Incomplete Label Multi-Task Ordinal Regression for Spatial Event Scale Forecasting

Abstract

Event scales are commonly used by practitioners to gauge subjective feelings on the magnitude and significance of social events. For example, the Centers for Disease Control and Prevention (CDC) utilizes a 10-level scale to distinguish the severity of flu outbreaks and governments typically categorize violent outbreaks based on their intensity as reflected in multiple aspects. Effective forecasting of future event scales can be used qualitatively to determine reasonable resource allocations and facilitate accurate proactive actions by practitioners. Existing spatial event forecasting methods typically focus on the occurrence of events rather than their ordinal event scales as this is very challenging in several respects, including 1) the ordinal nature of the event scale, 2) the spatial heterogeneity of event scaling in different geo-locations, 3) the incompleteness of scale label data for some spatial locations, and 4) the spatial correlation of event scale patterns. In order to address all these challenges concurrently, a MultI-Task Ordinal Regression (MITOR) framework is proposed to effectively forecast the scale of future events. Our model enforces similar feature sparsity patterns for different tasks while preserving the heterogeneity in their scale patterns. In addition, based on the first law of geography, we proposed to enforce spatially-closed tasks to share similar scale patterns with theoretical guarantees. Optimizing the proposed model amounts to a new non-convex and non-smooth problem with an isotonicity constraint, which is then solved by our new algorithm based on ADMM and dynamic programming. Extensive experiments on ten real-world datasets demonstrate the effectiveness and efficiency of the proposed model.