Improving Predictions in Travel Behavior Modeling

Travel behavior modeling helps us understand how people make choices about transportation. One common method used for this purpose is called Discrete Choice Models (DCMs). These models try to predict which option a person will choose from a set of alternatives. For instance, when deciding how to get to work, a person may choose between driving, taking the bus, or cycling.

However, the Data we collect to build these models often has errors. These errors can come from various sources, such as mistakes in survey responses or problems with how the data was recorded. Previous research mainly focused on improving how we estimate the underlying model parameters. While this is important, it does not directly help when trying to predict new choices based on the data that has errors.

In this discussion, we will focus on how to better predict new choices made by individuals when there are uncertainties in the data.

#Background on Discrete Choice Models

Discrete choice models work by calculating the probability that a person will choose a particular option based on certain factors. These factors might include travel time, cost, or personal preferences. A common type of discrete choice model is the multinomial logit model (MNL), where it is assumed that each person's preferences can be captured through specific variables.

In practice, we derive the model from utility theory, which helps explain how people make their choices. Each alternative has associated utility, which is the satisfaction or benefit a person gets from choosing that option. The utility can be influenced by various observed and unobserved factors.

Usually, a DCM will produce probabilities for each alternative, allowing us to predict which choice a person is likely to make. The data we use to build these models usually comes from surveys where individuals report their preferences.

#Challenges with Uncertainties in Data

One significant challenge in using discrete choice models is that the data can be uncertain. This includes Measurement Errors where the information collected does not accurately reflect reality. For example, a survey participant might incorrectly report their income, leading to biased results. These errors can occur in features (independent variables) or in labels (dependent variables).

Measurement errors can result in biased Predictions, which reduce the effectiveness of the models. Traditional methods to handle these errors often hinge on using instrumental variables, which assume that we have correct information available to help adjust for these inaccuracies. However, finding suitable auxiliary variables in practice can be difficult.

Most existing research has concentrated on addressing measurement errors during the training phase of model development. However, once the model is trained and we attempt to predict outcomes from new data, measurement errors can still persist. This situation raises the question: how can we improve predictions when faced with uncertainties in the data?

#The Proposed Approach: Robust Discrete Choice Models

To address the challenges presented by measurement errors, we propose a robust discrete choice model framework. This framework focuses on accounting for uncertainties in both features and labels to enhance prediction accuracy when dealing with new data.

The core idea behind the robust framework is to minimize the worst-case loss across a variety of data uncertainty scenarios. This involves recognizing that measurement errors will occur, and we need a solution that remains effective even in the presence of such issues.

#Handling Feature and Label Uncertainties

In our robust model, we treat feature uncertainties by assuming that the measurement error on each feature is smaller than a previously set threshold. This allows the model to be more resilient to inaccuracies in the input data. For label uncertainties, we consider that there are at most a limited number of incorrect choices.

By using this structured approach, we can derive robust counterparts for both robust-feature and robust-label discrete choice models. Initial evaluations suggest that these models can outperform standard DCMs in accuracy and predictive performance.

#Implementation of the Robust Framework

We applied our robust framework in two case studies: a binary choice data set and a multinomial choice data set. The first involved choices related to first- and last-mile travel in Singapore, while the second looked at preferences for different travel modes in Switzerland.

In both cases, we systematically generated synthetic data with known errors to test the robustness of our models. The results showed that models accounting for uncertainties yielded better testing accuracy and log-likelihood compared to conventional methods.

#Insights from Experiments

The experimental results demonstrated that as we increase the consideration of uncertainties in our models, the training accuracy may decline. This drop occurs because the model is prioritizing robustness over fitting the training data precisely. Despite this, when we apply the models to new data, the robust models perform significantly better than their traditional counterparts.

An important observation is that the robustness in our models functions similarly to regularization techniques commonly used in machine learning. Regularization helps models generalize better by preventing overfitting to the training data. In our case, the robustness approach leads to smaller parameter estimates, which promotes better generalization to new samples.

#Conclusion

In summary, we have presented a robust discrete choice model framework that effectively handles feature and label uncertainties. By focusing on robust optimization, our approach offers a way to improve predictions made from data that may contain inaccuracies. The positive results from our experiments suggest that this framework holds promise for enhancing the accuracy of travel behavior predictions.

Future research directions may include combining robust-feature and robust-label models into a unified framework and developing methods to automatically tune the hyper-parameters. Additionally, efforts could be made to refine the approximation methods used in our robust multinomial models to provide even more accurate predictions.

The challenge of data uncertainties is prevalent in many fields, and by addressing these issues within the context of travel behavior modeling, we can enhance the effectiveness of transportation planning and policy analysis efforts.