ML Interview Q Series: What's the difference between One-vs-Rest and One-vs-One?
📚 Browse the full ML Interview series here.
Comprehensive Explanation
One-vs-Rest (OVR) and One-vs-One (OVO) are popular strategies to extend binary classifiers to multi-class classification scenarios. Although both aim to classify inputs among multiple classes, they differ in how many binary classifiers are trained and how predictions are aggregated.
One-vs-Rest
In the One-vs-Rest scheme, we train one binary classifier per class. Each classifier is trained to distinguish the "current" class from all the "other" classes combined. Suppose there are K classes labeled from 1 to K:
We have K separate binary classifiers, where the c-th classifier outputs a score (or probability) indicating how likely the instance belongs to class c rather than any other class. At inference time, we typically pick the class for which the corresponding classifier's output is highest. In more formal terms, if f_c(x) is the output score of the c-th classifier, then the final predicted class y-hat is often computed as:
Here:
c ranges over all classes from 1 to K.
f_c(x) is the binary decision function (e.g., the output of a logistic regression or SVM) specialized for class c.
We predict the class c that yields the largest score.
One-vs-One
In the One-vs-One approach, we train one binary classifier per pair of classes. If we have K classes, we end up with K(K-1)/2 classifiers because for each pair (i, j), i < j, we train a classifier that distinguishes class i from class j. At inference time, each classifier in the ensemble casts a "vote," and the final prediction is often the class receiving the highest number of votes. Another perspective is to sum up the probabilities (or decision function outputs) for each class across all binary classifiers that involve that class and then pick the class with the highest total.
In a voting-based interpretation, if h_{i,j}(x) is the classifier for the class pair (i, j), then h_{i,j}(x) produces either i or j. One can tally the votes across all pairs and select the class with the maximum votes. Concretely, we might represent the prediction as:
Here:
h_{c,j}(x) is the outcome of the binary classifier that distinguishes class c from class j.
The indicator function 1[h_{c,j}(x) = c] is 1 if h_{c,j}(x) predicts class c, otherwise it is 0.
We choose the class c that gets the most "wins" over all other classes j.
Key Differences
In One-vs-Rest, the training procedure is simpler: K binary classifiers each sees many negative examples (all the other classes combined) but fewer positive examples (only the current class). This can be beneficial if one class has very distinct features relative to all other classes, but it can also lead to imbalanced training sets (each classifier sees only one class in positives and many classes lumped together as negatives).
In One-vs-One, each classifier is trained on just two classes at a time, so the training set for each classifier is smaller, but more balanced in terms of positive vs. negative examples. However, because we have many more classifiers to train, the OVO approach can be computationally more expensive when K is large.
How Training Data Is Distributed
Under OVR, each binary classifier sees all data points but labels only whether or not they belong to a single class. Hence every classifier is trained on the full dataset, but with a positive set from one class and a negative set of all other classes combined.
Under OVO, each of the K(K-1)/2 binary classifiers is trained only on data from two specific classes. This reduces the training data per classifier but drastically increases the number of classifiers.
Suitability for Different Models
When using methods like SVMs, One-vs-One is often preferred because SVMs can handle pairwise classification effectively. Many libraries implement OVO for multi-class SVM by default. For models like logistic regression or neural networks, people often prefer OVR, since logistic regression produces a clean probability estimate for each class, and neural networks can directly output multiple class probabilities via a softmax layer. However, in principle, you can combine both strategies with almost any base binary classifier.
Memory and Computation
One-vs-Rest usually trains K classifiers, and each classifier is trained on the entire dataset. If your dataset is extremely large and K is moderate, OVR can be more manageable than OVO in terms of the total number of models. On the other hand, One-vs-One trains K(K-1)/2 classifiers, but each classifier is trained on only two classes’ subset of data. For very large K, that can become quite expensive.
Follow-up Questions
Why might One-vs-One be more accurate in certain scenarios?
One-vs-One can be more accurate if each pair of classes is highly distinguishable, because each classifier specializes in separating those two classes only. With OVR, each classifier has to separate one class from all the others, which can become more challenging if other classes are very different from each other or if there are imbalances among classes. The localized focus of OVO classifiers sometimes yields better boundaries, especially with models like SVMs. However, this is not a blanket rule, as accuracy can vary depending on the data and the base classifier.
How do you handle large numbers of classes?
