Uncertainty quantification for complex systems : application to the study of cities

• Main Author: Steentoft, Aike Alexander
• Other Authors: Lee Bu Sung, Francis
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2021
• Subjects: Engineering::Computer science and engineering::Computing methodologies::Artificial intelligence; Social sciences::Statistics
• Online Access: https://hdl.handle.net/10356/152120
• Institution: Nanyang Technological University

Human interactions are the fundamental drivers that establish cities as the hubs for innovation and economic growth. Traditional urban planning methods -- aimed to facilitate these interactions -- are however becoming questionable as they are typically based on 'best practice', thus unable to cope with the increasing complexity of today's rapidly evolving cities. The quantitative description of interactivity and its relation to the spatial organization of urban spaces and transportation infrastructure is therefore of fundamental importance. In the first part of the thesis I asks the -- more obvious -- question: `What methods can help us to gain additional insights into how human interactivity is shaped by the spatial organization of urban spaces?'; here human interactivity is treated as the dependent variable. Unfortunately, the existing spatial interaction models are unable to accurately capture empirical observations; indicating that relevant structure, present in the real world system, is not modeled. More recently machine learning systems have been developed that could overcome these challenges. But more flexible models such as deep neural networks are not interpretable and therefore not as accepted by urban planners and transportation engineers. From a statistical perspective, the main difficulty is to develop a model that (i) allows for many, potentially relevant, input variables with complex relational structure and (ii) is interpretable with respect to the relevance of the inputs and is interpretable with respect to the confidence of its predictions. I address this problem with Bayesian neural networks. The expressiveness and flexibility of neural network models allows to automatically identify complex structure in data. A Bayesian approach allows to model uncertainty in a principled way and is also helpful to automatically determine the relevance of input variables. Bayesian learning in neural networks is however challenging. First, one needs to define a prior probability distribution over the network parameters that encodes prior knowledge of the problem. Second, one needs to integrate function values of interest with respect to the high-dimensional updated prior distribution. I address these problems with a new neural network model which offers both the flexibility of a deep neural network and the interpretability in terms of variable selection. In particular, I use the recently derived exact equivalence between infinitely wide deep neural networks and Gaussian processes to do exact Bayesian inference on the deep neural networks. I then introduce additional hyperparameters to the covariance function of the Gaussian process which enable automatic feature selection. Sparsity is handled via the horseshoe prior. I tested various implementations of network architectures and inference procedures on synthetic data sets and a real data set related to human interactivity. I found that my proposed approach can give more accurate predictions than traditional models while providing uncertainty estimates for its predictions and also providing additional insights into the importance of different urban measurements. Such insights can be of great value for urban planning -- aimed to facilitate interactions. In the second part of the thesis I asks the -- more subtle -- question: `What methods can help us to gain additional insights into how the spatial organization of urban spaces is shaped by human interactivity?'; here the spatial organization of urban spaces is treated as the dependent variable. More specifically, I address the problem of predicting from human interactivity patterns when and where urban neighborhoods will face urban change. To tackle this challenge, I adapt the concept of `bioindicators', borrowed from ecology, to the urban context. The objective is to use an `indicator group' of people to assess the quality of a complex environment and its changes over time. Specifically, I analyze millions of geolocated Twitter records across multiple US cities, allowing me to derive socio-economic user profiles based on individual movement patterns. As a proof-of-concept, I define users with a `high-income-profile' as an indicator group and show that their visitation patterns are a suitable indicator for expected future rent increases in different neighborhoods. The concept of indicator groups highlights the potential of closely monitoring only a specific subset of the population, rather than the population as a whole. If the indicator group is defined appropriately for the phenomenon of interest, this approach can yield early predictions while simultaneously reducing the amount of data that needs to be collected and analyzed.