GeMA: Learning Latent Manifold Frontiers for Benchmarking Complex Systems

Jia Ming Li, Anupriya and Daniel J. Graham

Papers from arXiv.org

Abstract: Benchmarking the performance of complex systems such as rail networks, renewable generation assets and national economies is central to transport planning, regulation and macroeconomic analysis. Classical frontier methods, notably Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), estimate an efficient frontier in the observed input-output space and define efficiency as distance to this frontier, but rely on restrictive assumptions on the production set and only indirectly address heterogeneity and scale effects. We propose Geometric Manifold Analysis (GeMA), a latent manifold frontier framework implemented via a productivity-manifold variational autoencoder (ProMan-VAE). Instead of specifying a frontier function in the observed space, GeMA represents the production set as the boundary of a low-dimensional manifold embedded in the joint input-output space. A split-head encoder learns latent variables that capture technological structure and operational inefficiency. Efficiency is evaluated with respect to the learned manifold, endogenous peer groups arise as clusters in latent technology space, a quotient construction supports scale-invariant benchmarking, and a local certification radius, derived from the decoder Jacobian and a Lipschitz bound, quantifies the geometric robustness of efficiency scores. We validate GeMA on synthetic data with non-convex frontiers, heterogeneous technologies and scale bias, and on four real-world case studies: global urban rail systems (COMET), British rail operators (ORR), national economies (Penn World Table) and a high-frequency wind-farm dataset. Across these domains GeMA behaves comparably to established methods when classical assumptions hold, and provides additional insight in settings with pronounced heterogeneity, non-convexity or size-related bias.

Date: 2026-03
New Economics Papers: this item is included in nep-eff
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2603.16729 Latest version (application/pdf)

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:arx:papers:2603.16729

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().