RegRocket: Scalable Multinomial Autologistic Regression with Unordered Categorical Variables Using Markov Logic Networks

Autologistic regression is one of the most popular statistical tools to predict spatial phenomena in several applications, including epidemic diseases detection, species occurrence prediction, earth observation, and business management. In general, autologistic regression divides the space into a two-dimensional grid, where the prediction is performed at each cell in the grid. The prediction at any location is based on a set of predictors (i.e., features) at this location and predictions from neighboring locations. In this article, we address the problem of building efficient autologistic models with multinomial (i.e., categorical) prediction and predictor variables, where the categories represented by these variables are unordered. Unfortunately, existing methods to build autologistic models are designed for binary variables in addition to being computationally expensive (i.e., do not scale up for large-scale grid data such as fine-grained satellite images). Therefore, we introduce RegRocket: a scalable framework to build multinomial autologistic models for predicting large-scale spatial phenomena. RegRocket considers both the accuracy and efficiency aspects when learning the regression model parameters. To this end, RegRocket is built on top of Markov Logic Network (MLN), a scalable statistical learning framework, where its internals and data structures are optimized to process spatial data. RegRocket provides an equivalent representation of the multinomial prediction and predictor variables using MLN where the dependencies between these variables are transformed into first-order logic predicates. Then, RegRocket employs an efficient framework that learns the model parameters from the MLN representation in a distributed manner. Extensive experimental results based on two large real datasets show that RegRocket can build multinomial autologistic models, in minutes, for 1 million grid cells with 0.85 average F1-score.