Linearly Constrained Generalized Linear Models with Applications in Origin-Destination Estimation
Abstract
We show that data censored by linear constraints can be fit within the generalized linear model (GLM) framework, recovering the expected latent counts together with their uncertainty in a single Fisher-scoring procedure. Our motivating application is origin-destination (OD) estimation in transportation studies, where the latent data are the OD trip demands and constraints are either origin and destination marginal counts per zone, as in OD matrix estimation, or observed link counts, as in network tomography. Casting the problem as a linearly constrained GLM lets us treat, within one model, three features that arise routinely in practice: unmatched constraints, trip predictors such as costs, and prior information such as diagonal dominance and seed counts. We demonstrate the methodology in synthetic and small scale studies and in a larger case study based on simulated data from the BO4Mob study.
Related
- A Parallel Adaptive Proximal ADMM for Linearly Constrained Separable Composite Optimization Problems
- Fast Rates and Strong Convergence of Tikhonov-Regularized Mixed-Order Primal-Dual Dynamics for Linearly Constrained Optimization Without Eventual Ball Conditions
- Cohomology of Linearly Constrained Kloosterman Families: Newton Polytopes, Weights, and Boundary Monodromy
- Moments and Large Geometric Monodromy for Linearly Constrained Kloosterman Families
- Efficient ADMM for Soft-Constrained Quadratic Programs via Generalized Slack Projections
BibTeX
@misc{chou2026linearly,
title = {{Linearly Constrained Generalized Linear Models with Applications in Origin-Destination Estimation}},
author = {Likun Chou and Luis Carvalho},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09021},
eprint = {2609.09021},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09021},
}
RIS
TY - UNPB
TI - Linearly Constrained Generalized Linear Models with Applications in Origin-Destination Estimation
AU - Likun Chou
AU - Luis Carvalho
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09021
UR - https://arxiv.org/abs/2609.09021
AB - We show that data censored by linear constraints can be fit within the generalized linear model (GLM) framework, recovering the expected latent counts together with their uncertainty in a single Fisher-scoring procedure. Our motivating application is origin-destination (OD) estimation in transportation studies, where the latent data are the OD trip demands and constraints are either origin and destination marginal counts per zone, as in OD matrix estimation, or observed link counts, as in network tomography. Casting the problem as a linearly constrained GLM lets us treat, within one model, three features that arise routinely in practice: unmatched constraints, trip predictors such as costs, and prior information such as diagonal dominance and seed counts. We demonstrate the methodology in synthetic and small scale studies and in a larger case study based on simulated data from the BO4Mob study.
ER -