The more I have interfaced with the VMware Big Data Extensions application, the more important accessibility to the REST API became. Documentation for the REST API is normally not exposed, but you can enable it with a single command on the management server.
# /opt/serengeti/sbin/cfgrestschema on
You can then access the documentation for the REST API at the following URL: http://bde.localdomain:8080/restschema/service?APPLICATION=BigDataExtensions
Important Note: There is a rather large disclaimer on the main page that the REST API is not supported by VMware.