Proximity Measure of Information Object Features for Solving the Problem of Their Identification in Information Systems

Reporting guidance for information-theoretic measures is rarely tested against ground truth. We test one guardrail in two multi-agent reinforcement learning games, a social dilemma and a coordination race, where directed influence between selected agent pairs is zero by construction, over 100 seeds. Omitting one precondition, exclusion of the non-stationary training transient, gives false-positive rates of 100.00% and 99.95%: agents annealing exploration independently, in runs that never met, are flagged as influencing one another. Excluding the transient reaches 3.0% in the social dilemma but 11.8% in the coordination game, which stationarity tests explain: 95.7% of social-dilemma series are stationary afterwards against 56.8% of coordination series. So the non-stationarity must be treated, and exclusion is neither the only way nor sufficient. What we recommend instead changes the null model rather than the data: permuting the source within blocks of training time reaches 5.25% and 5.50%, the only one of four constructions at the size of the test in both games, leaving series, statistic and estimand untouched. Titrating injected links of known strength in both games shows it is also the most sensitive of the three, detecting 89.0% in the coordination game where conditioning detects 61.0% on identical pairs, while the ablated test reports 100% with or without a link, so its apparent sensitivity is uninformative. The block count is not critical: every setting from 16 to 256 lands in the nominal region, and a partition derived from the stationarity test removes the parameter, though less sensitively. Code and data are released.

Supervised dimensionality reduction maps labeled data into a low-dimensional feature space while preserving class separation. A common strategy is to learn features that maximize a measure of statistical dissimilarity between the class-conditional probability distributions. Information geometry, which is rooted in Riemannian geometry, provides an alternative framework for measuring class dissimilarity. It treats probability distributions as points in a statistical manifold and uses the Fisher information metric to define a geodesic distance--the Fisher-Rao distance--between distributions The Fisher-Rao distance is an appealing candidate for measuring class separation because the Fisher information metric is a local measure of discriminability, and because it allows a geometric interpretation. Here, we present Supervised Quadratic Feature Analysis (SQFA), a supervised dimensionality reduction method which learns linear features that maximize Fisher-Rao distances between class-conditional distributions, under Gaussian assumptions. In multiple real world datasets, we find that SQFA features support classification accuracy that is competitive with features that maximize more popular measures of dissimilarity, or that are learned by other state-of-the-art dimensionality reduction methods. Notably, the best classification accuracy is achieved by SQFA-H features, a variant of SQFA that maximizes the Hellinger distance, a rarely used objective for dimensionality reduction. These results demonstrate the potential of information geometry as a tool for supervised dimensionality reduction. We provide a Python implementation of SQFA at https://github.com/dherrera1911/sqfa.

A classic account of the quantification of semantic information is that of Bar-Hiller and Carnap. Their account proposes an inverse relation between the informativeness of a statement and its probability. However, their approach assigns the maximum informativeness to a contradiction: which Floridi refers to as the Bar-Hillel-Carnap paradox. He developed a novel theory founded on a distance metric and parabolic relation, designed to remove this paradox. Unfortunately is approach does not succeed in that aim. In this paper I critique Floridi's theory of strongly semantic information on its own terms and show where it succeeds and fails. I then present a new approach based on the unit circle (a relation that has been the basis of theories from basic trigonometry to quantum theory). This is used, by analogy with von Neumann's quantum probability to construct a measure space for informativeness that meets all the requirements stipulated by Floridi and removes the paradox. In addition, while contradictions and tautologies have zero informativeness, it is found that messages which are contradictory to each other are equally informative. The utility of this is explained by means of an example.