Fei Zheng

Jiaxin Shen, Jinan Xu, Huiqi Hu et al.

While progress has been made in legal applications, law reasoning, crucial for fair adjudication, remains unexplored. We propose a transparent law reasoning schema enriched with hierarchical factum probandum, evidence, and implicit experience, enabling public scrutiny and preventing bias. Inspired by this schema, we introduce the challenging task, which takes a textual case description and outputs a hierarchical structure justifying the final decision. We also create the first crowd-sourced dataset for this task, enabling comprehensive evaluation. Simultaneously, we propose an agent framework that employs a comprehensive suite of legal analysis tools to address the challenge task. This benchmark paves the way for transparent and accountable AI-assisted law reasoning in the ``Intelligent Court''.

Fei Zheng, Nicolas Duchateau

Model-based clustering techniques have been widely applied to various application areas, while most studies focus on canonical mixtures with unique component distribution form. However, this strict assumption is often hard to satisfy. In this paper, we consider the more flexible Copula-Based Mixture Models (CBMMs) for clustering, which allow heterogeneous component distributions composed by flexible choices of marginal and copula forms. More specifically, we propose an adaptation of the Generalized Iterative Conditional Estimation (GICE) algorithm to identify the CBMMs in an unsupervised manner, where the marginal and copula forms and their parameters are estimated iteratively. GICE is adapted from its original version developed for switching Markov model identification with the choice of realization time. Our CBMM-GICE clustering method is then tested on synthetic two-cluster data (N=2000 samples) with discussion of the factors impacting its convergence. Finally, it is compared to the Expectation Maximization identified mixture models with unique component form on the entire MNIST database (N=70000), and on real cardiac magnetic resonance data (N=276) to illustrate its value for imaging applications.