Neural Network importance weights / coefficients

[jkaustin]

I would like to measure the importance / coefficient of each of a modest number of inputs toward a regression output for a neural network. I spent the morning searching for the best way to do this and only found things that worked sometimes or were rather complicated. I am wondering if there is some reason not to just add a delta to the inputs one at a time and rerun the predict function. I wrote the following function to use after doing a standard normalization of the inputs and running a neural network creating the model.

def marginal_effects(Data, model, delta):
    inputcount = Data.shape[1]
    baselevel = model.predict(Data).mean()
    identity = numpy.identity(inputcount)
    effects = numpy.zeros([inputcount, 1])
    for i in range(inputcount):
        addedterm = numpy.zeros([inputcount,inputcount])
        addedterm[i,i] = delta
        multiplier = identity + addedterm
        deltaData = Data.dot(multiplier)
        effects[i] = model.predict(deltaData).mean() - baselevel
    return effects * (1/delta)

And then used a delta of 0.01. And the effects could be rescaled if I wanted the importance weights to add to one. It seems to work, so I am just wondering if this is the preferred way to accomplish the task, and if it isn't, then why not.

[jefsummers]

I'm not sure weights in the traditional sense go with neural networks. Instead tend to be used as prediction engines.

If looking for weights, I would use a linear regression model and get the coefficients matrix.