Modelling the expected number of errors as a classification problem?

Question

A professor one day visited my school and presented his model for predicting the number of errors in electronic devices. The classifier emitted a probability distribution over the number of possible errors 0, 1, ..., 9, and 10 or more. I asked whouldn't a regressive model perform better? He said that makes no sense since the number of errors is discrete. I said, but you are modelling the expected number of errors, which is a continuous variable. He said, no, the distribution is discrete, you can't have one-and-a-half errors, for example. I don't remember how the discussion ended.

The question is who is right? Does it ever make sense to use classifiers for small counts like errors and similar things? I would think no since the outcomes are drawn from a partially ordered set.

Answer 1

Depends on what you mean by whouldn't a regressive model perform better.

The distribution of counts is indeed discrete so theoretically it is not correct to use vanilla (Gaussian) linear regression. In practice you will find some people dealing away with this assumption and using a Gaussian linear model on discrete outcomes, for ex. by rounding the outputs, but this is theoretically wrong.

A Poisson linear model, however, is also a regression model and is used for (discrete) Poisson processes, which could work in this case. If the number of errors is not bounded then using say a Poisson model would probably be better than using a "classifaction" model which has a fixed number of outcomes.