Spatial autocorrelation and spatial heterogeneity widely exist in spatial data, which make the traditional machine learning model perform badly. Spatial domain generalization is a spatial extension of domain generalization, which can generalize to unseen spatial domains in continuous 2D space. Specifically, it learns a model under varying data distributions that generalizes to unseen domains. Although tremendous success has been achieved in domain generalization, there exist very few works on spatial domain generalization. The advancement of this area is challenged by: 1) Difficulty in characterizing spatial heterogeneity, and 2) Difficulty in obtaining predictive models for unseen locations without training data. To address these challenges, this paper proposes a generic framework for spatial domain generalization. Specifically, We develop the spatial interpolation graph neural network that handles spatial data as a graph and learns the spatial embedding on each node and their relationships. The spatial interpolation graph neural network infers the spatial embedding of an unseen location during the test phase. Then the spatial embedding of the target location is used to decode the parameters of the downstream-task model directly on the target location. Finally, extensive experiments on thirteen real-world datasets demonstrate the proposed method's strength.

With the research directions described in this thesis, we seek to address the critical challenges in designing recommender systems that can understand the dynamics of continuous-time event sequences. We follow a ground-up approach, i.e., first, we address the problems that may arise due to the poor quality of CTES data being fed into a recommender system. Later, we handle the task of designing accurate recommender systems. To improve the quality of the CTES data, we address a fundamental problem of overcoming missing events in temporal sequences. Moreover, to provide accurate sequence modeling frameworks, we design solutions for points-of-interest recommendation, i.e., models that can handle spatial mobility data of users to various POI check-ins and recommend candidate locations for the next check-in. Lastly, we highlight that the capabilities of the proposed models can have applications beyond recommender systems, and we extend their abilities to design solutions for large-scale CTES retrieval and human activity prediction. A significant part of this thesis uses the idea of modeling the underlying distribution of CTES via neural marked temporal point processes (MTPP). Traditional MTPP models are stochastic processes that utilize a fixed formulation to capture the generative mechanism of a sequence of discrete events localized in continuous time. In contrast, neural MTPP combine the underlying ideas from the point process literature with modern deep learning architectures. The ability of deep-learning models as accurate function approximators has led to a significant gain in the predictive prowess of neural MTPP models. In this thesis, we utilize and present several neural network-based enhancements for the current MTPP frameworks for the aforementioned real-world applications.

Urban traffic speed prediction aims to estimate the future traffic speed for improving the urban transportation services. Enormous efforts have been made on exploiting spatial correlations and temporal dependencies of traffic speed evolving patterns by leveraging explicit spatial relations (geographical proximity) through pre-defined geographical structures ({\it e.g.}, region grids or road networks). While achieving promising results, current traffic speed prediction methods still suffer from ignoring implicit spatial correlations (interactions), which cannot be captured by grid/graph convolutions. To tackle the challenge, we propose a generic model for enabling the current traffic speed prediction methods to preserve implicit spatial correlations. Specifically, we first develop a Dual-Transformer architecture, including a Spatial Transformer and a Temporal Transformer. The Spatial Transformer automatically learns the implicit spatial correlations across the road segments beyond the boundary of geographical structures, while the Temporal Transformer aims to capture the dynamic changing patterns of the implicit spatial correlations. Then, to further integrate both explicit and implicit spatial correlations, we propose a distillation-style learning framework, in which the existing traffic speed prediction methods are considered as the teacher model, and the proposed Dual-Transformer architectures are considered as the student model. The extensive experiments over three real-world datasets indicate significant improvements of our proposed framework over the existing methods.

