Zhiliang Ying

Dapeng Shi, Tiandong Wang, Zhiliang Ying

Exploring and detecting community structures hold significant importance in genetics, social sciences, neuroscience, and finance. Especially in graphical models, community detection can encourage the exploration of sets of variables with group-like properties. In this paper, within the framework of Gaussian graphical models, we introduce a novel decomposition of the underlying graphical structure into a sparse part and low-rank diagonal blocks (non-overlapped communities). We illustrate the significance of this decomposition through two modeling perspectives and propose a three-stage estimation procedure with a fast and efficient algorithm for the identification of the sparse structure and communities. Also on the theoretical front, we establish conditions for local identifiability and extend the traditional irrepresentability condition to an adaptive form by constructing an effective norm, which ensures the consistency of model selection for the adaptive $\ell_1$ penalized estimator in the second stage. Moreover, we also provide the clustering error bound for the K-means procedure in the third stage. Extensive numerical experiments are conducted to demonstrate the superiority of the proposed method over existing approaches in estimating graph structures. Furthermore, we apply our method to the stock return data, revealing its capability to accurately identify non-overlapped community structures.

Yian Huang, Yang Feng, Zhiliang Ying

Representation-based multi-task learning (MTL) improves efficiency by learning a shared structure across tasks, but its practical application is often hindered by contamination, outliers, or adversarial tasks. Most existing methods and theories assume a clean or near-clean setting, failing when contamination is significant. This paper tackles representation MTL with an unknown and potentially large contamination proportion, while also allowing for heterogeneity among inlier tasks. We introduce a Robust and Adaptive Spectral method (RAS) that can distill the shared inlier representation effectively and efficiently, while requiring no prior knowledge of the contamination level or the true representation dimension. Theoretically, we provide non-asymptotic error bounds for both the learned representation and the per-task parameters. These bounds adapt to inlier task similarity and outlier structure, and guarantee that RAS performs at least as well as single-task learning, thus preventing negative transfer. We also extend our framework to transfer learning with corresponding theoretical guarantees for the target task. Extensive experiments confirm our theory, showcasing the robustness and adaptivity of RAS, and its superior performance in regimes with up to 80\% task contamination.

Zhi Wang, Xueying Tang, Jingchen Liu et al.

Response process data collected from human-computer interactive items contain rich information about respondents' behavioral patterns and cognitive processes. Their irregular formats as well as their large sizes make standard statistical tools difficult to apply. This paper develops a computationally efficient method for exploratory analysis of such process data. The new approach segments a lengthy individual process into a sequence of short subprocesses to achieve complexity reduction, easy clustering and meaningful interpretation. Each subprocess is considered a subtask. The segmentation is based on sequential action predictability using a parsimonious predictive model combined with the Shannon entropy. Simulation studies are conducted to assess performance of the new methods. We use the process data from PIAAC 2012 to demonstrate how exploratory analysis of process data can be done with the new approach.

Xueying Tang, Susu Zhang, Zhi Wang et al.

Process data refer to data recorded in the log files of computer-based items. These data, represented as timestamped action sequences, keep track of respondents' response processes of solving the items. Process data analysis aims at enhancing educational assessment accuracy and serving other assessment purposes by utilizing the rich information contained in response processes. The R package ProcData presented in this article is designed to provide tools for processing, describing, and analyzing process data. We define an S3 class "proc" for organizing process data and extend generic methods summary and print for class "proc". Two feature extraction methods for process data are implemented in the package for compressing information in the irregular response processes into regular numeric vectors. ProcData also provides functions for fitting and making predictions from a neural-network-based sequence model. These functions call relevant functions in package keras for constructing and training neural networks. In addition, several response process generators and a real dataset of response processes of the climate control item in the 2012 Programme for International Student Assessment are included in the package.

Xueying Tang, Zhi Wang, Jingchen Liu et al.

Computer simulations have become a popular tool of assessing complex skills such as problem-solving skills. Log files of computer-based items record the entire human-computer interactive processes for each respondent. The response processes are very diverse, noisy, and of nonstandard formats. Few generic methods have been developed for exploiting the information contained in process data. In this article, we propose a method to extract latent variables from process data. The method utilizes a sequence-to-sequence autoencoder to compress response processes into standard numerical vectors. It does not require prior knowledge of the specific items and human-computers interaction patterns. The proposed method is applied to both simulated and real process data to demonstrate that the resulting latent variables extract useful information from the response processes.

Yang Feng, Tengfei Li, Zhiliang Ying

A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study stability properties of the penalized maximum likelihood estimator, two types of asymptotic stability are defined. Theoretical properties, including the parameter estimation consistency, model selection consistency, and asymptotic stability, are established under suitable regularity conditions. An efficient coordinate-descent algorithm is proposed. Simulation results and real data analysis show that the proposed method has competitive performance in comparison with existing ones.