How unimportant features/words are being handled?

[pidahbus]

Hi @csinva, in linear regression or logistic regression we do calculate the standard error or do t-test to identify whether that variable is significant or not. Let me mathematically formulate my question here, assume I am doing one linear regression with two variables (variables can be words also), so the predicted equation will be,

y_hat = b0_hat + b1_hat * x1 + b2_hat * x2

and let's say that b1_hat = 100 and b2_hat = 2. We may think that as b1_hat is larger than b2_hat, then it has more positive effect on output, but it may happen that in spite of high value, x1 may come insignificant by doing t-test of b1_hat because of it's high standard error.

What I understood reading your paper that the ACD/CD score is somewhat similar to the b (or beta or coefficients) values of the above linear (or logistic) equation. Now in spite of very higher (or lower) CD/ACD score of a word or phrase, it may happen that the specific word/phrase is not important/insignificant to the model. Could you please tell me how your method is handling this scenario?

[csinva]

Thanks for the detailed question!

One quick thing to clarify, the ACD/CD score is actually not the same as the coefficient, but is more like the coefficient * the feature value. In your example above, the ACD/CD score for the feature x_1 is like b1_hat * x1 . As a result, it takes into account both the value of the feature and the coefficient when deciding how significant something is.

[pidahbus]

Hi @csinva,
your last answer arose two questions in my mind.

1. I think to check whether x1 is important or not, we need to consider the standard error of b1_hat. Values of x1 and b1_hat are not sufficient.

2. If the ACD/CD score is analogous to b1_hat * x1, that means while calculating feature importance it considers thee value of the feature also. This means you method will always give higher ACD/CD score to the outliers.

[csinva]

Thanks for the questions!

1. Re: standard error - this is a good point and something that would be good to look into! As far as I know there are basically no techniques to explicitly do this, although one might be able to co-opt some popular techniques for estimating neural network uncertainty (e.g. test-time dropout or model ensembling)

2. This is often true (although unlike a linear model, the contribution of extreme values of features can often saturate / behave nonlinearly). It's also usually worth comparing the relative contributions of different features for a single prediction (and if comparing across different predictions, normalizing by the prediction values for each data point).

Hope that helps!