Mapping Highly Nonconvex Energy Landscapes in Clustering, Grammatical and Curriculum Learning
We introduce Energy Landscape Maps (ELMs) as a new and powerful analysis tool of nonconvex problems to the machine learning community. An ELM characterizes and visualizes an energy function with a tree structure, in which each leaf node represents a local minimum and each non-leaf node represents the barrier between adjacent energy basins. We construct ELMs using an advanced MCMC sampling method that dynamically reweights
the energy function to facilitate efficient traversal of the hypothesis space. By providing an intuitive visualization of energy functions, ELMs could help researchers gain new insight into the non-convex problems and facilitate the design and analysis of non-convex optimization
algorithms. We demonstrate this on two classic machine learning problems: clustering with Gaussian mixture models and biclustering.