I am using a univariate filter to reduce the number of features prior to applying a learning algorithm to a huge binary classification dataset (22510066 features x 500 examples). All the features are binary-valued (0 or 1). Most of these features are supposed to be irrelevant. I am using a $\chi^2$ test to obtain a p-value for each feature and then, based on some significance threshold, I would like to keep only the significant features.
Since I am performing so many hypothesis tests, it is necessary to correct for multiple testing. I have chosen to use a method that limits the FDR, as it seems more natural for feature selection. The features in the dataset are not independent and some of them are negatively correlated, thus I am using the Benjamini-Yekutieli method to do the correction. After computing the p-value for each feature, the minimum p-value is 2.7061601033755451e-09.
I have noticed something that I do not understand. If I set the maximum FDR ($\alpha$) to 1.0, which means that the proportion of type I errors is $\leq 1.0$, even the smallest p-value is not small enough to be considered significant. I understand that alpha is an upper bound on the FDR and that if $\alpha=1.0$, it does not mean that 100% of the tests for which the null hypothesis was rejected are type I errors, but I still don't know how to interpret this result.
Could someone please help me interpret this result? Does this mean that the Benjamini-Yekutieli procedure is not powerful enough for such a huge number of tests?