Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

Richard V. Field (), Michael R. Smith, Ellery J. Wuest and Joe B. Ingram
Additional contact information
Richard V. Field: Sandia National Laboratories, Albuquerque, NM 87185, USA
Michael R. Smith: Sandia National Laboratories, Albuquerque, NM 87185, USA
Ellery J. Wuest: Klipsch School of Electrical and Computer Engineering, New Mexico State University, Las Cruces, NM 88003, USA
Joe B. Ingram: Sandia National Laboratories, Albuquerque, NM 87185, USA

Mathematics, 2024, vol. 12, issue 21, 1-25

Abstract: This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

Keywords: machine learning; explainability; probabilistic model; synthetic data; uncertainty quantification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/21/3392/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/21/3392/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:21:p:3392-:d:1510043

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().