Prediction Errors: Using ML For Measurement

1 Sep

Say you want to measure the how often people visit pornographic domains over some period. To measure that, you build a model to predict whether or not a domain hosts pornography. And let’s assume that for the chosen classification threshold, the False Positive rate (FP) is 10\% and the False Negative rate (FN) is 7\%. Here below, we discuss some of the concerns with using scores from such a model and discuss ways to address the issues.

Let’s get some notation out of the way. Let’s say that we have n users and that we can iterate over them using i. Let’s denote the total number of unique domains—domains visited by any of the n users at least once during the observation window—by k. And let’s use j to iterate over the domains. Let’s denote the number of visits to domain j by user i by c_{ij} = {0, 1, 2, ....}. And let’s denote the total number of unique domains a person visits (\sum (c_{ij} == 1)) using t_i. Lastly, let’s denote predicted labels about whether or not each domain hosts pornography by p, so we have p_1, ..., p_j, ... , p_k.

Let’s start with a simple point. Say there are 5 domains with p: {1_1, 1_2, 1_3, 1_4, 1_5}. Let’s say user one visits the first three sites once and let’s say that user two visits all five sites once. Given 10\% of the predictions are false positives, the total measurement error in user one’s score = 3 * .10 and the total measurement error in user two’s score = 5 * .10. The general point is that total false positives increase as a function of predicted 1s. And the total number of false negative increase as the number of predicted 0s.

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