Generative vs. discriminative

I know that generative means "based on $P(x,y)$" and discriminative means "based on $P(y|x)$," but I'm confused on several points: Wikipedia (+ many other hits on the web) classify things like SVMs and decision trees as being discriminative. But these don't even have probabilistic interpretations. What does discriminative mean here? Has discriminative just come to mean anything that isn't generative? Naive Bayes (NB) is generative because it captures $P(x|y)$ and $P(y)$, and thus you have $P(x,y)$ (as well as $P(y|x)$). Isn't it trivial to make, say, logistic regression (the poster boy of discriminative models) "generative" by simply computing $P(x)$ in a similar fashion (same independence assumption as NB, such that $P(x) = P(x_0) P(x_1)... P(x_d)$, where the MLE for $P(x_i)$ are just frequencies)? I know that discriminative models tend to outperform generative ones. What's the practical use of working with generative models? Being able to generate/simulate data is cited, but when does this come up? I personally only have experience with regression, classification, collab. filtering over structured data, so are the uses irrelevant to me here? The "missing data" argument ($P(x_i|y)$ for missing $x_i$) seems to only give you an edge with training data (when you actually know $y$ and don't need to marginalize over $P(y)$ to get the relatively dumb $P(x_i)$ which you could've estimated directly anyway), and even then imputation is much more flexible (can predict based not just on $y$ but other $x_i$'s as well). What's with the completely contradictory quotes from Wikipedia? "generative models are typically more flexible than discriminative models in expressing dependencies in complex learning tasks" vs. "discriminative models can generally express more complex relationships between the observed and target variables" Related question that got me thinking about this.