for an Outdated Problem
You might be coaching your mannequin for spam detection. Your dataset has many extra positives than negatives, so that you make investments numerous hours of labor to rebalance it to a 50/50 ratio. Now you might be glad since you have been capable of deal with the category imbalance. What if I informed you that 60/40 might have been not solely sufficient, however even higher?
In most machine studying classification purposes, the variety of situations of 1 class outnumbers that of different lessons. This slows down studying [1] and might probably induce biases within the skilled fashions [2]. Probably the most broadly used strategies to deal with this depend on a easy prescription: discovering a solution to give all lessons the identical weight. Most frequently, that is executed by means of easy strategies equivalent to giving extra significance to minority class examples (reweighting), eradicating majority class examples from the dataset (undersampling), or together with minority class situations greater than as soon as (oversampling).
The validity of those strategies is usually mentioned, with each theoretical and empirical work indicating that which resolution works greatest relies on your particular software [3]. Nevertheless, there’s a hidden speculation that’s seldom mentioned and too usually taken with no consideration: Is rebalancing even a good suggestion? To some extent, these strategies work, so the reply is sure. However ought to we absolutely rebalance our datasets? To make it easy, allow us to take a binary classification downside. Ought to we rebalance our coaching knowledge to have 50% of every class? Instinct says sure, and instinct guided follow till now. On this case, instinct is incorrect. For intuitive causes.
What Do We Imply by ‘Coaching Imbalance’?
Earlier than we delve into how and why 50% will not be the optimum coaching imbalance in binary classification, allow us to outline some related portions. We name n₀ the variety of situations of 1 class (normally, the minority class), and n₁ these of the opposite class. This manner, the whole variety of knowledge situations within the coaching set is n=n₀+n₁ . The amount we analyze in the present day is the coaching imbalance,
ρ⁽ᵗʳᵃⁱⁿ⁾ = n₀/n .
Proof that fifty% Is Suboptimal
Preliminary proof comes from empirical work on random forests. Kamalov and collaborators measured the optimum coaching imbalance, ρ⁽ᵒᵖᵗ⁾, on 20 datasets [4]. They discover its worth varies from downside to downside, however conclude that it is kind of ρ⁽ᵒᵖᵗ⁾=43%. Because of this, in line with their experiments, you need barely extra majority than minority class examples. That is nonetheless not the complete story. If you wish to intention at optimum fashions, don’t cease right here and straightaway set your ρ⁽ᵗʳᵃⁱⁿ⁾ to 43%.
The truth is, this yr, theoretical work by Pezzicoli et al. [5], confirmed that the the optimum coaching imbalance will not be a common worth that’s legitimate for all purposes. It isn’t 50% and it’s not 43%. It seems, the optimum imbalance varies. It could some instances be smaller than 50% (as Kamalov and collaborators measured), and others bigger than 50%. The particular worth of ρ⁽ᵒᵖᵗ⁾ will depend upon particulars of every particular classification downside. One solution to discover ρ⁽ᵒᵖᵗ⁾ is to coach the mannequin for a number of values of ρ⁽ᵗʳᵃⁱⁿ⁾, and measure the associated efficiency. This might for instance appear like this:
Though the precise patterns figuring out ρ⁽ᵒᵖᵗ⁾ are nonetheless unclear, it appears that evidently when knowledge is plentiful in comparison with the mannequin measurement, the optimum imbalance is smaller than 50%, as in Kamalov’s experiments. Nevertheless, many different elements — from how intrinsically uncommon minority situations are, to how noisy the coaching dynamics is — come collectively to set the optimum worth of the coaching imbalance, and to find out how a lot efficiency is misplaced when one trains away from ρ⁽ᵒᵖᵗ⁾.
Why Good Stability Isn’t All the time Finest
As we stated, the reply is definitely intuitive: as completely different lessons have completely different properties, there isn’t a motive why each lessons would carry the identical data. The truth is, Pezzicoli’s group proved that they normally don’t. Due to this fact, to deduce the perfect determination boundary we would want extra situations of a category than of the opposite. Pezzicoli’s work, which is within the context of anomaly detection, offers us with a easy and insightful instance.
