official journal of the International Neural Network Society}, year={2020}, volume={142}, pages={ 148-161 } }

## 23 Citations

### Risk Bounds for Robust Deep Learning

- Computer ScienceArXiv
- 2020

This paper shows that empirical-risk minimization with unbounded, Lipschitz-continuous loss functions, such as the least-absolute deviation loss, Huber loss, Cauchy loss, and Tukey's biweight loss, can provide efficient prediction under minimal assumptions on the data.

### Hierarchical Adaptive Lasso: Learning Sparse Neural Networks with Shrinkage via Single Stage Training

- Computer ScienceArXiv
- 2020

A novel penalty called Hierarchical Adaptive Lasso (HALO) which learns to adaptively sparsify weights of a given network via trainable parameters without learning a mask is presented.

### No Spurious Local Minima: on the Optimization Landscapes of Wide and Deep Neural Networks

- Computer ScienceArXiv
- 2020

These theories substantiate the common belief that increasing network widths not only improves the expressiveness of deep-learning pipelines but also facilitates their optimizations, and prove especially that constraint and unconstraint empirical-risk minimization over such networks has no spurious local minima.

### Statistical guarantees for sparse deep learning

- Computer ScienceAStA Advances in Statistical Analysis
- 2023

The guarantees have a mild dependence on network widths and depths, which means that they support the application of sparse but wide and deep networks from a statistical perspective.

### Deep neural network approximation of analytic functions

- Computer Science, MathematicsArXiv
- 2021

An oracle inequality for the expected error of the considered penalized deep neural network estimators is derived from ε-approximate functions that are analytic on certain regions of C.

### Analytic function approximation by path norm regularized deep networks

- Computer Science, Mathematics
- 2021

An entropy bound is provided for the spaces of path norm regularized neural networks with piecewise linear activation functions, such as the ReLU and the absolute value functions that are analytic on certain regions of C.

### Reducing Computational and Statistical Complexity in Machine Learning Through Cardinality Sparsity

- Computer Science
- 2023

It is shown that cardinality sparsity can improve deep learning and tensor regression both statistically and computationally, and generalize recent statistical theories in those fields.

### Statistical Guarantees for Approximate Stationary Points of Simple Neural Networks

- Computer ScienceArXiv
- 2022

Simple neural networks are developed that coincide up to logarithmic factors with the global optima but apply to stationary points and the points nearby, supporting the common notion that neural networks do not necessarily need to be optimized globally from a mathematical perspective.

### Function Approximation by Deep Neural Networks with Parameters {0,±12,±1,2}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docume

- Materials ScienceJournal of Statistical Theory and Practice
- 2022

In this paper, it is shown that Cβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

### Distribution Estimation of Contaminated Data via DNN-based MoM-GANs

- Computer ScienceArXiv
- 2022

The numerical results show that the MoM-GAN outperforms other competitive methods when dealing with contaminated data, and derives a non-asymptotic error bound for the DNN-based Mo M-GAN estimator measured by integral probability metrics with the b -smoothness H ¨ older class.

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