Bayesian Updating Defines Proportional Analogies on Probability Distributions
A recent study presents a structured approach for proportional analogies in probability distributions utilizing Bayesian updating. This research, categorized under Computer Science > Artificial Intelligence on arXiv, broadens the axiomatic exploration of analogical reasoning beyond Boolean, symbolic, and real-valued contexts into the realm of probability. The authors characterize a proportional analogy as a quaternary relation 'A is to B as C is to D,' suggesting that two distributions are interconnected if one can be converted into the other through Bayesian updating based on a specific set of observations. The framework is analyzed for standard exponential family members and further generalized to arbitrary distributions using Gaussian mixture approximations. This work addresses a significant gap in existing literature, as proportional analogies in probability distributions had been largely neglected. The paper can be found at arXiv:2608.11724.
Key facts
- The paper introduces a notion of proportional analogy for probability distributions based on Bayesian updating.
- Proportional analogies are quaternary relations of the form 'A is to B as C is to D'.
- The framework builds on the idea that two distributions are related if one can be transformed into the other through Bayesian updating induced by a set of observations.
- The approach is investigated for several standard members of the exponential family.
- The framework naturally extends to arbitrary probability distributions through Gaussian mixture approximations.
- The paper is categorized under Computer Science > Artificial Intelligence.
- The paper is available on arXiv with the identifier 2608.11724.
- The work addresses a gap: proportional analogies on probability distributions had been largely unexplored.
Entities
Institutions
- arXiv