• Corpus ID: 237266725

Convex Latent Effect Logit Model via Sparse and Low-rank Decomposition

@article{Zhan2021ConvexLE,
  title={Convex Latent Effect Logit Model via Sparse and Low-rank Decomposition},
  author={Hongyuan Zhan and Kamesh Madduri and Venkataraman N. Shankar},
  journal={ArXiv},
  year={2021},
  volume={abs/2108.09859}
}

• Hongyuan Zhan, Kamesh Madduri, V. Shankar
• Published 22 August 2021
• Computer Science
• ArXiv

In this paper, we propose a convex formulation for learning logistic regression model (logit) with latent heterogeneous effect on sub-population. In transportation, logistic regression and its variants are often interpreted as discrete choice models under utility theory (McFadden, 2001). Two prominent applications of logit models in the transportation domain are traffic accident analysis and choice modeling. In these applications, researchers often want to understand and capture the individual variation under the same accident or choice scenario. The mixed effect logistic regression (mixed logit) is a popular model employed by transportation researchers. To estimate the distribution of mixed logit parameters, a non-convex optimization problem with nested high-dimensional integrals needs to be solved. Simulation-based optimization is typically applied to solve the mixed logit parameter estimation problem, i.e., via Monte Carlo simulation of the marginal log-likelihood function. Despite its popularity, the mixed logit approach for learning sub-population or individual heterogeneity has several downsides. First, the parametric form of the distribution requires domain knowledge and assumptions imposed by users, although this issue can be addressed to some extent by using a non-parametric approach. Second, the optimization problems arise from parameter estimation for mixed logit and the non-parametric extensions are non-convex, which leads to unstable model interpretation. Third, the simulation size in simulationassisted estimation lacks finite-sample theoretical guarantees and is chosen somewhat arbitrarily in practice. To address these issues, we are motivated to develop a formulation that models the latent individual heterogeneity while preserving convexity, and avoids the need for simulation-based approximation. Our setup is based on decomposing the parameters into a sparse homogeneous component in the population and low-rank heterogeneous parts for each individual. ∗Corresponding author. Email: [e-mail]. This work was done while the author was at Penn State University. i ar X iv :2 10 8. 09 85 9v 1 [ cs .L G ] 2 2 A ug 2 02 1