Before revision:  As a byproduct of our analysis, we resolve a long-standing problem in statistics and machine learning: we show that a global optimum of  sparse principal component analysis can be found in polynomial time without any statistical assumption on the data .
After revision:  As a byproduct of our analysis, we resolve a long-standing problem in statistics and machine learning: we show that a global optimum of a form of sparse principal component analysis can be found in polynomial time without any statistical assumption on the data .