Causal Inference and Machine Learning: Mathematical Modeling, Analysis and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 1280

Editors


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Guest Editor
Department of Intelligent Data Science, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China
Interests: causal inference; machine learning

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Guest Editor Assistant
PolyU Academy for Artificial Intelligence (PAAI), The Hong Kong Polytechnic University, Hong Kong 999077, China
Interests: machine learning; deep learning

Special Issue Information

Dear Colleagues,

As machine learning systems are increasingly deployed in complex real-world environments, challenges such as noisy observations, incomplete supervision, heterogeneous data sources, and adaptive behaviors call for principled mathematical frameworks to ensure reliability, interpretability, and generalization. This Special Issue will focus on the integration of causal inference and machine learning through rigorous mathematical modeling, theoretical analysis, and practical applications.

We particularly welcome contributions that develop mathematical foundations for learning under imperfect data conditions, including noisy, weak, or biased supervision, and methods that leverage causal models to distinguish spurious correlations from stable causal mechanisms. Another key theme is the combination of symbolic reasoning and logic rule mining with statistical learning, aiming to enhance explainability and robustness through structured representations. In addition, we encourage research on agent behavior modeling and strategic learning, where causal demonstrate provides insights into multi-agent interactions, feedback dynamics, and distributional shifts.

This Special Issue aims to promote interdisciplinary research, bridging statistical learning theory, causal modeling, symbolic reasoning, and agent-based analysis. Applications of interest include trustworthy AI, decision-making systems, and learning in complex interactive environments. By emphasizing mathematical modeling and analysis, this Issue aims to advance machine learning systems that are reliable, interpretable, and resilient in noisy and dynamic settings.

Topics of interest include, but are not limited to, the following:

  • Mathematical modeling for causal inference in machine learning;
  • Learning under noisy, weak, or biased supervision;
  • Logic rule mining, symbolic reasoning, and structured learning;
  • Agent behavior modeling, strategic learning, and distributional shifts;
  • Applications of causal and mathematical learning frameworks.

Dr. Haotian Wang
Guest Editor

Dr. Zhiqiang Kou
Guest Editor Assistant

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Keywords

  • causal inference
  • mathematical modeling
  • machine learning theory
  • label noise
  • symbolic reasoning
  • agent behavior analysis

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Published Papers (2 papers)

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Research

19 pages, 67516 KB  
Article
Source-Seeking Approach with Non-Reversing Forward Velocity Regulation via Multi-Sensor Feedback
by Qianhao Sun, Guo Li, Jinxian Shen, Rui Wu, Weihua Zhang and Mingyang Geng
Mathematics 2026, 14(13), 2260; https://doi.org/10.3390/math14132260 - 24 Jun 2026
Viewed by 288
Abstract
Source-Seeking in unknown scalar fields is a fundamental problem in robotics with applications in environmental monitoring and disaster response. In this work, we present a source-seeking approach with non-reversing forward velocity regulation by fusing measurement data from multiple sensors within the Stochastic Extremum [...] Read more.
Source-Seeking in unknown scalar fields is a fundamental problem in robotics with applications in environmental monitoring and disaster response. In this work, we present a source-seeking approach with non-reversing forward velocity regulation by fusing measurement data from multiple sensors within the Stochastic Extremum Seeking (SES) framework. Specifically, a device model with multiple sensors is first constructed, and then a velocity regulation scheme is designed by leveraging the boundedness of the hyperbolic tangent function and the non-negativity of the exponential function to guarantee strictly positive forward velocity. We then evaluate the algorithm both in simulation environments and on the real-world Two-Wheeled Differential Drive Robot platform. The experiments show that our approach not only ensures the forward velocity remains non-negative, aligning with the design expectation, but also accurately locates the source. This work provides new insights into the design of velocity regulation strategies within the SES framework. Full article
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19 pages, 854 KB  
Article
STAGE: LLM-Driven Semantic and Topological Augmented Graph Embedding for Text-Attributed Graphs
by Shiwei Huang, Shunxin Xiao, Xu-Yao Zhang, Shunzhi Zhu, Luoqi Liu and Da-Han Wang
Mathematics 2026, 14(9), 1568; https://doi.org/10.3390/math14091568 - 6 May 2026
Viewed by 570
Abstract
Text-attributed graphs (TAGs) require models to jointly exploit node text and graph structure, yet doing so effectively remains difficult when node text is sparse and the structural context is large. Here, we propose STAGE (Semantic and Topological Augmented G [...] Read more.
Text-attributed graphs (TAGs) require models to jointly exploit node text and graph structure, yet doing so effectively remains difficult when node text is sparse and the structural context is large. Here, we propose STAGE (Semantic and Topological Augmented Graph Embedding), a two-stage framework for representation learning on TAGs. In Stage I, a frozen large language model is used offline to generate explanatory text that enriches compressed node attributes without introducing online LLM training cost. In Stage II, STAGE performs structure-aware representation learning under a fixed global token budget by combining random-walk-based structural context with graph-conditioned token reduction before PLM encoding. This design preserves informative semantic content while preventing unconstrained sequence expansion. Experiments on seven benchmark datasets show that STAGE consistently outperforms strong baselines under the same evaluation setting and maintains favorable efficiency under bounded input-length constraints. Full article
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