When K is large, OVO may require too many classifiers (K(K-1)/2). This can be computationally infeasible for extremely high K, and also requires significant memory. OVR might be more practical in that scenario, though each classifier is trained on the full dataset. In certain cases, hierarchical classification or dimensionality reduction methods might be employed to manage extremely large K, rather than strictly using OVR or OVO.
Could neural networks accomplish multi-class without OVR or OVO?
Many neural network architectures produce a single multi-class output layer with softmax activation. This natively supports multi-class classification by computing the probability distribution across all K classes in one forward pass. Such an approach avoids the need for an OVR or OVO scheme entirely. However, if the question specifically demands a method for combining binary classifiers, then the OVR approach is conceptually akin to training one binary output unit per class, while OVO would require multiple pairs of outputs. In practice, we almost always do direct multi-class with a single softmax layer for neural networks.
What if there is class imbalance?
In OVR, each binary classifier can be heavily imbalanced if one particular class is small compared to the union of all other classes. This imbalance can make training more difficult or can bias the classifiers in favor of the negative group. You could mitigate this by using class weights or different sampling strategies.
In OVO, each classifier sees data from only two classes. If any of those pairs is extremely imbalanced (e.g., one of the classes is still very rare in the dataset), you can also face imbalance issues, but typically the ratio might be less dramatic than in OVR. It depends heavily on the distribution of your classes.
Which method is more intuitive to explain to non-experts?
One-vs-Rest is often simpler to explain because each classifier answers: "Is this instance in class c or not?" By contrast, One-vs-One is slightly more complex from an outsider’s perspective, because you need to describe a voting mechanism over multiple pairwise classifiers. Depending on the use case and the audience, OVR might be easier to present.
How do you implement One-vs-One or One-vs-Rest in popular frameworks?
In scikit-learn, you can use built-in wrappers like OneVsRestClassifier or OneVsOneClassifier. For instance:
from sklearn.multiclass import OneVsRestClassifier, OneVsOneClassifier
from sklearn.svm import SVC
# One-vs-Rest
ovr_clf = OneVsRestClassifier(SVC())
# One-vs-One
ovo_clf = OneVsOneClassifier(SVC())
You can then fit these meta-classifiers on your multi-class dataset just as if they were single estimators, and scikit-learn will handle the logic under the hood.
For frameworks like PyTorch or TensorFlow, you usually develop a single model with a multi-class output layer by default. If you really need OVR or OVO logic, you can implement the approach manually by training separate models or heads for each class or each pair of classes, though this is less common because neural networks typically handle multi-class outputs directly with a single softmax.
In summary, One-vs-Rest is usually simpler to implement, requiring K classifiers, while One-vs-One can offer potentially more nuanced class distinctions at the expense of requiring K(K-1)/2 classifiers. The best choice depends on the size of K, data distribution, the complexity of the base classifier, and computational constraints.
Below are additional follow-up questions
Could One-vs-Rest or One-vs-One strategies produce inconsistent or contradictory predictions, and how do you detect or handle that?
In One-vs-Rest, since each classifier independently estimates whether an instance belongs to a single class versus all others, we might encounter situations where multiple classifiers strongly believe that the same instance belongs to their respective classes simultaneously. This can lead to multiple classes having very high scores or probabilities. A common detection mechanism is to observe if more than one class has a significantly high probability. If so, you might re-run the model with different thresholds or incorporate a more robust calibration step. Alternatively, you can compare the relative margins or confidence intervals for each class to break ties.
In One-vs-One, each pairwise classifier can yield a contradictory set of votes. For instance, you can have a cyclical voting pattern where class A is preferred over class B, B is preferred over class C, but class C is preferred over class A. Although this scenario is rare, it can happen in certain borderline decision regions. It is detected by noticing that your vote tallies end up in a tie or that the second round of voting yields inconsistent results. A practical fix can be to compute confidence scores alongside the votes and choose the class with the highest total confidence (e.g., sum of pairwise probabilities). Another approach is to use tie-breaking heuristics or to re-run the classification for the tied classes.
How does feature selection or dimensionality reduction affect One-vs-Rest versus One-vs-One performance?
When performing One-vs-Rest, the classifier for each class can be very sensitive to the features that differentiate that class from the rest. If many features are irrelevant or redundant, the classifier may struggle to isolate the most indicative features for that specific class. Good feature selection can improve performance dramatically by emphasizing the unique characteristics of each class. However, if feature selection is done globally (the same feature set for all classes), you might exclude features that are highly relevant for only one class.
