Does assigning class weights allow for the use of accuracy metrics that require balanced datasets?

If you have an unbalanced dataset, but you assign (inverse) class weights when fitting, does this mean that model loss and accuracy metrics will be computed to allow for using ROC AUC and accuracy, both metrics that require a balanced dataset?

ROC AUC and accuracy metrics can be misleading if you use an imbalanced dataset. You can achieve high accuracy or ROC AUC by simply selecting the majority class all the time. So, to appropriately measure a model's ability, using different metrics like Precision/Recall AUC, etc. might provide a better accuracy metric. Detailed discussion on this topic here

But if you assign class weights while fitting that essentially neutralizes the imbalance, does that mean that the resulting ROC AUC and accuracy metrics can be relied upon?

For example, if your binary classification dataset has a balance of 1:4, but you assign class weights 4:1 while fitting, the model should interpret the minority class with 4x the weight. This should neutralize the impact of class imbalance and allow the use of accuracy metrics that rely upon a balanced dataset.

Is this reasoning sound?

• How do you rig ROCAUC to be high by picking the majority class every time? ROCAUC is an evaluation of the probability outputs, regardless of how (or if) we use those probabilities to make hard classifications. // What's wrong with getting a high accuracy score by guessing the majority class every time? // Are you familiar with proper scoring-rules and why statisticians do not see class imbalance as an issue?
– Dave
Dec 17, 2021 at 16:47
• Here's why: Imagine you were using a ML model to predict whether a person has brain cancer. You would be very concerned about predicting True Positives and False Negatives, but False Positives are also very important. No one wants to undergo chemo/surgery for a false positive. However, the odds of developing brain cancer is <1%. If I used typical ROC AUC or accuracy, then I could easily get 99% without trying. Dec 17, 2021 at 17:30
• So the naïve model based on random guessing based on the known class ratio is $99\%$ accurate. What's the problem? Do you mean that $99\%$ accuracy makes it sounds like you have an $A$-grade model (like an $A$ in school), even though it is just random guessing?
– Dave
Dec 17, 2021 at 17:59
• I still don't see the problem. Do you mean that you want some metric that tells you what kind of grade your model gets the way that accuracy in the balanced case tells you that $50\%$ is an $\text{F}$ and $99\%$ is an $\text{A}?$ // Note that accuracy is problematic when the classes are perfectly balanced, too.
– Dave
Dec 17, 2021 at 18:27
– Dave
Dec 17, 2021 at 18:58

Assigning class weights does not allow for the use of Accuracy-like metrics that require balanced datasets. That is because strictly speaking no performance metrics requires balance datasets to be calculated - a particular metric (e.g. Accuracy, or Precision) might be almost totally uninformative when applied on a highly imbalanced dataset but that does not mean it doesn't do what it say "on the tin".

When we use class weights based on the relative occurrence rates, we effectively try to assign our misclassification costs such that they balance each other out. That is one approach but not the only approach and it can be argued that it is likely not the best approach either. When working with imbalanced data what happens is that we cannot ignore the fact that the utility of our algorithm (i.e. the decision we will take based on its predictions) will likely not coincide with the abstract metrics we used when performing model fitting. That is a fact of life. Re-weighting our instances might allow us to have a metric that represents our final utility somewhat better but that weight selection needs to be thought carefully rather than be assumed to be correct just because it balances the misclassification costs exactly. If we don't, we one again fall in the traps mentioned in the links provided by Dave on:

Finally please note that AUC-ROC and Accuracy are not directly comparable. AUC-ROC does not need to do hard-class assignment (i.e. it doesn't have to make a decision on class class label) to be evaluated, that is in contrast with AUC-ROC/AUC-PR/Brier score/etc. that allow for evaluating the classifiers output directly. (They are some classifiers, like SVMs, that do hard-class assignment by default but I don't consider them in this context)

• Note that weighting based on misclassification cost could be applied to balanced data sets, too.
– Dave
Dec 18, 2021 at 15:20
• Yes, of course (+1). In general, misclassification costs are very often an important (usually business) choice to make. For example, in a "good client" (e.g. clients spending between \$500 and \$5000 in our website) detection algorithm I once worked, misclassification costs where directly associated with a client's spend. So if we misclassified a client who say bought \$600 worth of items during our evaluation period we inquired a misclassification cost of 600 while if we misclassified on who spent \$4,000 we inquired a misclassification cost of 4,000. Dec 18, 2021 at 16:17
• Thank you 11852. This is helpful. My dataset is unbalanced when stratifying training and validation sets, but not unbalanced over the entire series (i.e. training set is bias with more class zeroes and validation set is bias with significantly more ones). The dataset is a timeseries, so I must preserve the order of training on "older" data and validating on "newer" data. When adjusting for class imbalance in the training set only, I'm having a difficult time interpreting the validation data accordingly. Any suggestions? Dec 19, 2021 at 23:22
• I am glad, I could help. Please note that in the situation you just described it is even more important to think of misclassification costs. We might have a particular data drift type called "concept drift" where our prediction target changes (or in this case becomes more rare), that means we really need to invest on the generalisation abilities of the selected learner. Dec 19, 2021 at 23:33
• This has been difficult to say the least. I've tried a few approaches, which appear to be helping: (1) using a sliding window for training, (2) small batch sizes, (3) significantly reduced the number of epochs the model can train on a particular window before sliding, (4) feature engineering to address drift (e.g. deflating), etc. I suppose much of this is like online-learning, except I didn't freeze layers before sliding, which could be contributing to "catastrophic interference". Have you read any decent papers on the subject? Thank you, this has given me lots to think about. Dec 20, 2021 at 14:09