Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Generalisation of Total Uncertainty in AI: A Theoretical Study

Keivan Shariatmadar

TL;DR

The work investigates generalized total uncertainty in AI by integrating epistemic and aleatoric uncertainties and surveying diverse uncertainty representations such as deterministic intervals, probability intervals, $\epsilon$-contaminations, credal sets, random sets, and p-boxes. It demonstrates that epistemic and aleatoric components can be dependent, motivating two concrete directions: (I) a linear-combination formulation of total uncertainty with tunable weights guided by entropy or bound-based metrics, and (II) a contamination neural network (ContNN) that combines Bayesian and interval neural components to separate AU and EU contributions. The proposed frameworks aim to provide a unified theoretical basis and practical estimation strategies for robust uncertainty quantification across AI domains. These approaches promise more reliable decision-making, safer deployments, and clearer characterizations of uncertainty under limited data and changing environments.

Abstract

AI has been dealing with uncertainty to have highly accurate results. This becomes even worse with reasonably small data sets or a variation in the data sets. This has far-reaching effects on decision-making, forecasting and learning mechanisms. This study seeks to unpack the nature of uncertainty that exists within AI by drawing ideas from established works, the latest developments and practical applications and provide a novel total uncertainty definition in AI. From inception theories up to current methodologies, this paper provides an integrated view of dealing with better total uncertainty as well as complexities of uncertainty in AI that help us understand its meaning and value across different domains.

Generalisation of Total Uncertainty in AI: A Theoretical Study

TL;DR

The work investigates generalized total uncertainty in AI by integrating epistemic and aleatoric uncertainties and surveying diverse uncertainty representations such as deterministic intervals, probability intervals, -contaminations, credal sets, random sets, and p-boxes. It demonstrates that epistemic and aleatoric components can be dependent, motivating two concrete directions: (I) a linear-combination formulation of total uncertainty with tunable weights guided by entropy or bound-based metrics, and (II) a contamination neural network (ContNN) that combines Bayesian and interval neural components to separate AU and EU contributions. The proposed frameworks aim to provide a unified theoretical basis and practical estimation strategies for robust uncertainty quantification across AI domains. These approaches promise more reliable decision-making, safer deployments, and clearer characterizations of uncertainty under limited data and changing environments.

Abstract

AI has been dealing with uncertainty to have highly accurate results. This becomes even worse with reasonably small data sets or a variation in the data sets. This has far-reaching effects on decision-making, forecasting and learning mechanisms. This study seeks to unpack the nature of uncertainty that exists within AI by drawing ideas from established works, the latest developments and practical applications and provide a novel total uncertainty definition in AI. From inception theories up to current methodologies, this paper provides an integrated view of dealing with better total uncertainty as well as complexities of uncertainty in AI that help us understand its meaning and value across different domains.
Paper Structure (16 sections, 28 equations, 3 figures)

This paper contains 16 sections, 28 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Epistemic and aleatoric uncertainties
  3. Total uncertainty
  4. Uncertainty models and Identifications
  5. Deterministic Intervals
  6. Probability Intervals
  7. $\epsilon$-contaminations
  8. Credal Sets
  9. Random Sets
  10. Probability Box
  11. Generalised Total Uncertainty Estimation
  12. Dependency
  13. Proposal I
  14. Proposal II
  15. Conclusion and future work
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Convex-closed set of probability distributions (credal set, in blue).
  • Figure 2: $\overline{F}:=U(a,b)$ is the upper bound and $\underline{F}=U(c,d)$ is the lower bound with uniform distributions
  • Figure 3: The blue $U_i$ lines represent the discrete upper bound for $\overline{F}$, and the red $L_i$ lines represent the discrete lower bound for $\underline{F}$ for $N=5$ partitions