Generalizability of experimental studies (2406.17374v2)

Abstract: Experimental studies are a cornerstone of ML research. A common, but often implicit, assumption is that the results of a study will generalize beyond the study itself, e.g. to new data. That is, there is a high probability that repeating the study under different conditions will yield similar results. Despite the importance of the concept, the problem of measuring generalizability remains open. This is probably due to the lack of a mathematical formalization of experimental studies. In this paper, we propose such a formalization and develop a quantifiable notion of generalizability. This notion allows to explore the generalizability of existing studies and to estimate the number of experiments needed to achieve the generalizability of new studies. To demonstrate its usefulness, we apply it to two recently published benchmarks to discern generalizable and non-generalizable results. We also publish a Python module that allows our analysis to be repeated for other experimental studies.

• The paper's main contribution is the formalization of experimental studies by introducing a quantifiable definition of generalizability using kernel methods.
• It details an algorithm to estimate the number of experimental conditions needed and validates the approach with case studies on categorical encoders and LLMs.
• The work emphasizes robust experimental design and replicability while offering practical strategies to optimize resource use in ML research.

Generalizability of Experimental Studies

The paper "Generalizability of Experimental Studies" addresses the crucial aspect of how results from experimental studies in ML can be considered generalizable. Generalizability refers to the likelihood that the results of an experiment will extend beyond the specific conditions under which it was conducted, such as when applied to new datasets.

Formalization of Experimental Studies

A major contribution of this work is the formalization of experimental studies and the introduction of a quantifiable definition of generalizability. Traditional interpretations ensure that methodologies applied in studies are replicable, emphasizing robustness through repeated experiments under varied conditions~\cite{committee_on_reproducibility_and_replicability_in_science_reproducibility_2019, pineau_improving_2021}. The handling of replicability, a subset of generalizability, has seen significant theoretical work, but practical quantification has been underexplored till this work.

Concepts

1. Experiments and Factors: The paper defines experiments as evaluations of alternatives under specified conditions, referred to as experimental factors. These factors are categorized into three types: design factors chosen by the experimenter, held-constant factors that do not change throughout the paper, and allowed-to-vary factors influencing generalizability.
2. Generalizability Assessment: The approach quantifies generalizability via a probabilistic method revolving around how empirical studies approximate the results of an ideal, extensive paper. The use of kernel functions is proposed to measure similarity between outcomes of different experimental configurations. Notably, the Maximum Mean Discrepancy (MMD) is employed to compare the distributions of paper results.

Methodological Contributions

A unique aspect of this work is the introduction of a systematic approach to estimate the number of experimental conditions (e.g., datasets) required to achieve a desired level of generalizability. This estimation is vital for designing efficient studies that do not waste resources while maximizing the robustness of conclusions.

1. Kernel Methods: The paper details three kernels—Borda, Jaccard, and Mallows—to measure experimental result similarity based on the paper's goals, which could concern ranking consistency or other criteria. For example, the Borda kernel allows evaluation based on the relative ranks of a specific alternative.
2. Algorithm for Estimating Study Size: An algorithm is introduced to estimate the sample size required to reach a pre-specified generalizability threshold. This is significant because it offers a practical method for assessing whether current studies are sufficiently large to ensure robust, generalizable findings.

Case Studies

The research includes case studies on categorical encoders and LLMs, scrutinizing whether established benchmarks in these domains meet generalizability criteria. The conclusions drawn suggest substantial variation depending on design factors such as the choice of model or task, advocating for a careful reevaluation of experimental designs in ML research.

Implications and Future Work

The implications of this work are both theoretical and practical. The formalization of experimental studies introduces a more structured framework that researchers can use to design studies capable of yielding transferable conclusions. The real-world applications already analyzed in the case studies suggest areas for improving generalizability which can, in turn, enhance the reliability of machine learning research outcomes globally.

This work sets the stage for further explorations into the mathematical underpinnings of ML experiments, particularly through expanding the kernel definitions to cover different types of research questions and potentially integrating these models into real-time adaptive experimental designs. Further, this framework could align computational and statistical approaches to better understand the complex landscape of experimental paper design and its implications across diverse scientific domains.