Search arXivSearch

arXiv · 2406.10948

Incorporating uncertainty quantification into travel mode choice modeling: a Bayesian neural network (BNN) approach and an uncertainty-guided active survey framework

Abstract

Existing deep learning approaches for travel mode choice modeling fail to inform modelers about their prediction uncertainty. Even when facing scenarios that are out of the distribution of training data, which implies high prediction uncertainty, these approaches still provide deterministic answers, potentially leading to misguidance. To address this limitation, this study introduces the concept of uncertainty from the field of explainable artificial intelligence into travel mode choice modeling. We propose a Bayesian neural network-based travel mode prediction model (BTMP) that quantifies the uncertainty of travel mode predictions, enabling the model itself to "know" and "tell" what it doesn't know. With BTMP, we further propose an uncertainty-guided active survey framework, which dynamically formulates survey questions representing travel mode choice scenarios with high prediction uncertainty. Through iterative collection of responses to these dynamically tailored survey questions, BTMP is iteratively trained to achieve the desired accuracy faster with fewer questions, thereby reducing survey costs. Experimental validation using synthetic datasets confirms the effectiveness of BTMP in quantifying prediction uncertainty. Furthermore, experiments, utilizing both synthetic and real-world data, demonstrate that the BTMP model, trained with the uncertainty-guided active survey framework, requires 20% to 50% fewer survey responses to match the performance of the model trained on randomly collected survey data. Overall, the proposed BTMP model and active survey framework innovatively incorporate uncertainty quantification into travel mode choice modeling, providing model users with essential insights into prediction reliability while optimizing data collection for deep learning model training in a cost-efficient manner.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shuwen Zheng, Zhou Fang, Liang Zhao. 2024-06-16. Incorporating uncertainty quantification into travel mode choice modeling: a Bayesian neural network (BNN) approach and an uncertainty-guided active survey framework. https://arxiv.org/abs/2406.10948

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG

DeepSPoC: A Deep Learning Based Sequential Propagation of Chaos

Classical particle methods based on propagation of chaos (PoC) have been developed for solving mean-field stochastic differential equations and their associated nonlinear Fokker--Planck equations. However, direct PoC implementations are difficult to apply to high-dimensional problems because they require simulating and storing large numbers of interacting particles, often with high particle-particle interaction costs. Motivated by these limitations, we build on the recently proposed sequential propagation of chaos (SPoC) framework, which replaces the fully interacting particle system in PoC with a sequential interaction mechanism. Based on this structure, we present DeepSPoC, a neural particle method that embeds a neural density representation into the sequential particle dynamics. DeepSPoC simulates particles batch by batch, while the neural network represents the evolving empirical law and is substituted into the coefficients of the mean-field SDE, thereby replacing direct particle-particle interactions with particle-network interactions. In DeepSPoC, a recently developed normalizing flow model called KRnet is used to approximate the empirical measure of particles. Compared with direct particle implementations, DeepSPoC substantially reduces memory consumption and evaluates interaction terms more efficiently, thereby improving scalability for high-dimensional problems. We apply DeepSPoC to a wide range of mean-field equations and verify its effectiveness and computational advantages.

cs.LG