Sampling for multi categorical variable My hypothesis h depends on multiple categorical variables (a,b,c) each with their corresponding set of possible values (A,B,C). Now each of my data point exist in this space where I have no control over the values (observational data). 


  For e.g. Hypothesis to predict user shopping probability say depends
  on (Age, Country, Gender, Devicetype etc.)


How could I sample the above data set so that it would give me a good representation. The techniques I have learned from the books very well apply to one dimension but that is a rare case in practice. If I sample across one dimension my other dimensions will be heavily skewed towards some values. Is there any standard algorithm to give good sampling?
Let me give you some pointers (assuming that I'm right on this, which might not necessarily be true, so proceed with caution :-). First, I'd figure out the applicable terminology. It seems to me that your case can be categorized as multivariate sampling from a categorical distribution (see this section on categorical distribution sampling). Perhaps, the simplest approach to it is to use R ecosystem's rich functionality. In particular, standard stats package contains rmultinom function (link).

If you need more complex types of sampling, there are other packages that might be worth exploring, for example sampling (link), miscF (link), offering rMultinom function (link). If your complex sampling is focused on survey data, consider reading this interesting paper "Complex Sampling and R" by Thomas Lumley.

If you use languages other than R, check multinomial function from Python's numpy package and, for Stata, this blog post. Finally, if you are interested in Bayesian statistics, the following two documents seems to be relevant: this blog post and this survey paper. Hope this helps.