# Doesn't over(/under)sampling an imbalanced dataset cause issues?

I'm reading a lot about how to use different metrics specifically for imbalanced datasets (e.g. two classes present, but 80% of the data is one class) and how to tackle the issue of imbalanced datasets.

One trick is to oversample, so to take more (or even duplicate some) data belonging to the underrepresented class. I've tried this and did achieve better results (before my models would easily just predict a single class for everything, achieving 80% accuracy lol).

However, I was wondering, will this model work well with real-life data? One of the 'laws' of data science/machine learning is that your training data has to have the same/similar attributes as your live data you're intending to use your model on. However, by oversampling, I create a dataset that's 50% one class and 50% other, as opposed to the "natural", real-life-data having 80% of one class and 20% of the other.

So I guess the question in short is: Will oversampling my imbalanced dataset of 80/20 class distribution to 50/50 class distribution impact the usability of my model for real-life data? Why?

Yes, the classifier will expect the relative class frequencies in operation to be the same as those in the training set. This means that if you over-sample the minority class in the training set, the classifier is likely to over-predict that class in operational use.

To see why it is best to consider probabilistic classifiers, where the decision is based on the posterior probability of class membership p(C_i|x), but this can be written using Bayes' rule as

$$p(C_i|x) = \frac{p(x|C_i)p(C_i)}{p(x)}\qquad$$ where $$\qquad p(x) = \sum_j p(x|C_j)p(c_j)$$,

so we can see that the decision depends on the prior probabilities of the classes, $$p(C_i)$$, so if the prior probabilities in the training set are different than those in operation, the operational performance of our classifier will be suboptimal, even if it is optimal for the training set conditions.

Some classifiers have a problem learning from imbalanced datasets, so one solution is to oversample the classes to ameliorate this bias in the classifier. There are to approaches. The first is to oversample by just the right amount to overcome this (usually unknown) bias and no more, but that is really difficult. The other approach is to balance the training set and then post-process the output to compensate for the difference in training set and operational priors. We take the output of the classifier trained on an oversampled dataset and multiply by the ratio of operational and training set prior probabilities,

$$q_o(C_i|x) \propto p_t(x|C_i)p_t(C_i) \times \frac{p_o(C_i)}{p_t(C_i} = p_t(x|C_i)p_o(C_i)$$

Quantities with the o subscript relate to operational conditions and those wit the t subscript relate to training set conditions. I have written this as $$q_o(C_i|x)$$ as it is an un-normalised probability, but it is straight forward to renormalise them by dividing by the sum of $$q_o(C_i|x)$$ over all classes. For some problems it may be better to use cross-validation to chose the correction factor, rather than the theoretical value used here, as it depends on the bias in the classifier due to the imbalance.

So in short, for imbalanced datasets, use a probabilistic classifier and oversample (or reweight) to get a balanced dataset, in order to overcome the bias a classifier may have for imbalanced datasets. Then post-process the output of the classifier so that it doesn't over-predict the minority class in operation.

• Magical answer, thank you!! May 4, 2021 at 11:31
• @lte__ no problem, I'm working on a tutorial at the moment and this is one of the topics May 4, 2021 at 15:51

Undersampling should mostly not be preferred because it causes a huge amount of data loss. In the end, we are giving so much effort to collect data and it basically does not make sense when we throw them away. The issue is here is that you lose samples where your model could learn new things.

Oversampling usually works better as you observed but the problem is that the synthesized samples might be noisy and might not perfectly reflect real-world situations. So, it also creates some deficiencies. So, to what extent oversampling will work depends on your capabilities of generating synthesized samples that are just like real-world samples. Of course, it is again dependent on the problem's complexity. If your generated samples are not like real-world samples, your model will learn on noisy samples which will probably reduce your accuracy in the wild.

• You shouldn't undersample or oversample, unless you know the imbalance is causing a problem. Apparently nobody knows how to determine whether there is a problem stats.stackexchange.com/questions/539638/… and are probably making their classifier worse by fixing a problem that doesn't exist. Imbalance causes no problem whatsoever, provided you have enough data - in which case, just leave the data as it is. Aug 19, 2021 at 9:38