Michel Bierlaire | José Ángel Martín Baos

Scalable kernel logistic regression with Nyström approximation: Theoretical analysis and application to discrete choice modelling

Fri, 07 Feb 2025 00:00:00 +0000

Nyström-based approximations for kernel logistic regression: Application to transport choice modelling

Mon, 17 Jul 2023 00:00:00 +0000

Abstract

The application of machine learning techniques, more specifically kernel-based techniques, to discrete choice modelling using large datasets is limited by the great number of parameters to be considered when building the kernel matrix and the size of the kernel matrix itself. The spatial and temporal complexity is such that these methods are not applicable to large sample sizes. However, there are techniques that allow generating a low-rank matrix approximation to the kernel matrix, one of them is the Nyström method. One limitation of the Nyström method is that the quality of the kernel matrix approximation depends on the proper choice of landmark points. In this work, four variants of this technique are implemented, a basic uniform method, one based on the K-means algorithm and two different implementations of a non-uniform method based on leverage scores. Later, in the experimentation, we conduct a comparison of these methods applied to two big transport mode choice datasets, which contain a large number of samples and variables. Finally, these results are compared with Multinomial Logit and other techniques currently relevant in the Machine Learning field.

A Unimodal Ordered Logit model for ranked choices

Sun, 12 Sep 2021 00:00:00 +0000

Abstract

Ordinal scale responses capture qualitative user feedback which can be used to model individual choice preference, or are employed in traffic accident analysis to evaluate accident severity. We present a new choice model for ordinal scale responses in choice tasks that combines a Multinomial Logit model with a Poisson probability mass function. The Poisson distribution, which is suitable for modelling the occurrence of the number of events in a fixed time frame, independent of previous events, can be adapted into the unobserved error distribution of a standard MNL model to capture the natural ordering of the choices by imposing a unimodal constraint on the a posteriori choice probability. In this paper we describe the theoretical framework and the specification of the Unimodal Logit model. We apply our model to evaluate accident severity concerning road collisions. Our results are compared against the traditional ordered logit model and the MNL model.