A primary challenge faced in few-shot action recognition is inadequate video data for training. To address this issue, current methods in this field mainly focus on devising algorithms at the feature level while little attention is paid to processing input video data. Moreover, existing frame sampling strategies may omit critical action information in temporal and spatial dimensions, which further impacts video utilization efficiency. In this paper, we propose a novel video frame sampler for few-shot action recognition to address this issue, where task-specific spatial-temporal frame sampling is achieved via a temporal selector (TS) and a spatial amplifier (SA). Specifically, our sampler first scans the whole video at a small computational cost to obtain a global perception of video frames. The TS plays its role in selecting top-T frames that contribute most significantly and subsequently. The SA emphasizes the discriminative information of each frame by amplifying critical regions with the guidance of saliency maps. We further adopt task-adaptive learning to dynamically adjust the sampling strategy according to the episode task at hand. Both the implementations of TS and SA are differentiable for end-to-end optimization, facilitating seamless integration of our proposed sampler with most few-shot action recognition methods. Extensive experiments show a significant boost in the performances on various benchmarks including long-term videos.The code is available at https://github.com/R00Kie-Liu/Sampler

In the wake of the COVID-19 pandemic, the World Bank's 2020 Global Economic Prospects forecasts a baseline global GDP contraction of 5.2 percent, making it the deepest global recession in decades. Between 71 to 100 million people are expected to be pushed into extreme poverty, almost half of them in South Asia and more than a third in Sub-Saharan Africa. As a result, since March 2020 over 215 countries and territories have implemented 1,414 social protection measures to respond to the pandemic and ensuing economic crisis. Social assistance programs account for 62 percent of all social protection response measures, half of them being cash-based transfers of some sort. This major shock has revealed the many challenges governments face when attempting to quickly respond to crises in order to protect the poor and vulnerable. Providing timely assistance and support to those households most in need can increase their resilience and reduce the negative impacts of the shock on their short and medium-term well-being. Nonetheless, the lack of readily available and up-to-date socioeconomic data necessary to prioritize shock-responsive social protection measures is an important binding constraint for many governments in developing countries. This paper presents a portion of our work on a larger project with the World Bank to identify the most vulnerable populations in these countries. Having timely access to such information, particularly in data-deprived contexts, can improve the capacity of governments to design and operationalize better and more shock-responsive social protection measures.

Accurate spatial-temporal traffic flow forecasting is essential for helping traffic managers to take control measures and drivers to choose the optimal travel routes. Recently, graph convolutional networks (GCNs) have been widely used in traffic flow prediction owing to their powerful ability to capture spatial-temporal dependencies. The design of the spatial-temporal graph adjacency matrix is a key to the success of GCNs, and it is still an open question. This paper proposes reconstructing the binary adjacency matrix via tensor decomposition, and a traffic flow forecasting method is proposed. First, we reformulate the spatial-temporal fusion graph adjacency matrix into a three-way adjacency tensor. Then, we reconstructed the adjacency tensor via Tucker decomposition, wherein more informative and global spatial-temporal dependencies are encoded. Finally, a Spatial-temporal Synchronous Graph Convolutional module for localized spatial-temporal correlations learning and a Dilated Convolution module for global correlations learning are assembled to aggregate and learn the comprehensive spatial-temporal dependencies of the road network. Experimental results on four open-access datasets demonstrate that the proposed model outperforms state-of-the-art approaches in terms of the prediction performance and computational cost.

Accurate and timely rain prediction is crucial for decision making and is also a challenging task. This paper presents a solution which won the 2 nd prize in the Weather4cast 2022 NeurIPS competition using 3D U-Nets and EarthFormers for 8-hour probabilistic rain prediction based on multi-band satellite images. The spatial context effect of the input satellite image has been deeply explored and optimal context range has been found. Based on the imbalanced rain distribution, we trained multiple models with different loss functions. To further improve the model performance, multi-model ensemble and threshold optimization were used to produce the final probabilistic rain prediction. Experiment results and leaderboard scores demonstrate that optimal spatial context, combined loss function, multi-model ensemble, and threshold optimization all provide modest model gain. A permutation test was used to analyze the effect of each satellite band on rain prediction, and results show that satellite bands signifying cloudtop phase (8.7 um) and cloud-top height (10.8 and 13.4 um) are the best predictors for rain prediction. The source code is available at https://github.com/bugsuse/weather4cast-2022-stage2.

