Prof. Dr. Hamparsum Bozdogan, Ph.D.

Toby McKenzie Professor

Department of Business Analytics and Statistics

The University of Tennessee

Knoxville,  U.S.A.

Bridging Artificial Intelligence and Statistical Inference: Expected Volume Confidence Region Complexity (EVCR-COMP) Criterion in High Dimensions

In modern high-dimensional statistical modeling, classical model selection criteria such as AIC and BIC (or SBC) often encounter limitations due to their reliance on parameter counting and asymptotic approximations, particularly under model misspecification and complex covariance structures.

In this talk, we introduce a new framework based on the expected volume of confidence regions, termed the Expected Volume Confidence Region Complexity (EVCR-COMP) criterion, which unifies geometric, inferential, and information-theoretic principles for model selection.

We first develop the theoretical foundations of EVCR by deriving explicit expressions for the volume and expected volume of confidence regions in multivariate settings. These include finite-sample formulations based on Hotelling’s T² distribution as well as large-sample approximations. Unlike classical criteria, the proposed approach penalizes models through geometric uncertainty rather than solely through dimensionality. Importantly, it explicitly incorporates the confidence level into the model selection process, thereby linking model adequacy with statistical inference in a unified framework.

We then demonstrate the performance of EVCR-COMP through several applications, including polynomial regression, Bayesian regression, and high-dimensional modeling scenarios. The results show that EVCR-COMP provides a more stable and informative selection criterion in complex settings, particularly when covariance structure and uncertainty play a dominant role.

Finally, we discuss emerging synergies between EVCR-COMP and artificial intelligence (AI), highlighting connections to representation learning, neural network regularization, and geometric control of latent spaces. These results suggest that EVCR-based complexity measures offer a principled pathway for bridging statistical inference with modern AI methodologies

This perspective suggests a fundamental shift: from parameter-based penalties to uncertainty-driven model selection, providing a unified framework for statistical inference and modern AI.

Software & Artificial Intelligence Expert
Udemy – Best Seller AI Instructor

Venue: Yıldız Teknik Üniversitesi, Davutpaşa Campus, Congress Center – Istanbul
Date: May 11, 2026 (Monday)
Time: 11:00