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Gaussian Process Latent Class Choice Models

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Document pages: 34 pages

Abstract: We present a Gaussian Process - Latent Class Choice Model (GP-LCCM) tointegrate a non-parametric class of probabilistic machine learning withindiscrete choice models (DCMs). Gaussian Processes (GPs) are kernel-basedalgorithms that incorporate expert knowledge by assuming priors over latentfunctions rather than priors over parameters, which makes them more flexible inaddressing nonlinear problems. By integrating a Gaussian Process within a LCCMstructure, we aim at improving discrete representations of unobservedheterogeneity. The proposed model would assign individuals probabilistically tobehaviorally homogeneous clusters (latent classes) using GPs and simultaneouslyestimate class-specific choice models by relying on random utility models.Furthermore, we derive and implement an Expectation-Maximization (EM) algorithmto jointly estimate infer the hyperparameters of the GP kernel function and theclass-specific choice parameters by relying on a Laplace approximation andgradient-based numerical optimization methods, respectively. The model istested on two different mode choice applications and compared against differentLCCM benchmarks. Results show that GP-LCCM allows for a more complex andflexible representation of heterogeneity and improves both in-sample fit andout-of-sample predictive power. Moreover, behavioral and economicinterpretability is maintained at the class-specific choice model level whilelocal interpretation of the latent classes can still be achieved, although thenon-parametric characteristic of GPs lessens the transparency of the model.

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