(Written with Claude-3.5-Sonnet. I have checked and edited the content. -Joni)
Summary of the Issue
The holdout paradigm, commonly implemented as a train-test split, is a fundamental technique in machine learning for assessing model performance. However, when applied to cross-sectional data, it can lead to significant challenges in terms of model generalizability. Cross-sectional data, by its nature, provides a snapshot of a population or phenomenon at a single point. While this can offer valuable insights, it also presents limitations when used for machine learning benchmarking.
TL;DR: This is a problem in applying machine learning in research, especially in fields that have fast-moving data distributions. Benchmarks (and evaluation) are based on one collected dataset, and the holdout paradigm (train-test) gives you a false sense of testing on “unseen” data. The data is unseen, yes—but it is collected the same time from same place by the same people using the same collection procedure than the training data. So, it is not *independent* data. There could be some fairly easy fixes, such as using independent datasets, yet these are rare for some reason.
Why Does This Issue Emerge?
One of the primary issues stems from the potential lack of diversity in the dataset. Cross-sectional data may not capture the full spectrum of variability that exists in the real world. When this data is split into training and test sets, both subsets inherit this limitation. As a result, a model that performs well on the test set may still fail to generalize effectively to new, unseen data that falls outside the narrow slice of reality captured in the original dataset.
The holdout paradigm assumes that the test set is a good proxy for future, unseen data. However, with cross-sectional data, this assumption can be particularly problematic. The test set, being drawn from the same distribution as the training set, may not represent the true variety of scenarios the model will encounter in deployment. This can lead to overly optimistic performance estimates and a false sense of the model’s generalizability.
Furthermore, cross-sectional data may inadvertently capture specific patterns or relationships that are unique to the particular sample, rather than being truly representative of the broader population. The train-test split does not address this issue; instead, it may reinforce these sample-specific patterns. A model trained and evaluated on such data might excel at recognizing these specific patterns but fail to identify more general, robust relationships that would allow it to perform well on truly diverse, real-world data.
The problem of hidden confounders becomes more acute when dealing with cross-sectional data in the holdout paradigm. Certain factors that influence the relationships in the data may not be evident in the snapshot provided by cross-sectional data. When the data is split, these hidden confounders can create spurious correlations that the model learns, leading to poor generalization when deployed in environments where these confounders are different or absent.
Another significant challenge lies in the assessment of model stability and robustness. The holdout method with cross-sectional data provides only a single evaluation of the model’s performance. It doesn’t allow for understanding how the model’s predictions might vary under different conditions or with (slightly) different input distributions. This limitation can mask potential brittleness in the model, where even small changes in input data might lead to large fluctuations in performance.
The issue of dataset shift, where the joint distribution of inputs and outputs differs between training and test stages, is particularly relevant when considering cross-sectional data and the holdout paradigm. While this problem can occur with any type of data, it’s especially pernicious with cross-sectional data because the snapshot nature of the data makes it difficult to anticipate or account for potential shifts that might occur in real-world applications.
The Problem is Domain Specific
The cross-sectional data problem in machine learning benchmarking varies significantly in its impact depending on the nature of the phenomenon being modeled. This issue is less pronounced when dealing with slow-moving or relatively immutable phenomena, such as human facial features. In these cases, cross-sectional data can provide a reasonably representative sample of the population, and the holdout paradigm is more likely to yield test results that genuinely reflect the model’s ability to generalize to new instances (unless we, for example, only include certain ethnicities in the dataset!).
When modeling stable phenomena like facial features, geological formations, or certain physical laws, the cross-sectional nature of the data is less likely to hinder the model’s generalizability. These domains change slowly over time, if at all, making a snapshot view often adequate for many applications. The basic anatomy of a species, for instance, remains consistent over long periods, allowing models trained on cross-sectional data to maintain their relevance and accuracy. Similarly, models predicting outcomes based on fundamental physical principles can often rely on cross-sectional data, as these laws remain constant regardless of when the data was collected.
However, the problem becomes much more pronounced when dealing with dynamic, rapidly evolving phenomena, particularly in social, economic, and technological domains. In these areas, cross-sectional data can quickly become outdated, and models trained on such data may fail to capture important trends or shifts. Social media trends, financial markets, consumer preferences, technological adoption rates, and public opinion are all examples of fast-moving phenomena where cross-sectional data combined with the holdout paradigm can lead to models that quickly become obsolete or, worse, make misleading predictions.
Toward Some Solutions
To address these challenges, researchers and practitioners need to approach cross-sectional data and the holdout paradigm with caution. Techniques such as (1) collecting temporally and spatially independent samples and (2) statistical testing of feature associations can provide some help. One could also (3) train a model on one dataset and test it on a completely independent dataset (completely independent == deals with the same prediction task or phenomon but is collected by different people at different place at a different time, possibly using a different collection methodology).
Moreover, (4) ensemble methods, combining models trained on data from different time points, can sometimes create more robust predictions.
Furthermore, focusing on (5) stable features (e.g., theoretically derived, known relationships) that are less likely to change rapidly can improve model stability, even when using cross-sectional data. Finally, (6) scenario modeling, which involves developing models under various possible future scenarios, can help prepare for different potential outcomes. These approaches can help mitigate the limitations of cross-sectional data in dynamic environments.