For the purpose of research and publications, the ability to translate mathematical models into programming environment should suffice: it is not like you have to code up production-ready machine learning engine anyways.
Try MATLAB. I have Computer Science / Social Sciences PhD. student friends in Machine Learning / Learning Sciences research, and MATLAB is their platform of choice: simple, easy to get the ideas going, and there exist several toolboxes and packages for machine learning. (Provided that you apply(ied) for Computer Science PhD., I assume that the basic constructs of programming is not foreign to you.) Plus, it has superb data visualization support: it can generate all the fancy graphs that your publication will be using.
Another platform you might want to be in would be Python: relatively simpler compared to other platforms (Weka + Java or Weka + CPP) and the machine learning packages are evolving there. And a lot of pretty pretty data visualization packages available too.