Efficient Learning with Exponentially-Many Conjunctive Precursors for Interpretable Spatial Event Forecasting

Forecasting spatial societal events in social media is significant and challenging. Most existing methods consider the frequencies of keywords or n-grams to be features, but have not explored the exponentially large space of the conjunctions of those features, such as keyword co-occurrence in messages, which can serve as crucial precursor rules. Due to the inherent exponential complexity of ensemble rule learning, existing work typically adopts greedy/heuristic strategies. This means that they cannot guarantee the solution's optimality, which would require a considerably more sophisticated model for spatial event forecasting, while still suffering from major challenges: 1) Exponentially-dimensional feature learning with distant supervision, 2) Numerical values of conjunctive features, and 3) Spatially heterogeneous conjunction patterns. To concurrently address all these challenges with a theoretical guarantee, we propose a novel spatial event forecasting model which learns numerical conjunctive features efficiently. Specifically, to consider their magnitude, traditional Boolean rules are innovatively generalized to deal with numerical conjunctive features with amenable computational properties. To handle the geographical similarity and heterogeneity in numerical conjunctive feature learning, we propose a new model that implements through a new bi-space hierarchical sparsity regularization for locations and features. Moreover, we propose a new algorithm to optimize the model parameters and prove that it enjoys theoretical guarantees for both the error bounds and time efficiency. Extensive experiments on multiple datasets demonstrate the effectiveness and efficiency of the proposed method.