Incorporating Unsupervised Learning into the Unified Inductive Logic Framework

Determine whether and how unsupervised learning can be incorporated into the unified inductive logic framework by formulating unsupervised learning tasks as empirical problems (with a hypothesis space, an evidence tree, a set of possible worlds, and a loss function that provides a well-defined notion of truth) and by identifying an appropriate mode-of-convergence-based evaluative standard; if incorporation is possible, characterize the necessary conditions that supply the missing ground truth for such tasks.

Background

The paper proposes a Peircean, convergence-based unification of formal learning theory, statistics, and supervised learning by evaluating inference methods via modes of convergence to the truth, guided by the principle "Strive for the Highest Achievable."

While supervised learning admits a clear notion of truth (e.g., predictive risk minimization under an IID data-generating distribution), the author notes that unsupervised learning typically lacks an explicit ground truth, making it unclear how to define convergence-to-truth standards within the proposed framework.

This leads to an explicit uncertainty about whether and how unsupervised learning can be brought under the same unified inductive logic, motivating a concrete open problem about formalizing appropriate notions of truth and convergence for unsupervised tasks.

References

However, the prospect for incorporating unsupervised learning into the unified picture remains unclear. In fact, even theorists of machine learning have difficulty evaluating algorithms of unsupervised learning by a rigorous standard---let alone a standard defined as a mode of convergence.

— Unified Inductive Logic: From Formal Learning to Statistical Inference to Supervised Learning (2412.02969 - Lin, 4 Dec 2024) in Section 7 (Closing)