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This work addresses a key limitation in current federated learning approaches, which predominantly focus on homogeneous tasks, neglecting the task diversity on local devices. We propose a principled integration of multi-task learning using multi-output Gaussian processes (MOGP) at the local level and federated learning at the global level. MOGP handles correlated classification and regression tasks, offering a Bayesian non-parametric approach that naturally quantifies uncertainty. The central server aggregates the posteriors from local devices, updating a global MOGP prior redistributed for training local models until convergence. Challenges in performing posterior inference on local devices are addressed through the P\'{o}lya-Gamma augmentation technique and mean-field variational inference, enhancing computational efficiency and convergence rate. Experimental results on both synthetic and real data demonstrate superior predictive performance, OOD detection, uncertainty calibration and convergence rate, highlighting the method's potential in diverse applications. Our code is publicly available at https://github.com/JunliangLv/task_diversity_BFL.

The Bayesian two-step change point detection method is popular for the Hawkes process due to its simplicity and intuitiveness. However, the non-conjugacy between the point process likelihood and the prior requires most existing Bayesian two-step change point detection methods to rely on non-conjugate inference methods. These methods lack analytical expressions, leading to low computational efficiency and impeding timely change point detection. To address this issue, this work employs data augmentation to propose a conjugate Bayesian two-step change point detection method for the Hawkes process, which proves to be more accurate and efficient. Extensive experiments on both synthetic and real data demonstrate the superior effectiveness and efficiency of our method compared to baseline methods. Additionally, we conduct ablation studies to explore the robustness of our method concerning various hyperparameters. Our code is publicly available at https://github.com/Aurora2050/CoBay-CPD., Comment: 10 pages, accepted by NeurIPS 2024

Topic evolution modeling has received significant attentions in recent decades. Although various topic evolution models have been proposed, most studies focus on the single document corpus. However in practice, we can easily access data from multiple sources and also observe relationships between them. Then it is of great interest to recognize the relationship between multiple text corpora and further utilize this relationship to improve topic modeling. In this work, we focus on a special type of relationship between two text corpora, which we define as the "lead-lag relationship". This relationship characterizes the phenomenon that one text corpus would influence the topics to be discussed in the other text corpus in the future. To discover the lead-lag relationship, we propose a jointly dynamic topic model and also develop an embedding extension to address the modeling problem of large-scale text corpus. With the recognized lead-lag relationship, the similarities of the two text corpora can be figured out and the quality of topic learning in both corpora can be improved. We numerically investigate the performance of the jointly dynamic topic modeling approach using synthetic data. Finally, we apply the proposed model on two text corpora consisting of statistical papers and the graduation theses. Results show the proposed model can well recognize the lead-lag relationship between the two corpora, and the specific and shared topic patterns in the two corpora are also discovered.

Hierarchical classification problems are commonly seen in practice. However, most existing methods do not fully utilize the hierarchical information among class labels. In this paper, a novel label embedding approach is proposed, which keeps the hierarchy of labels exactly, and reduces the complexity of the hypothesis space significantly. Based on the newly proposed label embedding approach, a new angle-based classifier is developed for hierarchical classification. Moreover, to handle massive data, a new (weighted) linear loss is designed, which has a closed form solution and is computationally efficient. Theoretical properties of the new method are established and intensive numerical comparisons with other methods are conducted. Both simulations and applications in document categorization demonstrate the advantages of the proposed method.