The promises of persistent homology, machine learning, and deep neural networks in topological data analysis of democracy survival

Badredine Arfi ()
Additional contact information
Badredine Arfi: University of Florida

Quality & Quantity: International Journal of Methodology, 2024, vol. 58, issue 2, No 31, 1685-1727

Abstract: Abstract This paper presents a new approach to survival analysis using topological data analysis (TDA) within Bayesian statistics combined with machine learning algorithms suitable to time-to-event data. The paper brings into the analysis aspects of topological invariance through what is known as persistence homology. TDA demonstrates the existence and statistical significance of a kind of unmeasured heterogeneity originating from the topology of the data as a whole. Combined with machine learning tools persistence homology provides us with new tools to construct a rich set of ways to analyze data and build predictive models that are optimized using inherent topological invariants such as one-dimensional loops as regularization. Specifically, this paper incorporates persistent homology effects in different ways in the analysis of survival data through the technique of functional principal component analysis (FPCA): first, by using topological invariants converted into FPCA factors that shape Bayesian statistical analysis of time-to-event data; second, by using FPCA measures of topological invariants in regularizing the process of optimizing the data and the posterior distributions of the Bayesian estimation; three, by using FPCA factors of measures of topological invariants in machine learning algorithms and deep neural networks suitable for analyzing survival data as a way of going beyond usual parametric and semi-parametric models of survival analysis. The approach is illustrated through a running example of multi-frailty survival analysis of democracies in the period of 1950–2010.

Keywords: Topological data analysis; Persistent homology; Machine learning; Deep neural networks; Bayesian multi-frailty survival analysis; Democracy breakdown (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11135-023-01708-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:qualqt:v:58:y:2024:i:2:d:10.1007_s11135-023-01708-6

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/11135

DOI: 10.1007/s11135-023-01708-6

Access Statistics for this article

Quality & Quantity: International Journal of Methodology is currently edited by Vittorio Capecchi

More articles in Quality & Quantity: International Journal of Methodology from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().