In One-vs-One, each pairwise classifier focuses on distinguishing just two classes. Therefore, feature selection might highlight features that differentiate those two classes more effectively. This localized view can be beneficial but also means you can end up with different subsets of features across the various pairwise classifiers. Some frameworks automatically handle local feature selection, but managing it can become cumbersome with a large number of classes. Additionally, you risk overfitting on particular class pairs if your dataset for each pair is too small.
Are there any scenarios where data noise or label noise significantly impacts One-vs-Rest or One-vs-One?
Data noise, such as corrupted features or outliers, can compromise either strategy. However, label noise might affect One-vs-Rest more starkly in scenarios where some classes are mis-labeled as “others.” In that case, the negative set for each classifier becomes a noisy mix of many classes, possibly including mislabeled samples that belong to the positive class. This can degrade the learned decision boundary in a broad way.
For One-vs-One, label noise is more critical in any pairwise subset of classes. Each pairwise classifier’s performance can be severely impacted by even a modest fraction of mis-labeled examples in those two classes, especially if the dataset is small and every mislabeled point drastically changes the local decision boundary. Spotting such noise typically involves carefully validating the classifiers’ predictions and potentially implementing noise handling strategies, such as outlier detection or label correction mechanisms.
How might you adapt One-vs-Rest or One-vs-One for real-time or online learning?
In real-time or online learning, each arriving sample must update the model quickly. One-vs-Rest can be adapted by incrementally updating each binary classifier as new data comes in. This is relatively straightforward if your base binary classifier supports an online training procedure (e.g., incremental variants of logistic regression or linear SVM).
For One-vs-One, you similarly must update K(K-1)/2 classifiers. The computational overhead can be higher because you update each pairwise classifier whenever an instance belongs to either of the two classes in that pair. If K is large, this becomes more time-consuming. You must track which classes appear most frequently in the stream and allocate resources accordingly. In practice, you might adopt a hybrid strategy: train a simpler OVR model online for speed, then periodically re-train an OVO ensemble offline using a batch of collected data if you need finer distinctions.
Is there a risk of overfitting when using complex models in One-vs-Rest or One-vs-One?
Overfitting can occur if each classifier is too complex relative to the amount of data available. In One-vs-Rest, each classifier is typically exposed to all samples, so overfitting can emerge from the model complexity (e.g., deep networks or high-capacity ensemble methods) or from heavily imbalanced classes. Regularization techniques, cross-validation, and proper hyperparameter tuning can help mitigate this risk.
In One-vs-One, each classifier sees fewer training samples since it only handles two classes. If you have a large number of classes and only a modest number of samples per class, some pairwise classifiers might end up with very limited training examples, increasing the risk of overfitting. Monitoring validation performance for each pairwise classifier and applying techniques like early stopping, dropout (in neural networks), or reduced model capacity can help keep overfitting in check.
What happens if the dataset includes “out-of-distribution” or “none-of-the-above” samples?
In practical applications, you might encounter inputs that do not belong to any of the trained classes. Neither One-vs-Rest nor One-vs-One inherently accounts for the possibility that a new instance might not match any of the known classes. In One-vs-Rest, all classifiers might produce very low confidence scores, or they might collectively produce spurious probabilities if the feature distribution is far from what they have seen. Similarly, in One-vs-One, all pairwise classifiers could produce highly uncertain or inconsistent votes.
A common solution is to include a rejection class, or “none-of-the-above” class, in the training set if you have data reflecting that condition. Alternatively, you can use thresholds on confidence scores and declare an input “unclassifiable” when no class meets that threshold. Another approach is outlier detection that flags unusual data points that deviate significantly from the training data distributions.
Can One-vs-Rest or One-vs-One be extended to multi-label classification?
Traditional One-vs-Rest can be readily extended to multi-label tasks by maintaining one binary classifier per label and allowing multiple labels to fire for the same instance. This is a common approach called the Binary Relevance method in multi-label classification. You do not combine “all other labels” into a single negative class, but rather you treat each label’s presence or absence as an independent binary problem. That said, it often ignores label correlations and might miss patterns like “if label A is present, label B is more likely.”
One-vs-One is less common for multi-label classification because you typically need to handle pairs of labels, and an instance might have either both labels or neither label. The concept of pairwise classifiers becomes more complicated in multi-label contexts, leading to confusion about how to interpret pairwise votes if an instance legitimately belongs to multiple classes. Consequently, specialized multi-label methods (e.g., classifier chains) or neural network architectures with multiple output heads are often preferred.