Regression by Composition: A New Foundational Framework for Statistical Modeling
Coverage of lessw-blog
In a recent post, lessw-blog discusses a significant advancement in statistical theory known as "Regression by Composition" (RBC), a framework accepted for presentation to the Royal Statistical Society.
In a recent post, lessw-blog highlights a manuscript titled "Regression by Composition," which proposes a foundational shift in how regression models are constructed. For decades, Generalized Linear Models (GLMs) have served as the primary workhorse of statistical analysis. Whether a data scientist is performing linear regression, logistic regression, or Poisson regression, they are typically operating within the GLM framework. This approach relies on connecting a linear predictor to an outcome variable via a specific "link function." While this method has been incredibly successful, it is not without limitations, particularly regarding modularity and the handling of specific phenomena like Switch Relative Risk (SRR).
The post details how Regression by Composition (RBC) addresses these constraints by reframing the underlying mathematics of regression. Rather than relying on the traditional link function and linear predictor architecture, RBC utilizes group actions and invariance. This is a move toward a more algebraic perspective, where models are built through the composition of modular transformations. The core argument is that by viewing regression through the lens of group theory, statisticians can achieve a higher degree of flexibility and logical consistency.
The significance of this framework lies in its unifying power. RBC does not discard previous methods; instead, it demonstrates that almost all standard regression models are special cases of this broader theory. Furthermore, it substantially enlarges the class of allowable models, allowing researchers to construct bespoke regression analyses that were previously difficult or impossible to formulate under GLM constraints. This modularity suggests a future where model features can be mixed and matched with greater ease, potentially influencing how machine learning architectures are designed for regression tasks.
The academic weight behind this proposal is substantial. The manuscript has been accepted as a discussion paper in the Journal of the Royal Statistical Society, Series B (JRSS-B). In the statistics community, this is a prestigious distinction reserved for papers expected to stimulate major debate and define the future direction of the field. The acceptance indicates that RBC is not merely a theoretical curiosity but a serious contender to evolve the standard toolkit used by statisticians and data scientists globally.
For practitioners interested in the theoretical underpinnings of the models they use daily, or for those looking for alternatives when GLMs fall short, this development represents a critical evolution in the field.
Key Takeaways
- Regression by Composition (RBC) is a new framework that reframes regression using group actions and invariance rather than link functions.
- The framework unifies almost all standard regression models (like GLMs) as special cases while expanding the scope of possible models.
- RBC specifically addresses limitations in Generalized Linear Models, such as issues with Switch Relative Risk (SRR).
- The manuscript has been accepted as a discussion paper in JRSS-B, signaling high academic importance and potential widespread adoption.