Deep-Learning-Assisted Statistical Methods with Examples in R.

Format:

Book

Author/Creator:

Zhan, Tianyu.

Series:

Chapman and Hall/CRC Data Science Series

Language:

English

Physical Description:

1 online resource (184 pages)

Edition:

1st ed.

Place of Publication:

Milton : CRC Press LLC, 2026.

Summary:

This book explores how deep learning enhances statistical methods for hypothesis testing, point estimation, optimization, interpretation, and other aspects. This book is a valuable resource for students, practitioners, and researchers integrating statistics and data science techniques to solve impactful real-world problems.

Contents:

Cover

Half Title

Series Page

Title Page

Copyright Page

Dedication

Contents

Foreword: Navigating the Intersection of Statistical Thinking and Deep Learning

Preface

List of Figures

List of Tables

Acronyms

I. Introduction and Preparation

1. Introduction to Deep Neural Networks (DNNs)

1.1. Artificial Intelligence, Machine Learning, and Deep Learning

1.2. Advantages of Deep Learning

1.2.1. Free of Feature Engineering

1.2.2. Scalability

1.2.3. Continual Learning

1.2.4. Reusability

1.3. Selected Successful Applications

1.3.1. Image Recognition

1.3.2. Language Processing

1.3.3. Reinforcement Learning

1.4. Some Motivating Problems

1.5. Leverage Both Human Intelligence and Artificial Intelligence to Assist Statistical Methods

1.5.1. A Deep Understanding of the Problem

1.5.2. A Good Knowledge of Related Statistical Methods

1.5.3. Additional Mitigations to Safeguard Unexpected Outcomes

2. How to Implement DNN in Regression

2.1. Introduction

2.2. Components of a Deep Neural Network (DNN)

2.2.1. Activation Function

2.2.2. DNN Structure

2.3. DNN Training

2.3.1. Learning Rate

2.3.2. Dropout Rate

2.3.3. Batch Size

2.3.4. Number of Epochs

2.4. An Illustrative Example

2.4.1. Step 1: Generate or Obtain Training Data

2.4.2. Step 2a: Univariate Hyperparameter Tuning

2.4.3. Step 2b: Multivariate Hyperparameter Tuning

2.4.4. Step 3: Final DNN Training with All Data

2.5. Concluding Remarks

II. Statistical Inference

3. Two-sample Parametric Hypothesis Testing

3.1. Introduction

3.2. Problem Setup

3.3. DNN-assisted Testing Statistics and Critical Values

3.3.1. Motivation with Simple Hypothesis

3.3.2. Generalization to Composite Hypothesis

3.4. Computational Framework

3.4.1. Step 1: Define Parameter Spaces.

3.4.2. Step 2: Train the First DNN to Construct Testing Statistics

3.4.3. Step 3: Train the Second DNN to Estimate Critical Values

3.4.4. Step 4: Perform Hypothesis Testing based on Observed Data

3.5. Demonstration via Adaptive Clinical Trials

3.6. Additional Results

3.7. Discussion

4. Point Estimation

4.1. Introduction

4.2. Method 1: DNN-assisted Ensemble Estimator

4.2.1. A Linear Combination of Base Estimators

4.2.2. Step 1: Generate Training Data

4.2.3. Step 2: Train a DNN to Approximate the Optimal Weight

4.2.4. Step 3: Construct the Ensemble Estimator

4.2.5. An Example with Response-Adaptive Randomization (RAR) Design

4.3. Method 2: DNN-assisted Direct Estimator

4.3.1. A Flexible Estimator from DNN

4.3.2. Application to the Example of RAR

4.4. Discussion

III. Numerical Methods

5. Optimization with Unavailable Gradient Information

5.1. Introduction

5.2. A Motivating Problem of Optimizing the Graphical Approach for Multiplicity Control

5.2.1. Review of the Graphical Approach

5.2.2. The Objective Function

5.3. DNN-assisted Optimization

5.3.1. Step 1: Generate Training Data

5.3.2. Step 2: Train DNN to Approximate the Objective Function

5.3.3. Step 3: Conduct Derivative-based Optimization

5.3.4. Step 4: Fine Tune with Derivative-free Optimization

5.4. A Case Study to Optimize the Graphical Approach

5.5. Discussion

6. Protect Integrity and Save Computational Time

6.1. Introduction

6.2. Build a Pre-specified Procedure

6.2.1. Historical Data Borrowing for Multiple Endpoints

6.2.2. Step 1: Identify Parameters for the Prediction Model

6.2.3. Step 2: Generate Training Data for DNN

6.2.4. Step 3: Train DNN to Construct a Pre-specified Model

6.2.5. A Numerical Study

6.3. Save Computational Time in Large-Scale Simulations.

6.3.1. Nonparametric Bootstrap

6.3.2. A Simple Example

6.4. Discussion

7. Interpretable Models in Regression Analysis

7.1. Introduction

7.2. A Proposed Formulation of Interpretable Models

7.2.1. A Multi-layer Structure

7.2.2. Base Components based on Domain Knowledge

7.3. The Workflow to Construct Interpretable Functions

7.3.1. Step 1: Obtain Training Data

7.3.2. Step 2: Define Modified Mallows's Cp-statistic to Evaluate Model Performance

7.3.3. Step 3: Final Model Update

7.4. A Numerical Example

7.5. Concluding Remarks

IV. Extensions

8. Substitutions of Other Methods for DNN

8.1. Introduction

8.2. Some Other Machine Learning Methods

8.2.1. Support Vector Machine (SVM)

8.2.2. Random Forest (RF)

8.2.3. XGBoost (XG)

8.3. Two-sample Hypothesis Testing with the Scale-Uniform Distribution

8.3.1. DNN to Construct Both Testing Statistics and Critical Values

8.3.2. XGBoost to Construct Both Testing Statistics and Critical Values

8.3.3. SVM or RF to Construct Both Testing Statistics and Critical Values

8.3.4. XGBoost or SVM or RF to Construct only Critical Values

8.4. Point Estimation in Adaptive Clinical Trials

8.5. Conclusion and Discussion

9. Limitations and Mitigations

9.1. Potential Limitations

9.2. Ranges or Supports of Training Data

9.2.1. A Concern of Out-of-range

9.2.2. Mitigation 1: Use Wider Ranges

9.2.3. Mitigation 2: Build a More Robust Framework

9.3. Variable Selection in Training Data

9.3.1. Objective-driven Input Variable Selection

9.3.2. Flexible Input Variable Selection

9.4. How to Obtain Training Data

9.4.1. Known Data Generating Mechanism

9.4.2. Nonparametric Approach

10. Some Future Works

10.1. Introduction

10.2. Hypothesis Testing

10.2.1. Nonparametric Hypothesis Testing

10.2.2. Multiple Testing.

10.3. Point Estimation

10.3.1. Construction of Confidence Intervals

10.3.2. Connection with Hypothesis Testing

10.4. Optimization

10.4.1. General to Cover Varying Observed Data

Bibliography

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

1-04-060076-X

1-003-68148-4

1-04-060071-9

9781003681489

OCLC:

1568050434

Publisher Number:

CIPO000336110