Spatiotemporal Causal Decoupling Model for Air Quality Forecasting

Due to the profound impact of air pollution on human health, livelihoods, and economic development, air quality forecasting is of paramount significance. Initially, we employ the causal graph method to scrutinize the constraints of existing research in comprehensively modeling the causal relationships between the air quality index (AQI) and meteorological features. In order to enhance prediction accuracy, we introduce a novel air quality forecasting model, AirCade, which incorporates a causal decoupling approach. AirCade leverages a spatiotemporal module in conjunction with knowledge embedding techniques to capture the internal dynamics of AQI. Subsequently, a causal decoupling module is proposed to disentangle synchronous causality from past AQI and meteorological features, followed by the dissemination of acquired knowledge to future time steps to enhance performance. Additionally, we introduce a causal intervention mechanism to explicitly represent the uncertainty of future meteorological features, thereby bolstering the model's robustness. Our evaluation of AirCade on an open-source air quality dataset demonstrates over 20\% relative improvement over state-of-the-art models.

Randomly Projected Convex Clustering Model: Motivation, Realization, and Cluster Recovery Guarantees

In this paper, we propose a randomly projected convex clustering model for clustering a collection of $n$ high dimensional data points in $\mathbb{R}^d$ with $K$ hidden clusters. Compared to the convex clustering model for clustering original data with dimension $d$, we prove that, under some mild conditions, the perfect recovery of the cluster membership assignments of the convex clustering model, if exists, can be preserved by the randomly projected convex clustering model with embedding dimension $m = O(\epsilon^{-2}\log(n))$, where $0 < \epsilon < 1$ is some given parameter. We further prove that the embedding dimension can be improved to be $O(\epsilon^{-2}\log(K))$, which is independent of the number of data points. Extensive numerical experiment results will be presented in this paper to demonstrate the robustness and superior performance of the randomly projected convex clustering model. The numerical results presented in this paper also demonstrate that the randomly projected convex clustering model can outperform the randomly projected K-means model in practice.