Advances in Statistical AI and Causal Inference

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 2683

Special Issue Editors


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Guest Editor
Institute of Artificial Intelligence, Beihang University, Beijing 100083, China
Interests: high-dimensional statistics; non-asymptotic theory; functional data analysis; robust statistical learning; the mathematics of deep learning; concentration inequalities; subsampling
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China
Interests: design of experiments; drug combination studies; systems biology

Special Issue Information

Dear Colleagues, 

This Special Issue focuses on recent advancements in statistical models and machine learning methods at the intersection of artificial intelligence (AI) and causal inference, with applications in genomics, bioinformatics, and precision medicine. Although AI has achieved remarkable success, there remain challenges in developing statistical theory and methodology for AI. This issue particularly highlights theoretical advancements involving deep neural networks and causal inference, particularly with regard to non-asymptotic theory and small sample learning. The theoretical analysis of deep neural networks can be divided into three components: approximation, optimization, and generalization. Causal inference includes frameworks such as the Rubin causal model, mediation analysis, causal graphs, observational studies, and instrumental variables to enable our understanding of causality and reasoning. We highlight how machine learning and deep learning can be effectively integrated with causal inference, enabling researchers to address potential biases in estimating causal effects and heterogeneous causal effects. We also encourage researchers to incorporate novel insights into their empirical research and experimental design.

The sub-topics to be covered within the issue are as follows:

  • deep neural networks
  • finite sample theory
  • non-asymptotic statistics
  • precision medicine
  • treatment effect estimation
  • uncertainty quantification
  • reinforcement learning
  • adaptive experiments and bandit algorithms
  • experimental design
  • high-dimensional statistics
  • multiple testing

Dr. Huiming Zhang
Dr. Hengzheng Huang
Guest Editors

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Keywords

  • deep neural networks
  • causal inference
  • precision medicine
  • non-asymptotic theory
  • treatment effect
  • statistical machine learning

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Published Papers (3 papers)

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Research

16 pages, 1683 KiB  
Article
Projection-Uniform Subsampling Methods for Big Data
by Yuxin Sun, Wenjun Liu and Ye Tian
Mathematics 2024, 12(19), 2985; https://doi.org/10.3390/math12192985 - 25 Sep 2024
Viewed by 438
Abstract
The idea of experimental design has been widely used in subsampling algorithms to extract a small portion of big data that carries useful information for statistical modeling. Most existing subsampling algorithms of this kind are model-based and designed to achieve the corresponding optimality [...] Read more.
The idea of experimental design has been widely used in subsampling algorithms to extract a small portion of big data that carries useful information for statistical modeling. Most existing subsampling algorithms of this kind are model-based and designed to achieve the corresponding optimality criteria for the model. However, data generating models are frequently unknown or complicated. Model-free subsampling algorithms are needed for obtaining samples that are robust under model misspecification and complication. This paper introduces two novel algorithms, called the Projection-Uniform Subsampling algorithm and its extension. Both algorithms aim to extract a subset of samples from big data that are space-filling in low-dimensional projections. We show that subdata obtained from our algorithms perform superiorly under the uniform projection criterion and centered L2-discrepancy. Comparisons among our algorithms, model-based and model-free methods are conducted through two simulation studies and two real-world case studies. We demonstrate the robustness of our proposed algorithms in building statistical models in scenarios involving model misspecification and complication. Full article
(This article belongs to the Special Issue Advances in Statistical AI and Causal Inference)
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20 pages, 376 KiB  
Article
Sequential Ignorability and Dismissible Treatment Components to Identify Mediation Effects
by Yuhao Deng, Haoyu Wei, Xia Xiao, Yuan Zhang and Yuanmin Huang
Mathematics 2024, 12(15), 2332; https://doi.org/10.3390/math12152332 - 25 Jul 2024
Viewed by 837
Abstract
Mediation analysis is a useful tool to study the mechanism of how a treatment exerts effects on the outcome. Classical mediation analysis requires a sequential ignorability assumption to rule out cross-world reliance of the potential outcome of interest on the counterfactual mediator in [...] Read more.
Mediation analysis is a useful tool to study the mechanism of how a treatment exerts effects on the outcome. Classical mediation analysis requires a sequential ignorability assumption to rule out cross-world reliance of the potential outcome of interest on the counterfactual mediator in order to identify the natural direct and indirect effects. In recent years, the separable effects framework has adopted dismissible treatment components to identify the separable direct and indirect effects. In this article, we compare the sequential ignorability and dismissible treatment components for longitudinal outcomes and time-to-event outcomes with time-varying confounding and random censoring. We argue that the dismissible treatment components assumption has advantages in interpretation and identification over sequential ignorability, whereas these two conditions lead to identical estimators for the direct and indirect effects. As an illustration, we study the effect of transplant modalities on overall survival mediated by leukemia relapse in patients undergoing allogeneic stem cell transplantation. We find that Haplo-SCT reduces the risk of overall mortality through reducing the risk of relapse, and Haplo-SCT can serve as an alternative to MSDT in allogeneic stem cell transplantation. Full article
(This article belongs to the Special Issue Advances in Statistical AI and Causal Inference)
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16 pages, 312 KiB  
Article
Estimating the Complier Average Causal Effect with Non-Ignorable Missing Outcomes Using Likelihood Analysis
by Jierui Du, Gao Wen and Xin Liang
Mathematics 2024, 12(9), 1300; https://doi.org/10.3390/math12091300 - 25 Apr 2024
Viewed by 846
Abstract
Missing data problems arise in randomized trials, which complicates the inference of causal effects if the missing mechanism is non-ignorable. We tackle the challenge of identifying and estimating the complier average causal effect parameters under non-ignorable missingness by increasing the covariates to mitigate [...] Read more.
Missing data problems arise in randomized trials, which complicates the inference of causal effects if the missing mechanism is non-ignorable. We tackle the challenge of identifying and estimating the complier average causal effect parameters under non-ignorable missingness by increasing the covariates to mitigate the sensitivity to the violation of specific identification assumptions. The missing data mechanism is assumed to follow a logistic model, wherein the absence of the outcome is explained by the outcome itself, the treatment received, and the covariates. We establish the identifiability of the models under mild conditions by assuming that the outcome follows a normal distribution. We develop a computational method to estimate model parameters through a two-step likelihood estimation approach, employing subgroup analysis. The bootstrap method is employed for variance estimation, and the effectiveness of our approach is confirmed through simulation. We applied the proposed method to analyze the household income dataset from the Chinese Household Income Project Survey 2013. Full article
(This article belongs to the Special Issue Advances in Statistical AI and Causal Inference)
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