Oversampling and undersampling in data analysis

Oversampling techniques

Random oversampling

Random Oversampling involves supplementing the training data with multiple copies of some of the minority classes. Oversampling can be done more than once (2x, 3x, 5x, 10x, etc.) This is one of the earliest proposed methods, that is also proven to be robust. Instead of duplicating every sample in the minority class, some of them may be randomly chosen with replacement.

SMOTE

There are a number of methods available to oversample a dataset used in a typical classification problem (using a classification algorithm to classify a set of images, given a labelled training set of images). The most common technique is known as SMOTE: Synthetic Minority Over-sampling Technique. However, this technique has been shown to yield poorly calibrated models, with an overestimated probability to belong to the minority class.

To illustrate how this technique works consider some training data which has s samples, and f features in the feature space of the data. Note that these features, for simplicity, are continuous. As an example, consider a dataset of birds for classification. The feature space for the minority class for which we want to oversample could be beak length, wingspan, and weight (all continuous). To then oversample, take a sample from the dataset, and consider its k nearest neighbors (in feature space). To create a synthetic data point, take the vector between one of those k neighbors, and the current data point. Multiply this vector by a random number x which lies between 0, and 1. Add this to the current data point to create the new, synthetic data point.

Many modifications and extensions have been made to the SMOTE method ever since its proposal.

ADASYN

The adaptive synthetic sampling approach, or ADASYN algorithm, builds on the methodology of SMOTE, by shifting the importance of the classification boundary to those minority classes which are difficult. ADASYN uses a weighted distribution for different minority class examples according to their level of difficulty in learning, where more synthetic data is generated for minority class examples that are harder to learn.

Augmentation

Data augmentation in data analysis are techniques used to increase the amount of data by adding slightly modified copies of already existing data or newly created synthetic data from existing data. It acts as a regularizer and helps reduce overfitting when training a machine learning model. (See: Data augmentation)

Undersampling techniques

Random undersampling

Randomly remove samples from the majority class, with or without replacement. This is one of the earliest techniques used to alleviate imbalance in the dataset, however, it may increase the variance of the classifier and is very likely to discard useful or important samples. For a statistical analysis of the conditions under which undersampling is effective, refer to

Cluster

Cluster centroids is a method that replaces cluster of samples by the cluster centroid of a K-means algorithm, where the number of clusters is set by the level of undersampling.

Tomek links

Tomek links remove unwanted overlap between classes where majority class links are removed until all minimally distanced nearest neighbor pairs are of the same class. A Tomek link is defined as follows: given an instance pair ${\displaystyle (x_i,x_j)}$, where ${\displaystyle x_i\in S_{min},x_j\in S_{\max }}$ and ${\displaystyle d(x_i,x_j)}$ is the distance between ${\displaystyle x_i}$ and ${\displaystyle x_j}$, then the pair ${\displaystyle (x_i,x_j)}$ is called a Tomek link if there's no instance ${\displaystyle x_k}$ such that ${\displaystyle d(x_i,x_k)<d(x_i,x_j)}$ or ${\displaystyle d(x_j,x_k)<d(x_i,x_j)}$. In this way, if two instances form a Tomek link then either one of these instances is noise or both are near a border. Thus, one can use Tomek links to clean up overlap between classes. By removing overlapping examples, one can establish well-defined clusters in the training set and lead to improved classification performance.

Undersampling with ensemble learning

A 2013 study shows that the combination of Undersampling with ensemble learning can sometimes achieve better results, see IFME: information filtering by multiple examples with under-sampling in a digital library environment.

Techniques for regression problems

Although sampling techniques have been developed mostly for classification tasks, growing attention is being paid to the problem of imbalanced regression. Adaptations of popular strategies are available, including undersampling, oversampling and SMOTE. Sampling techniques have also been explored in the context of numerical prediction in dependency-oriented data, such as time series forecasting and spatio-temporal forecasting.

Additional techniques

It's possible to combine oversampling and undersampling techniques into a hybrid strategy. Common examples include SMOTE and Tomek links or SMOTE and Edited Nearest Neighbors (ENN). Additional ways of learning on imbalanced datasets include weighing training instances, introducing different misclassification costs for positive and negative examples and bootstrapping.

Implementations

• A variety of data re-sampling techniques are implemented in the imbalanced-learn package compatible with the scikit-learn Python library. The re-sampling techniques are implemented in four different categories: undersampling the majority class, oversampling the minority class, combining over and under sampling, and ensembling sampling.
• The Python implementation of 85 minority oversampling techniques with model selection functions are available in the smote-variants package.

Criticism

Poor models in [the binary classification] setting are often a result of—any combination of—fitting deterministic classifiers, using re-sampling or re-weighting methods to balance class frequencies in the training data and evaluating the model with a score such as accuracy. ... No re-sampling technique will magically generate more information out of the few cases with the rare class.

— Model Comparison and Calibration Assessment User Guide for Consistent Scoring Functions in Machine Learning and Actuarial Practice, Tobias Fissler, arXiv:2202.12780v3, Christian Lorentzen, Michael Mayer, 2023

Probabilistic machine learning models trying to model a conditional distribution ${\displaystyle P(Y|X)=\frac{P(X|Y)P(Y)}{P(X)}}$ (through Bayes' rule) will be wrongly calibrated if modifying the natural distribution ${\displaystyle P(Y)}$ during training by applying undersampling or downsampling.

This point can be illustrated with a simple example: Assume no predictive variables ${\displaystyle X}$ and where the proportion of ${\displaystyle Y=1}$ is 0.01 and the proportion of ${\displaystyle Y=0}$ is 0.99. Is a model which learns ${\displaystyle \hat{P}(Y=1)=0.01}$ useless and should be modified via undersampling or oversampling? The answer is no. Class imbalance is not a problem in itself at all.

Additionally,

1. oversampling
2. undersampling
3. as well as assigning weights to samples

may be applied by practitioners in multi-class classification or situations with very imbalanced cost structure. This might be done in order to achieve "desirable", best performances for each class (potentially measured as precision and recall in each class). Finding the best multi-class classification performance or the best tradeoff between precision and recall is, however, inherently a multi-objective optimization problem. It is well known that these problems typically have multiple incomparable Pareto optimal solutions. Oversampling or undersampling as well as assigning weights to samples is an implicit way to find a certain pareto optimum (and it sacrifices the calibration of the estimated probabilities). A more explicit way than oversampling or downsampling could be to select a Pareto optimum by

• assign explicit costs to misclassified samples and then minimize the total (scalarized) costs via cost-sensitive machine learning
• perform threshold tuning in a binary classification setting so that a certain validation precision and recall are achieved.

Literature

• Kubat, M. (2000). Addressing the Curse of Imbalanced Training Sets: One-Sided Selection. Fourteenth International Conference on Machine Learning.
• Chawla, Nitesh V. (2010) Data Mining for Imbalanced Datasets: An Overview doi:10.1007/978-0-387-09823-4_45 In: Maimon, Oded; Rokach, Lior (Eds) Data Mining and Knowledge Discovery Handbook, Springer ISBN 978-0-387-09823-4 (pages 875–886)
• Lemaître, G. Nogueira, F. Aridas, Ch.K. (2017) Imbalanced-learn: A Python Toolbox to Tackle the Curse of Imbalanced Datasets in Machine Learning, Journal of Machine Learning Research, vol. 18, no. 17, 2017, pp. 1–5.