Identifying Information from Observations with Uncertainty and Novelty

2026-04-17 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This research unifies the concept of "identification" across computational theory, asymptotic statistics, and PAC-Bayes learning, addressing how machine learning systems process uncertainty and novelty. The authors formalize identifiable information based on the language used to express relationships between distinct states. They define model identifiability and sample complexity through an indicator function over a hypothesis set, detailing their properties and asymptotic statistics for processes ranging from deterministic to ergodic stationary stochastic. The work connects finite-step identification with asymptotic statistics and PAC-learning, formalizing novelty identification from observations. A key finding is that computable PAC-Bayes learners' sample complexity distribution is determined by its moments, which are proven to be finite, providing a more complete understanding of information quantification and novelty detection in machine learning.

Key takeaway

For AI Scientists and Research Scientists working on robust machine learning systems, this work provides a rigorous framework for understanding model identifiability and sample complexity under uncertainty and novelty. You should consider how the formalization of identifiable information and the moment-determined sample complexity distribution can inform the design of more efficient and reliable learning algorithms, especially when dealing with finite computational resources and the need to detect truly novel data points. This framework offers a path to quantifying the information required for identification and assessing the certainty of novelty detection.

Key insights

Identification and sample complexity are unified across computational, statistical, and PAC-Bayes learning frameworks.

Principles

• Information is quantified by distinct states and their language-based relationships.
• Novelty is identified via probable exhaustive falsification of known models.
• Sample complexity distribution is determined by its finite moments in PAC-Bayes.

Method

The paper refines model identifiability and sample complexity definitions using an indicator function. It extends this computation from direct observations to unknown stochastic processes, generalizing algorithmic identification to PAC-Bayes learning for i.i.d. and stationary ergodic processes.

In practice

• Quantify information by measuring observations needed for set membership verification.
• Use Bayesian posterior convergence to determine probable sample complexity.
• Detect novelty by checking if observations fall outside known models' typical sets.

Topics

• Identifiability
• Sample Complexity
• PAC-Bayes Learning
• Novelty Detection
• Computability Theory

Best for: AI Scientist, Research Scientist, AI Student

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.