数据科学中的数学方法

期刊简介

Aim Mathematical Methods in Data Science (MMDS) is an interdisciplinary, peer-reviewed academic journal dedicated to advancing the foundational role of mathematics in driving innovation and rigor in data science. Its core aim is to bridge the gap between mathematical theory and real-world data science applications, publishing high-quality research that develops, refines, or applies mathematical frameworks to address complex data-centric challenges. The journal seeks to foster scholarly dialogue across mathematics, statistics, computer science, and domain-specific fields (e.g., engineering, biology, finance), with the goal of enhancing the theoretical depth, methodological robustness, and practical impact of data science. Additionally, it aims to serve as a resource for researchers, practitioners, and educators—supporting the adoption of rigorous mathematical approaches to solve emerging data problems and shaping the future direction of data science as a discipline. Scope The journal encompasses a broad range of topics that integrate mathematical methods with data science, including but not limited to: Foundational mathematical frameworks for data science: Linear and nonlinear algebra, calculus of variations, optimization theory (e.g., convex/non-convex optimization, stochastic optimization), probability theory, and mathematical statistics (e.g., Bayesian inference, hypothesis testing, statistical learning theory) as applied to data analysis. Machine learning and deep learning: Mathematical foundations of supervised/unsupervised/reinforcement learning; theoretical analysis of neural networks (e.g., convergence, generalization, robustness); mathematical modeling of deep learning architectures (e.g., transformers, graph neural networks). Data representation and dimensionality reduction: Mathematical methods for feature extraction, manifold learning, sparse representation, and low-rank matrix/tensor decomposition; their application to high-dimensional data (e.g., image, text, sensor data). Uncertainty quantification and robustness: Mathematical approaches to modeling and mitigating uncertainty in data (e.g., probabilistic programming, fuzzy logic, robust statistics); analysis of data science models under noise, missing data, or adversarial perturbations. Graph theory and network data science: Mathematical modeling of graph-structured data (e.g., social networks, biological networks); methods for network analysis (e.g., centrality measures, community detection, graph embedding) using combinatorics, algebraic graph theory, or topological data analysis. Time series and spatio-temporal data: Mathematical methods for time series forecasting (e.g., differential equations, autoregressive models, wavelet analysis); spatio-temporal data modeling (e.g., Gaussian processes, geostatistics) for applications in climate science, epidemiology, or urban analytics. Domain-specific applications: Mathematical data science methods tailored to fields such as computational biology (e.g., genomic data analysis), finance (e.g., risk modeling, algorithmic trading), engineering (e.g., signal processing, computer vision), and environmental science (e.g., climate data assimilation).

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