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On the unknowable limits to prediction

Nature Computational Science volume 5, pages 188–190 (2025)Cite this article

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The classic dichotomization of prediction error into statically defined ‘reducible’ and ‘irreducible’ terms is unable to capture the intricacies of progressive research design where specific types of truly reducible error are being rapidly eliminated at differential speeds. While this is generalizably true — including in the domain of large language models (LLMs) — it is none more apparent than in social systems, where questions regarding the ‘predictability’ of outcomes are gradually reaching the fore1. Canonical work that convenes common predictive tasks involving conventional social surveys2 shows low power, but rapidly emerging computational approaches that utilize non-standard administrative data and information contained within things such as children’s autobiographical essays — often combined with generative artificial intelligence and distributed computing3,4 — begin to allow high accuracy. We propose an enhanced framework that builds upon existing work5 in a way that we believe helpfully decomposes various types of truly reducible ‘epistemic’ error, which are in theory eliminable (resulting from a lack of knowledge), and isolates residual, ‘aleatoric’ error (inherent randomness that can never be modeled) that research endeavor will not be able to capture in the limit of human progress. We further emphasize the impossibility of claiming whether things are ‘predictable’, especially with regards to open, dynamically evolving systems.

Decomposing prediction error into reducible and irreducible terms is not new. The work of Trevor J. Hastie et al.6 — a landmark instruction manual in the field — uses the term ‘reducible’ to taxonomically classify errors into a type that can be eliminated, and the term ‘irreducible’ to denote errors that cannot be eliminated, but only given current models and information on target variables and feature sets. For example, the insightful mixed-methods work of Ian Lundberg et al.7 begins its abstract with ‘Why are some life outcomes difficult to predict?’. In that case, they are difficult to predict based on information that is currently measurable, and the ‘task’ at hand. An outcome that is difficult to predict with one feature set may not be ‘unpredictable’ in an aleatoric sense: life trajectories may be trivial to predict in the future. Reflexive terminology is essential, lest conclusions be drawn that there is no space for future positive policy interventions based on ever increasingly accurate predictions that prevent negative outcomes. It is impossible to know whether we have eliminated all reducible epistemic error to approach the practical ‘ceiling’ of accuracy, to make statements about how predictable outcomes will become, or to understand where we are in the process. Predictability of an outcome can only be asserted when all epistemic errors are eliminated: when ‘unmeasured’ information is measured and constructed perfectly, features are constructed perfectly, and when functional forms are able to be exactly recovered.

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Fig. 1: Decomposed learning curves.

Code availability

A GitHub repository that replicates the figures in this manuscript is available at https://github.com/crahal/unpredictability. This is also indexed in Zenodo9.

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Acknowledgements

Funding from the Leverhulme Research Centres Grant (grant RC-2018-003) for the Leverhulme Centre for Demographic Science, Nuffield College, and the Economic and Social Research Council is gratefully acknowledged. We are grateful for comments received from K. Chasalow, M. Verhagen, R. Kashyap, B. Domingue, M. Biggs, S. Wagner, H. Lei, and E. Darin. Special thanks go to N. Irons for his particularly insightful comments.

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Author notes

  1. These authors contributed equally: Jiani Yan, Charles Rahal.

Authors and Affiliations

  1. Leverhulme Centre for Demographic Science, Demographic Science Unit, University of Oxford, Oxford, UK

    Jiani Yan & Charles Rahal

  2. Department of Sociology, University of Oxford, Oxford, UK

    Jiani Yan

  3. Wolfson College, University of Oxford, Oxford, UK

    Jiani Yan

  4. Nuffield College, University of Oxford, Oxford, UK

    Charles Rahal

Authors
  1. Jiani Yan
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  2. Charles Rahal
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Each author contributed equally to this work in terms of conceptualization, design, drafting, and revision. J.Y. led on the technical derivation, and C.R. led on visualization.

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Correspondence to Jiani Yan or Charles Rahal.

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The authors declare no competing interests, and as the work is entirely theoretical, an ethical review with regards to data processing was not otherwise necessary.

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Nature Computational Science thanks the anonymous reviewer(s) for their contribution to the peer review of this work.

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Yan, J., Rahal, C. On the unknowable limits to prediction. Nat Comput Sci 5, 188–190 (2025). https://doi.org/10.1038/s43588-025-00776-y

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