Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Can Machines Learn the True Probabilities?
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
A theoretical paper proving under basic assumptions when machines can learn true objective probabilities (only when they are directly observable), linking learning to truly guaranteed well-calibration and a forecasting game with Nature.
Problem
Whether AI machines can learn true objective probabilities from data, and under what conditions learning is possible or impossible, in an epistemic and computational sense.
Approach
Defines learning epistemically (correct most of the time and self-assured) and shows learning the true probability implies truly guaranteed well-calibration; uses a forecasting game between Nature and the machine to prove machines learn the true probability iff it is directly observable from a population.
Key results
- Learning the true objective probability implies P(p_k -> alpha) = 1, i.e., truly guaranteed well-calibration (Theorem on learning and calibration).
- A machine directly observes the true probability as alpha if and only if it learns it as alpha.
- Machines cannot learn the true probability when Nature is uniformly perverse or when the machine is not self-assured of the stopping time in selectively perverse cases.
Surprising findings
- Machines cannot learn a true probability even when they are correct infinitely often, if they are also wrong infinitely often.
- Winning the forecasting game does not imply learning: a machine can be truly well-calibrated yet fail to learn the true probability.
Limitations
- Assumes an ideal machine with no practical limits on time or storage.
- Formal results rely on several informal notions (e.g., effective computation, success) that are not mathematically defined.
- No empirical experiments are reported.
Experimental setup
Builds on: Dawid's calibration result Oakes (1985) counterexample Success Criterion of learning (epistemic notion)
Closest papers by meaning
- Rethinking Aleatoric and Epistemic Uncertainty (ICML 2025 · similarity 0.78)
- Does Reasoning Emerge? Examining the Probabilities of Causation in Large Language Models (NeurIPS 2024 · similarity 0.78)
- Explaining Probabilistic Models with Distributional Values (ICML 2024 · similarity 0.77)
- The Limits of Predicting Agents from Behaviour (ICML 2025 · similarity 0.77)
- Position: Rethinking Explainable Machine Learning as Applied Statistics (ICML 2025 · similarity 0.76)
- Everything, Everywhere, All at Once: Is Mechanistic Interpretability Identifiable? (ICLR 2025 · similarity 0.76)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.