A Quasi-Wasserstein Loss for Learning Graph Neural Networks

When learning graph neural networks (GNNs) in node-level prediction tasks, most existing loss functions are applied for each node independently, even if node embeddings and their labels are non-i.i.d. because of their graph structures. To eliminate such inconsistency, in this study we propose a novel Quasi-Wasserstein (QW) loss with the help of the optimal transport defined on graphs, leading to new learning and prediction paradigms of GNNs. In particular, we design a "Quasi-Wasserstein" distance between the observed multi-dimensional node labels and their estimations, optimizing the label transport defined on graph edges. The estimations are parameterized by a GNN in which the optimal label transport may determine the graph edge weights optionally. By reformulating the strict constraint of the label transport to a Bregman divergence-based regularizer, we obtain the proposed Quasi-Wasserstein loss associated with two efficient solvers learning the GNN together with optimal label transport. When predicting node labels, our model combines the output of the GNN with the residual component provided by the optimal label transport, leading to a new transductive prediction paradigm. Experiments show that the proposed QW loss applies to various GNNs and helps to improve their performance in node-level classification and regression tasks

Regularized Optimal Transport Layers for Generalized Global Pooling Operations

Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical fundamentals, its practical implementations often depend on empirical mechanisms and thus lead to sub-optimal, even unsatisfactory performance. In this work, we develop a novel and generalized global pooling framework through the lens of optimal transport. The proposed framework is interpretable from the perspective of expectation-maximization. Essentially, it aims at learning an optimal transport across sample indices and feature dimensions, making the corresponding pooling operation maximize the conditional expectation of input data. We demonstrate that most existing pooling methods are equivalent to solving a regularized optimal transport (ROT) problem with different specializations, and more sophisticated pooling operations can be implemented by hierarchically solving multiple ROT problems. Making the parameters of the ROT problem learnable, we develop a family of regularized optimal transport pooling (ROTP) layers. We implement the ROTP layers as a new kind of deep implicit layer. Their model architectures correspond to different optimization algorithms. We test our ROTP layers in several representative set-level machine learning scenarios, including multi-instance learning (MIL), graph classification, graph set representation, and image classification. Experimental results show that applying our ROTP layers can reduce the difficulty of the design and selection of global pooling -- our ROTP layers may either imitate some existing global pooling methods or lead to some new pooling layers fitting data better. The code is available at \url{https://github.com/SDS-Lab/ROT-Pooling}

The Economic Benefits of Built Environment Supportive of Active Living in Dallas Tax Increment Financing Districts

This dissertation consists of three studies to systematically evaluate the economic benefits of activity-friendly environmental features in Dallas Tax Increment Financing (TIF) districts, Dallas, Texas, and to examine if TIF developments deliver more walkable/accessible environments, as compared to non-TIF comparison neighborhoods. Topic 1 employed a quasi-experimental design and the propensity score matching approach to establish a causal inference between TIF development effects and housing value growth and destination accessibility. The findings suggested that the overall TIF development effects accounted for $27,840 (or 95.6$1,267 (or 4.4%) of the housing value growth, as compared to their counterparts in comparison neighborhoods. In terms of destination accessibility, the overall TIF effects accounted for 8 additional points (of the 100-point scale) on Walk Score, while the other factors only accounted for 2 additional points. The results suggested that TIF developments do stimulate housing value growth, while increasing accessibility to various destinations. Topic 2 followed a socio-ecological framework to examine the effect of personal, neighborhood, and built environmental factors on active commuting to work in TIF and non-TIF comparison neighborhoods, using fractional logit models with margin effects and margin plots. The findings suggested that the built environmental factors only influenced active commuting to work in the neighborhoods that are already fairly walkable. The findings also suggested that travel time and personal factors played a consistently important role in influencing the active commuting behavior in both models, regardless of the variation of physical walking environments. In addition, TIF neighborhoods mitigated the negative impact on active commuting from disadvantaged areas. Topic 3 utilized a 7Ds measurement framework to systematically examine and compare the economic benefits of various activity-friendly environments in TIF and comparison neighborhoods, using ordinary least squares (OLS) regression, spatial regression, and hierarchical linear modeling (HLM) approaches. The finding suggested (1) destination accessibility and transportation facilities were positively associated with appreciation rates, but other activity-friendly environmental features are not associated with higher appreciation rates, and (2) neighborhoods with better walkable environments are associated with higher appreciation rates (1.36% in TIF vs. 0.95% in comparison neighborhoods)

Denitrification rates in tidal marsh soils : the roles of soil texture, salinity and nitrogen enrichment

The denitrification rates of freshwater and oligohaline tidal marsh soils with different textures (loam and sandy soils) in a subtropical estuary, and their responses to nitrogen (N) loading, were investigated. In both marshes, the denitrification rates varied significantly with the season only in loam soil. The denitrification rates were highest in oligohaline marsh loam soil and lowest in freshwater marsh sandy soil. NH4NO3 addition significantly increased the denitrification rates of all the marsh soils. Our findings suggest that soil texture, soil organic matter (OM) content and low-level increases in salinity all had large effects on denitrification, indicating that the dynamics of denitrification rates in estuarine marshes with low-level salinity were controlled by the interaction of salinity and soil texture but mainly depended on OM content. We propose that denitrification in tidal marshes plays an important role in regulating current and future N loading into estuary and inshore coastal waters, especially for tidal freshwater marshes, which introduces great uncertainty into the N dynamics of estuaries under global changes