Learning discriminative model with *multiple* input vectors per instance

Have you thought about applying multiple instance learning? If the multiple instance learning assumption is not met in your problem, there are some methods in the multiple instance learning literature that map bags to single feature vectors.

You could also look at set kernels. For example the multiple instance kernel of Gaertner et al. seems to be pretty directly applicable. It corresponds to summing the instances up in feature space. This means it still loses some information.

A completely different approach would be to use bag of word representations. This is very popular in computer vision. There, an image is represented as a "bag" of interesting features. Each feature (=instance) is vector quantized and then a histogram over code occurrences is build. If you look up bag of features or bag of words you'll find a lot about this.

Assuming that all N vectors have the same (sparse) feature set, and taking into account that the feature co-occurance is potentially important, I would construct a new derived feature set by "aggregating" vectors while keeping track of feature co-occurances. This, for each data point, would produce a sparse feature set consisting of the following:

1. Counts of each feature present in the data point (i.e. the main effects)
2. Counts of two-feature-combinations present in the data point (i.e. two-way interactions)
3. Counts of three-feature-combinations present in the data point (i.e. three-way interactions)
4. ..5 ..6 .. You get the idea - one can go on as long as computational power and the dataset's sparsity allow (I suspect the point of diminishing returns will be reached pretty quickly)

Once this data transformation is done one can train one's favorite discriminative learner on it.

You might try the paper Classification of Sets using Restricted Boltzmann Machines. I recently skimmed over it and I believe they address the exact problem you are discussing using a hybrid discriminative/generative approach.