An Entropy-Based Model for Hierarchical Learning

Machine learning is the dominant approach to artificial intelligence, through which computers learn from data and experience. In the framework of supervised learning, for a computer to learn from data accurately and efficiently, some auxiliary information about the data distribution and target function should be provided to it through the learning model. This notion of auxiliary information relates to the concept of regularization in statistical learning theory. A common feature among real-world datasets is that data domains are multiscale and target functions are well-behaved and smooth. In this paper, we propose a learning model that exploits this multiscale data structure and discuss its statistical and computational benefits. The hierarchical learning model is inspired by the logical and progressive easy-to-hard learning mechanism of human beings and has interpretable levels. The model apportions computational resources according to the complexity of data instances and target functions. This property can have multiple benefits, including higher inference speed and computational savings in training a model for many users or when training is interrupted. We provide a statistical analysis of the learning mechanism using multiscale entropies and show that it can yield significantly stronger guarantees than uniform convergence bounds.