Machine Learning

http://machinelearningmastery.com/a-tour-of-machine-learning-algorithms

The following are some APIs for Machine Language/Statistics that can be used in a Java environment.  

Deep Learning
http://deeplearning4j.org/gettingstarted.html

Machine Learning Libraries/Tool Kits
https://github.com/josephmisiti/awesome-machine-learning

http://scottlocklin.wordpress.com/2014/07/22/neglected-machine-learning-ideas/

Weka is a package of Machine Learning algorithms written in Java that is commonly referred to one as one of the main data mining libraries.  Weka does have a Graphical User Interface, as well as, a Java API that the algorithms can be accessed with.  

Weka does offer a commercial license — which is through Pentaho.  

R has a package that allows one to access Weka called RWeka.

JSat is a java machine learning library.  

It can be accessed at:
https://code.google.com/p/java-statistical-analysis-tool/

A blog is maintained at:  http://jsatml.blogspot.ca/

JMSL is a commercial statistical library for Java.  They offer an academic version, however, I believed it was a license that expired and it had a registration key that JMSL had to access when the code was being executed. 

http://www.roguewave.com/products/imsl-numerical-libraries/java-library.aspx