Cumulative Restricted Boltzmann Machines for Ordinal Matrix Data Analysis

Restricted Boltzmann machines (RBMs) [36, 9, 20] have recently attracted significant interest due to their versatility in a variety of unsupervised and supervised learning tasks [35, 18, 25], and in building deep architectures [14, 31]. A RBM is a bipartite undirected model that captures the generative process in which a data vector is generated from a binary hidden vector. The bipartite architecture enables very fast data encoding and sampling-based inference; and together with recent advances in learning procedures, we can now process massive data with large models [13, 37, 2]. This paper presents our contributions in developing RBM specifications as well as learning and inference procedures for multivariate ordinal data. This extends and consolidates the reach of RBMs to a wide range of user-generated domains - social responses, recommender systems, product/paper reviews, and expert assessments of health and ecosystems indicators.