Statistical Machine Learning for Astronomy -- A Textbook

• URL: http://arxiv.org/abs/2506.12230v1
• Date: Fri, 13 Jun 2025 21:17:50 GMT
• Title: Statistical Machine Learning for Astronomy -- A Textbook
• Authors: Yuan-Sen Ting,
• Abstract summary: This book provides a systematic treatment of statistical machine learning for astronomical research.<n>It develops a unified framework that reveals connections between modern data analysis techniques and traditional statistical methods.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques and traditional statistical methods. We show how these techniques emerge from familiar statistical foundations. The consistently Bayesian perspective prioritizes uncertainty quantification and statistical rigor essential for scientific inference in astronomy. The textbook progresses from probability theory and Bayesian inference through supervised learning including linear regression with measurement uncertainties, logistic regression, and classification. Unsupervised learning topics cover Principal Component Analysis and clustering methods. We then introduce computational techniques through sampling and Markov Chain Monte Carlo, followed by Gaussian Processes as probabilistic nonparametric methods and neural networks within the broader statistical context. Our theory-focused pedagogical approach derives each method from first principles with complete mathematical development, emphasizing statistical insight and complementing with astronomical applications. We prioritize understanding why algorithms work, when they are appropriate, and how they connect to broader statistical principles. The treatment builds toward modern techniques including neural networks through a solid foundation in classical methods and their theoretical underpinnings. This foundation enables thoughtful application of these methods to astronomical research, ensuring proper consideration of assumptions, limitations, and uncertainty propagation essential for advancing astronomical knowledge in the era of large astronomical surveys.

Related papers

• Recent Advances in Simulation-based Inference for Gravitational Wave Data Analysis [9.608109856126267]
  This review examines the emerging role of simulation-based inference methods in gravitational wave astronomy.<n>We provide a comprehensive overview of the theoretical foundations underlying various simulation-based inference methods.<n>We explore the applications of these methods across diverse gravitational wave data processing scenarios.
  arXiv  Detail & Related papers  (2025-07-15T10:52:57Z)
• Uncertainty quantification for Markov chains with application to temporal difference learning [63.49764856675643]
  We develop novel high-dimensional concentration inequalities and Berry-Esseen bounds for vector- and matrix-valued functions of Markov chains.<n>We analyze the TD learning algorithm, a widely used method for policy evaluation in reinforcement learning.
  arXiv  Detail & Related papers  (2025-02-19T15:33:55Z)
• Neural Methods for Amortized Inference [0.0]
  Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The resulting tools are amortized, in the sense that, after an initial setup cost, they allow rapid inference through fast feed-forward operations.
  arXiv  Detail & Related papers  (2024-04-18T19:57:06Z)
• A step towards the integration of machine learning and classic model-based survey methods [0.0]
  The usage of machine learning methods in traditional surveys is still very limited.<n>We propose a predictor supported by these algorithms, which can be used to predict any population or subpopulation characteristics.
  arXiv  Detail & Related papers  (2024-02-12T09:43:17Z)
• Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control [22.549914935697366]
  We present a method to incorporate priori knowledge into data-driven control algorithms using kernel embeddings. Our proposed approach incorporates prior knowledge of the system dynamics as a bias term in the kernel learning problem. We demonstrate the improved sample efficiency and out-of-sample generalization of our approach over a purely data-driven baseline.
  arXiv  Detail & Related papers  (2023-01-09T18:35:32Z)
• MARS: Meta-Learning as Score Matching in the Function Space [79.73213540203389]
  We present a novel approach to extracting inductive biases from a set of related datasets. We use functional Bayesian neural network inference, which views the prior as a process and performs inference in the function space. Our approach can seamlessly acquire and represent complex prior knowledge by metalearning the score function of the data-generating process.
  arXiv  Detail & Related papers  (2022-10-24T15:14:26Z)
• Rethinking Bayesian Learning for Data Analysis: The Art of Prior and Inference in Sparsity-Aware Modeling [20.296566563098057]
  Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. This article reviews some recent advances in incorporating sparsity-promoting priors into three popular data modeling tools.
  arXiv  Detail & Related papers  (2022-05-28T00:43:52Z)
• An Extensible Benchmark Suite for Learning to Simulate Physical Systems [60.249111272844374]
  We introduce a set of benchmark problems to take a step towards unified benchmarks and evaluation protocols. We propose four representative physical systems, as well as a collection of both widely used classical time-based and representative data-driven methods.
  arXiv  Detail & Related papers  (2021-08-09T17:39:09Z)
• Online Bootstrap Inference For Policy Evaluation in Reinforcement Learning [90.59143158534849]
  The recent emergence of reinforcement learning has created a demand for robust statistical inference methods. Existing methods for statistical inference in online learning are restricted to settings involving independently sampled observations. The online bootstrap is a flexible and efficient approach for statistical inference in linear approximation algorithms, but its efficacy in settings involving Markov noise has yet to be explored.
  arXiv  Detail & Related papers  (2021-08-08T18:26:35Z)
• Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms [91.3755431537592]
  We analyze four broad meta-learning strategies which rely on plug-in estimation and pseudo-outcome regression. We highlight how this theoretical reasoning can be used to guide principled algorithm design and translate our analyses into practice.
  arXiv  Detail & Related papers  (2021-01-26T17:11:40Z)
• Model-Based Deep Learning [155.063817656602]
  Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Deep neural networks (DNNs) use generic architectures which learn to operate from data, and demonstrate excellent performance. We are interested in hybrid techniques that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches.
  arXiv  Detail & Related papers  (2020-12-15T16:29:49Z)
• A Joint introduction to Gaussian Processes and Relevance Vector Machines with Connections to Kalman filtering and other Kernel Smoothers [5.035807711584951]
  This article introduces and discusses two methods which straddle the areas of probabilistic Bayesian schemes and kernel methods for regression. We provide understanding of the mathematical concepts behind these models, and highlight the relationship to other methods. This is the most in-depth study of its kind to date focused on these two methods, and will be relevant to theoretical understanding and practitioners throughout the domains of data-science, signal processing, machine learning, and artificial intelligence in general.
  arXiv  Detail & Related papers  (2020-09-19T12:22:41Z)
• Consistency of Empirical Bayes And Kernel Flow For Hierarchical Parameter Estimation [18.852474191260445]
  This paper studies two paradigms of learning hierarchical parameters. One is from the probabilistic Bayesian perspective, in particular, the empirical Bayes approach. The other is from the deterministic and approximation theoretic view, and in particular the kernel flow algorithm.
  arXiv  Detail & Related papers  (2020-05-22T20:17:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.