Best way to pass distribution estimates as a feature into deep learning I have been googling a lot and somehow cannot find a good answer.
Lets say we have deep neural net model, arbitrary topology. Also we have 10 features and for each features we got 1000 observations for each time step. 
What is the best way to pass the data into our network? Perhaps some initial central moments, like mean, variance, skewness, kurtozis...? Or should we find the distribution that best explains our features (relying somehow on expert judgment), like lognormal and pass only the two parameters obtained with MLE?
Any ideas or experiences?
EDIT (on answer):
The goal is binary classification. 
If we input whole 10*1000 as features we obtain the curse of dimensioanlity. Maybe I wasn't clear. We have 10 000 different observations at each time step, while we know that they come from 10 separate distributions. Learning a neural net with 10K input features is at least for my hardware currently impossible.
We obtain those samples at each time step as an output of some meta model, and we have 10 different meta models. Sorry for unclear question before.
SECOND EDIT:
Perhaps we can teach 10 variational autoencoders, that will map our distributions to lets say 3 parameters and then manage to decode the information and we minimize KL loss. Has anyone tried that with unknown distributions?
Best JJ
 A: Feed in the observations themselves.
Feeding in the distribution of your observations will not be helpful. What is it that drives your target variable? It's actual observations, not their distribution. If the value of feature A correlates with outcome X, then you want to detect this, and it doesn't matter (primarily) how prevalent A is, or what shape it has.
A: I think the approaches you have suggested are all good ideas (calculating moments, seeing if the outputs of the meta models follow standard distributions etc). I would try approximating the outputs of the meta-models with simple distributions first (e.g. normal, exponential...) The problem with this as you have identified is that they may not capture the structure of the output of the meta models very well.
If this is the case, you could take a more non-parametric approach. You could feed the values at certain percentiles of the output of your meta-models in and do this for each meta-model. Assuming they are continuously distributed, you could for example feed the values at each 2% percentile into your data. This way you could reduce the dimensionality of of the output of each meta-models to 50, but still capture the shape of the distribution of outputs. You can obviously smooth the distribution over meta-model outputs prior to doing this etc etc.
