The investigation of legal judgment prediction (LJP), such as sentencing prediction, has attracted broad attention for its potential to promote judicial fairness, making the accuracy and reliability of its computation result an increasingly critical concern. In view of this, we present a new sentencing model that shares both legal logic interpretability and strong prediction capability by introducing a two-stage learning algorithm. Specifically, we first construct a hybrid model that synthesizes a mechanism model based on the main factors for sentencing with a neural network modeling possible uncertain features. We then propose a two-stage learning algorithm: First, an adaptive stochastic gradient (ASG) algorithm is used to get good estimates for the unknown parameters in the mechanistic component of the hybrid model. Then, the Adam optimizer tunes all parameters to enhance the predictive performance of the entire hybrid model. The asymptotic convergence of the ASG-based adaptive predictor is established without requiring any excitation data conditions, thereby providing a good initial parameter estimate for prediction. Based on this, the fast-converging Adam optimizer further refines the parameters to enhance overall prediction accuracy. Experiments on a real-world dataset of intentional injury cases in China show that our new hybrid model combined with our two-stage ASG-Adam algorithm, outperforms the existing related methods in sentencing prediction performance, including those based on neural networks and saturated mechanism models.

This paper considers the parameter learning and data clustering problem for MLR with multiple sub-models and arbitrary mixing weights. To deal with the data streaming case, we propose an online learning algorithm to estimate the unknown parameters. By utilizing Ljung’s ODE method, we establish the almost sure convergence results of this MLR problem without the traditional i.i.d. assumption on the input data for the first time. Based on the convergence property and using the classical stochastic Lyapunov function method, we also obtain the convergence rate analysis of the proposed algorithm for the first time. In addition, the data clustering can asymptotically achieve the same performance as the case with known parameters. Future work will consider how to relax the asymptotically stationary and ergodic assumption on the input data, and how to design algorithms with global convergence performance for the MLR problem.

In many large-scale machine learning applications, data are accumulated over time, and thus, an appropriate model should be able to update in an online style. In particular, it would be ideal to have a storage independent from the data volume, and scan each data item only once. Meanwhile, the data distribution usually changes during the accumulation procedure, making distribution-free one-pass learning a challenging task. In this paper, we propose a simple yet effective approach for this task, without requiring prior knowledge about the change, where every data item can be discarded once scanned. We also present a variant for high-dimensional situations, by exploiting compressed sensing to reduce computational and storage complexity. Theoretical analysis shows that our proposal converges under mild assumptions, and the performance is validated on both synthetic and real-world datasets.