Deep Learning has significantly impacted the application of data-to-decision throughout research and industry, however, they lack a rigorous mathematical foundation, which creates situations where algorithmic results fail to be practically invertible. In this paper we present a nearly invertible mapping between $\mathbb{R}^{2^n}$ and $\mathbb{R}^{n+1}$ via a topological connection between $S^{2^n-1}$ and $S^n$. Throughout the paper we utilize the algebra of Multicomplex rotation groups and polyspherical coordinates to define two maps: the first is a contraction from $S^{2^n-1}$ to $\displaystyle \otimes^n_{k=1} SO(2)$, and the second is a projection from $\displaystyle \otimes^n_{k=1} SO(2)$ to $S^{n}$. Together these form a composite map that we call the LG Fibration. In analogy to the generation of Hopf Fibration using Hypercomplex geometry from $S^{(2n-1)} \mapsto CP^n$, our fibration uses Multicomplex geometry to project $S^{2^n-1}$ onto $S^n$. We also investigate the algebraic properties of the LG Fibration, ultimately deriving a distance difference function to determine which pairs of vectors have an invariant inner product under the transformation. The LG Fibration has applications to Machine Learning and AI, in analogy to the current applications of Hopf Fibrations in adaptive UAV control. Furthermore, the ability to invert the LG Fibration for nearly all elements allows for the development of Machine Learning algorithms that may avoid the issues of uncertainty and reproducibility that currently plague contemporary methods. The primary result of this paper is a novel method of nearly invertible geometric dimensional reduction from $S^{2^n-1}$ to $S^n$, which has the capability to extend the research in both mathematics and AI, including but not limited to the fields of homotopy groups of spheres, algebraic topology, machine learning, and algebraic biology.

GPS trajectories are the essential foundations for many trajectory-based applications, such as travel time estimation, traffic prediction and trajectory similarity measurement. Most applications require a large amount of high sample rate trajectories to achieve a good performance. However, many real-life trajectories are collected with low sample rate due to energy concern or other constraints.We study the task of trajectory recovery in this paper as a means for increasing the sample rate of low sample trajectories. Currently, most existing works on trajectory recovery follow a sequence-to-sequence diagram, with an encoder to encode a trajectory and a decoder to recover real GPS points in the trajectory. However, these works ignore the topology of road network and only use grid information or raw GPS points as input. Therefore, the encoder model is not able to capture rich spatial information of the GPS points along the trajectory, making the prediction less accurate and lack spatial consistency. In this paper, we propose a road network enhanced transformer-based framework, namely RNTrajRec, for trajectory recovery. RNTrajRec first uses a graph model, namely GridGNN, to learn the embedding features of each road segment. It next develops a spatial-temporal transformer model, namely GPSFormer, to learn rich spatial and temporal features along with a Sub-Graph Generation module to capture the spatial features for each GPS point in the trajectory. It finally forwards the outputs of encoder model into a multi-task decoder model to recover the missing GPS points. Extensive experiments based on three large-scale real-life trajectory datasets confirm the effectiveness of our approach.

Spatial-temporal (ST) graph modeling, such as traffic speed forecasting and taxi demand prediction, is an important task in deep learning area. However, for the nodes in graph, their ST patterns can vary greatly in difficulties for modeling, owning to the heterogeneous nature of ST data. We argue that unveiling the nodes to the model in a meaningful order, from easy to complex, can provide performance improvements over traditional training procedure. The idea has its root in Curriculum Learning which suggests in the early stage of training models can be sensitive to noise and difficult samples. In this paper, we propose ST-Curriculum Dropout, a novel and easy-to-implement strategy for spatial-temporal graph modeling. Specifically, we evaluate the learning difficulty of each node in high-level feature space and drop those difficult ones out to ensure the model only needs to handle fundamental ST relations at the beginning, before gradually moving to hard ones. Our strategy can be applied to any canonical deep learning architecture without extra trainable parameters, and extensive experiments on a wide range of datasets are conducted to illustrate that, by controlling the difficulty level of ST relations as the training progresses, the model is able to capture better representation of the data and thus yields better generalization.