Deep Learning and Statistics

Deep Learning and Statistics: Toward Automated Inference and Uncertainty-Aware AI presents modern deep learning through a statistical lens, emphasizing theoretical foundations and methodologies for automated inference and uncertainty-aware AI. The book begins with foundational material on neural network architectures, representation power, stochastic optimization, and Monte Carlo methods. It then develops two complementary directions—“deep learning for statistics” and “statistics for deep learning”—covering topics such as sparse deep learning, stochastic deep learning, extended fiducial inference, deep generative modelling, and deep reinforcement learning. The book is guided by the view that statistical principles can deepen our understanding of deep learning and support its further development. In particular, sparse learning, stochastic modelling, and extended fiducial inference offer complementary tools for making deep learning models more interpretable, uncertainty-aware, and practically useful in modern data science. Conversely, deep neural networks serve as flexible approximators of unknown data-generating mechanisms, enabling new approaches to classical statistical inference problems, including nonlinear variable selection, sufficient dimension reduction, and causal inference in general settings. A distinctive feature of the book is its development of extended fiducial inference as a new paradigm for statistical inference, in which inference is formulated as the problem of solving data-generating equations. Extended fiducial inference uses deep neural networks to approximate parameter inverse mappings and adaptive stochastic-gradient Markov chain Monte Carlo to simulate latent random errors. Through a push-forward mechanism, the uncertainty embedded in the observations is then propagated to model parameters and predictions. This framework generalizes R. A. Fisher’s fiducial insights to broader classes of statistical problems and provides a concrete step toward automated statistical inference and uncertainty-aware AI. The book is intended for researchers in machine learning and statistics, data scientists interested in modern deep learning methodology, and graduate students in statistics, biostatistics, and related data science disciplines. It can also serve as a textbook for special-topics graduate courses focused on the interaction between deep learning and statistics. Key FeaturesProvides a statistical treatment of deep learning, with particular attention to model interpretability, automated statistical inference, and uncertainty-aware AI. Covers foundational material on neural network architectures, representation power, stochastic optimization, and Monte Carlo methods. Offers a systematic treatment of sparse deep learning and stochastic deep learning as tools for structure learning and uncertainty-aware prediction. Explores modern deep learning topics, including generative modelling and reinforcement learning, through a statistical lens. Introduces extended fiducial inference as a new paradigm of statistical inference, recasting statistical inference as the problem of solving data-generating equations and thereby supporting automated statistical inference and uncertainty-aware AI.