After having read Gunnar Carlsson's [*Topology and Data*][1] I feel enthusiastic to use some topological data analysis (TDA) methods in my current research, mostly in social sciences. We often handle huge databases and I think it can be an interesting exercise to do TDA. I wonder two things about the current state and purpose of TDA (I do understand TDA's main advantages are not for the social sciences though):

> 1. Are there TDA methods than can be used to establish a relationship among a variable of interest and a set of (possible) explanatory variables? That is, to do some sort of statistical inference?
> 2. Can we make predictions based on TDA tools?

Any bibliographical reference or explanation about why this is not possible is appreciated.

 [1]: http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf