for an Previous Problem
You’re 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 happy since you have been capable of deal with the category imbalance. What if I advised you that 60/40 might have been not solely sufficient, however even higher?
In most machine studying classification functions, the variety of situations of 1 class outnumbers that of different courses. This slows down studying [1] and may probably induce biases within the skilled fashions [2]. Probably the most extensively used strategies to handle this depend on a easy prescription: discovering a approach to give all courses the identical weight. Most frequently, that is executed by easy strategies reminiscent of 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 commonly mentioned, with each theoretical and empirical work indicating that which resolution works finest depends upon your particular software [3]. Nevertheless, there’s a hidden speculation that’s seldom mentioned and too typically 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 (often, the minority class), and n₁ these of the opposite class. This fashion, the overall variety of knowledge situations within the coaching set is n=n₀+n₁ . The amount we analyze as we speak 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%. Which means, in response to their experiments, you need barely extra majority than minority class examples. That is nevertheless not the total story. If you wish to intention at optimum fashions, don’t cease right here and straightaway set your ρ⁽ᵗʳᵃⁱⁿ⁾ to 43%.
In reality, this 12 months, 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 functions. It’s not 50% and it’s not 43%. It seems, the optimum imbalance varies. It could possibly some occasions be smaller than 50% (as Kamalov and collaborators measured), and others bigger than 50%. The precise worth of ρ⁽ᵒᵖᵗ⁾ will rely upon particulars of every particular classification downside. One approach 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 ample in comparison with the mannequin dimension, the optimum imbalance is smaller than 50%, as in Kamalov’s experiments. Nevertheless, many different components — 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 Steadiness Isn’t At all times Finest
As we mentioned, the reply is definitely intuitive: as totally different courses have totally different properties, there isn’t a purpose why each courses would carry the identical info. In reality, Pezzicoli’s crew proved that they often don’t. Due to this fact, to deduce the perfect choice boundary we would want extra situations of a category than of the opposite. Pezzicoli’s work, which is within the context of anomaly detection, gives 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 fitting of a choice boundary as anomalies. In 2D, it might appear like this:
The dashed line is our choice boundary, and the factors on the fitting 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. For the reason that anomalies are uncommon, people who we’re more than likely to search out are near the choice boundary. Already by eye, the state of affairs 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 suppose that it’s higher to privilege minority class factors. On the opposite facet, anomalies solely cowl one facet of the choice boundary, so as soon as one has sufficient minority class factors, it might change into handy to put money into extra majority class factors, to be able to higher cowl the opposite facet of the choice boundary. As a consequence of those two competing results, ρ⁽ᵒᵖᵗ⁾ is mostly not 50%, and its actual worth is downside dependent.
The Root Trigger Is Class Asymmetry
Pezzicoli’s concept exhibits that the optimum imbalance is mostly totally different from 50%, as a result of totally different courses have totally different properties. Nevertheless, they solely analyze one supply of variety amongst courses, that’s, outlier conduct. But, as it’s for instance proven by Sarao-Mannelli and coauthors [6], there are many results, such because the presence of subgroups inside courses, which may produce an identical impact. It’s the concurrence of a really massive variety of results figuring out variety amongst courses, that tells us what the optimum imbalance for our particular downside is. Till we now have a concept that treats all sources of asymmetry within the knowledge collectively (together with these induced by how the mannequin structure processes them), we can’t know the optimum coaching imbalance of a dataset beforehand.
Key Takeaways & What You Can Do Otherwise
If till now you rebalanced your binary dataset to 50%, you have been doing effectively, however you have been more than likely not doing the very best. Though we nonetheless don’t have a concept that may inform us what the optimum coaching imbalance ought to be, now you recognize that it’s seemingly not 50%. The excellent news is that it’s on the best way: 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 every other hyperparameter, to rebalance your knowledge in probably the most environment friendly manner. So earlier than your subsequent mannequin coaching run, ask your self: is 50/50 actually optimum? Attempt tuning your class imbalance — your mannequin’s efficiency may shock you.
References
[1] E. Francazi, M. Baity-Jesi, and A. Lucchi, A theoretical analysis of the learning dynamics under class imbalance (2023), ICML 2023
[2] Okay. Ghosh, C. Bellinger, R. Corizzo, P. Branco,B. Krawczyk,and N. Japkowicz, The class imbalance problem in deep learning (2024), Machine Studying, 113(7), 4845–4901
[3] E. Loffredo, M. Pastore, S. Cocco and R. Monasson, Restoring balance: principled under/oversampling of data for optimal classification (2024), ICML 2024
[4] F. Kamalov, A.F. Atiya and D. Elreedy, Partial resampling of imbalanced data (2022), arXiv preprint arXiv:2207.04631
[5] F.S. Pezzicoli, V. Ros, F.P. Landes and M. Baity-Jesi, Class imbalance in anomaly detection: Learning from an exactly solvable model (2025). AISTATS 2025
[6] S. Sarao-Mannelli, F. Gerace, N. Rostamzadeh and L. Saglietti, Bias-inducing geometries: an exactly solvable data model with fairness implications (2022), arXiv preprint arXiv:2205.15935
