Tianhua Chen

Pu Zhang, Tianhua Chen, Bin Liu

Deep learning has become the dominating approach for object detection. To achieve accurate fine-grained detection, one needs to employ a large enough model and a vast amount of data annotations. In this paper, we propose a commonsense knowledge inference module (CKIM) which leverages commonsense knowledge to assist a lightweight deep neural network base coarse-grained object detector to achieve accurate fine-grained detection. Specifically, we focus on a scenario where a single image contains objects of similar categories but varying sizes, and we establish a size-related commonsense knowledge inference module (CKIM) that maps the coarse-grained labels produced by the DL detector to size-related fine-grained labels. Considering that rule-based systems are one of the popular methods of knowledge representation and reasoning, our experiments explored two types of rule-based CKIMs, implemented using crisp-rule and fuzzy-rule approaches, respectively. Experimental results demonstrate that compared with baseline methods, our approach achieves accurate fine-grained detection with a reduced amount of annotated data and smaller model size. Our code is available at: https://github.com/ZJLAB-AMMI/CKIM.

Tianhua Chen

This book provides a compact, derivation-oriented introduction to the mathematical foundations of modern generative artificial intelligence. Rather than surveying every recent architecture or implementation detail, it develops a coherent route through the ideas connecting major families of generative models, from PCA, probabilistic PCA, variational autoencoders, and diffusion models to normalising flows, autoregressive factorisations, GANs, Wasserstein GANs, and energy-based models. The aim is to make the structure of generative modelling more accessible without removing the mathematical substance needed to understand how these models are derived and related. The book is intended as a foundation-building primer for mathematically curious researchers, practitioners, and students.

Tianhua Chen

From large language models to multi-modal agents, Generative Artificial Intelligence (AI) now underpins state-of-the-art systems. Despite their varied architectures, many share a common foundation in probabilistic latent variable models (PLVMs), where hidden variables explain observed data for density estimation, latent reasoning, and structured inference. This paper presents a unified perspective by framing both classical and modern generative methods within the PLVM paradigm. We trace the progression from classical flat models such as probabilistic PCA, Gaussian mixture models, latent class analysis, item response theory, and latent Dirichlet allocation, through their sequential extensions including Hidden Markov Models, Gaussian HMMs, and Linear Dynamical Systems, to contemporary deep architectures: Variational Autoencoders as Deep PLVMs, Normalizing Flows as Tractable PLVMs, Diffusion Models as Sequential PLVMs, Autoregressive Models as Explicit Generative Models, and Generative Adversarial Networks as Implicit PLVMs. Viewing these architectures under a common probabilistic taxonomy reveals shared principles, distinct inference strategies, and the representational trade-offs that shape their strengths. We offer a conceptual roadmap that consolidates generative AI's theoretical foundations, clarifies methodological lineages, and guides future innovation by grounding emerging architectures in their probabilistic heritage.

Tianhua Chen

This paper explores foundational and applied aspects of survival analysis, using fall risk assessment as a case study. It revisits key time-related probability distributions and statistical methods, including logistic regression, Poisson regression, Exponential regression, and the Cox Proportional Hazards model, offering a unified perspective on their relationships within the survival analysis framework. A contribution of this work is the step-by-step derivation and clarification of the relationships among these models, particularly demonstrating that Poisson regression in the survival context is a specific case of the Cox model. These insights address gaps in understanding and reinforce the simplicity and interpretability of survival models. The paper also emphasizes the practical utility of survival analysis by connecting theoretical insights with real-world applications. In the context of fall detection, it demonstrates how these models can simultaneously predict fall risk, analyze contributing factors, and estimate time-to-event outcomes within a single streamlined framework. In contrast, advanced deep learning methods often require complex post-hoc interpretation and separate training for different tasks particularly when working with structured numerical data. This highlights the enduring relevance of classical statistical frameworks and makes survival models especially valuable in healthcare settings, where explainability and robustness are critical. By unifying foundational concepts and offering a cohesive perspective on time-to-event analysis, this work serves as an accessible resource for understanding survival models and applying them effectively to diverse analytical challenges.