Allow us to assume that the information comes from a multivariate Gaussian distribution, and that we label all of the factors to the precise of a choice boundary as anomalies. In 2D, it might appear like this:
The dashed line is our determination boundary, and the factors on the precise of the choice boundary are the n₀ anomalies. Allow us to now rebalance our dataset to ρ⁽ᵗʳᵃⁱⁿ⁾=0.5. To take action, we have to discover extra anomalies. Because the anomalies are uncommon, those who we’re most certainly to seek out are near the choice boundary. Already by eye, the situation is strikingly clear:
Anomalies, in yellow, are stacked alongside the choice boundary, and are subsequently extra informative about its place than the blue factors. This may induce to assume that it’s higher to privilege minority class factors. On the opposite aspect, anomalies solely cowl one aspect of the choice boundary, so as soon as one has sufficient minority class factors, it may possibly change into handy to spend money on extra majority class factors, with a purpose to higher cowl the opposite aspect of the choice boundary. As a consequence of those two competing results, ρ⁽ᵒᵖᵗ⁾ is usually not 50%, and its precise worth is downside dependent.
The Root Trigger Is Class Asymmetry
Pezzicoli’s idea exhibits that the optimum imbalance is usually completely different from 50%, as a result of completely different lessons have completely different properties. Nevertheless, they solely analyze one supply of variety amongst lessons, that’s, outlier habits. But, as it’s for instance proven by Sarao-Mannelli and coauthors [6], there are many results, such because the presence of subgroups inside lessons, which may produce an analogous impact. It’s the concurrence of a really massive variety of results figuring out variety amongst lessons, that tells us what the optimum imbalance for our particular downside is. Till now we have a idea that treats all sources of asymmetry within the knowledge collectively (together with these induced by how the mannequin structure processes them), we can not know the optimum coaching imbalance of a dataset beforehand.
Key Takeaways & What You Can Do In a different way
If till now you rebalanced your binary dataset to 50%, you have been doing properly, however you have been most certainly not doing the very best. Though we nonetheless would not have a idea that may inform us what the optimum coaching imbalance ought to be, now you realize that it’s doubtless not 50%. The excellent news is that it’s on the way in which: machine studying theorists are actively addressing this subject. Within the meantime, you’ll be able to consider ρ⁽ᵗʳᵃⁱⁿ⁾ as a hyperparameter which you’ll tune beforehand, simply as some other hyperparameter, to rebalance your knowledge in essentially the most environment friendly means. So earlier than your subsequent mannequin coaching run, ask your self: is 50/50 actually optimum? Strive tuning your class imbalance — your mannequin’s efficiency may shock you.
References
[1] E. Francazi, M. Baity-Jesi, and A. Lucchi, A theoretical evaluation of the training dynamics beneath class imbalance (2023), ICML 2023
[2] Okay. Ghosh, C. Bellinger, R. Corizzo, P. Branco,B. Krawczyk,and N. Japkowicz, The category imbalance downside in deep studying (2024), Machine Studying, 113(7), 4845–4901
[3] E. Loffredo, M. Pastore, S. Cocco and R. Monasson, Restoring steadiness: principled beneath/oversampling of information for optimum classification (2024), ICML 2024
[4] F. Kamalov, A.F. Atiya and D. Elreedy, Partial resampling of imbalanced knowledge (2022), arXiv preprint arXiv:2207.04631
[5] F.S. Pezzicoli, V. Ros, F.P. Landes and M. Baity-Jesi, Class imbalance in anomaly detection: Studying from an precisely solvable mannequin (2025). AISTATS 2025
[6] S. Sarao-Mannelli, F. Gerace, N. Rostamzadeh and L. Saglietti, Bias-inducing geometries: an precisely solvable knowledge mannequin with equity implications (2022), arXiv preprint arXiv:2205.15935
