Lingfei Wang

Shaoxuan Cui, Lingfei Wang, Hildeberto Jardon-Kojakhmetov et al.

Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains with memory. Our formulation introduces an even-order paired tensor that links folded and unfolded dynamics and characterizes their steady states and convergence. We further show that a Markov chain with memory can be approximated by a low-dimensional nonlinear tensor-based system and then provide a full system analysis. As an application, we define random walks on hypergraphs where memory naturally arises from the hyperedge structure, providing new tools for analyzing higher-order networks with time-dependent effects.

Lingfei Wang, Tom Michoel

Wisdom of the crowd, the collective intelligence derived from responses of multiple human or machine individuals to the same questions, can be more accurate than each individual, and improve social decision-making and prediction accuracy. This can also integrate multiple programs or datasets, each as an individual, for the same predictive questions. Crowd wisdom estimates each individual's independent error level arising from their limited knowledge, and finds the crowd consensus that minimizes the overall error. However, previous studies have merely built isolated, problem-specific models with limited generalizability, and mainly for binary (yes/no) responses. Here we show with simulation and real-world data that the crowd wisdom problem is analogous to one-dimensional unsupervised dimension reduction in machine learning. This provides a natural class of crowd wisdom solutions, such as principal component analysis and Isomap, which can handle binary and also continuous responses, like confidence levels, and consequently can be more accurate than existing solutions. They can even outperform supervised-learning-based collective intelligence that is calibrated on historical performance of individuals, e.g. penalized linear regression and random forest. This study unifies crowd wisdom and unsupervised dimension reduction, and thereupon introduces a broad range of highly-performing and widely-applicable crowd wisdom methods. As the costs for data acquisition and processing rapidly decrease, this study will promote and guide crowd wisdom applications in the social and natural sciences, including data fusion, meta-analysis, crowd-sourcing, and committee decision making.