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The goal of this paper is to investigate a control theoretic analysis of linear stochastic iterative algorithm and temporal difference (TD) learning. TD-learning is a linear stochastic iterative algorithm to estimate the value function of a given policy for a Markov decision process, which is one of the most popular and fundamental reinforcement learning algorithms. While there has been a series of successful works in theoretical analysis of TD-learning, it was not until recently that researchers found some guarantees on its statistical efficiency. In this paper, we propose a control theoretic finite-time analysis TD-learning, which exploits standard notions in linear system control communities. Therefore, the proposed work provides additional insights on TD-learning and reinforcement learning with simple concepts and analysis tools in control theory.

There recently has been a surge of interest in developing a new class of deep learning (DL) architectures that integrate an explicit time dimension as a fundamental building block of learning and representation mechanisms. In turn, many recent results show that topological descriptors of the observed data, encoding information on the shape of the dataset in a topological space at different scales, that is, persistent homology of the data, may contain important complementary information, improving both performance and robustness of DL. As convergence of these two emerging ideas, we propose to enhance DL architectures with the most salient time-conditioned topological information of the data and introduce the concept of zigzag persistence into time-aware graph convolutional networks (GCNs). Zigzag persistence provides a systematic and mathematically rigorous framework to track the most important topological features of the observed data that tend to manifest themselves over time. To integrate the extracted time-conditioned topological descriptors into DL, we develop a new topological summary, zigzag persistence image, and derive its theoretical stability guarantees. We validate the new GCNs with a time-aware zigzag topological layer (Z-GCNETs), in application to traffic forecasting and Ethereum blockchain price prediction. Our results indicate that Z-GCNET outperforms 13 state-of-the-art methods on 4 time series datasets.

Traffic forecasting is an important factor for the success of intelligent transportation systems. Deep learning models including convolution neural networks and recurrent neural networks have been applied in traffic forecasting problems to model the spatial and temporal dependencies. In recent years, to model the graph structures in the transportation systems as well as the contextual information, graph neural networks (GNNs) are introduced as new tools and have achieved the state-of-the-art performance in a series of traffic forecasting problems. In this survey, we review the rapidly growing body of recent research using different GNNs, e.g., graph convolutional and graph attention networks, in various traffic forecasting problems, e.g., road traffic flow and speed forecasting, passenger flow forecasting in urban rail transit systems, demand forecasting in ride-hailing platforms, etc. We also present a collection of open data and source resources for each problem, as well as future research directions. To the best of our knowledge, this paper is the first comprehensive survey that explores the application of graph neural networks for traffic forecasting problems. We have also created a public Github repository to update the latest papers, open data and source resources.

Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.

Graph deep learning has recently emerged as a powerful ML concept allowing to generalize successful deep neural architectures to non-Euclidean structured data. Such methods have shown promising results on a broad spectrum of applications ranging from social science, biomedicine, and particle physics to computer vision, graphics, and chemistry. One of the limitations of the majority of the current graph neural network architectures is that they are often restricted to the transductive setting and rely on the assumption that the underlying graph is known and fixed. In many settings, such as those arising in medical and healthcare applications, this assumption is not necessarily true since the graph may be noisy, partially- or even completely unknown, and one is thus interested in inferring it from the data. This is especially important in inductive settings when dealing with nodes not present in the graph at training time. Furthermore, sometimes such a graph itself may convey insights that are even more important than the downstream task. In this paper, we introduce Differentiable Graph Module (DGM), a learnable function predicting the edge probability in the graph relevant for the task, that can be combined with convolutional graph neural network layers and trained in an end-to-end fashion. We provide an extensive evaluation of applications from the domains of healthcare (disease prediction), brain imaging (gender and age prediction), computer graphics (3D point cloud segmentation), and computer vision (zero-shot learning). We show that our model provides a significant improvement over baselines both in transductive and inductive settings and achieves state-of-the-art results.

Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.

Traffic forecasting is of great importance to transportation management and public safety, and very challenging due to the complicated spatial-temporal dependency and essential uncertainty brought about by the road network and traffic conditions. Latest studies mainly focus on modeling the spatial dependency by utilizing graph convolutional networks (GCNs) throughout a fixed weighted graph. However, edges, i.e., the correlations between pair-wise nodes, are much more complicated and interact with each other. In this paper, we propose the Multi-Range Attentive Bicomponent GCN (MRA-BGCN), a novel deep learning model for traffic forecasting. We first build the node-wise graph according to the road network distance and the edge-wise graph according to various edge interaction patterns. Then, we implement the interactions of both nodes and edges using bicomponent graph convolution. The multi-range attention mechanism is introduced to aggregate information in different neighborhood ranges and automatically learn the importance of different ranges. Extensive experiments on two real-world road network traffic datasets, METR-LA and PEMS-BAY, show that our MRA-BGCN achieves the state-of-the-art results.

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.

Multivariate time series forecasting is extensively studied throughout the years with ubiquitous applications in areas such as finance, traffic, environment, etc. Still, concerns have been raised on traditional methods for incapable of modeling complex patterns or dependencies lying in real word data. To address such concerns, various deep learning models, mainly Recurrent Neural Network (RNN) based methods, are proposed. Nevertheless, capturing extremely long-term patterns while effectively incorporating information from other variables remains a challenge for time-series forecasting. Furthermore, lack-of-explainability remains one serious drawback for deep neural network models. Inspired by Memory Network proposed for solving the question-answering task, we propose a deep learning based model named Memory Time-series network (MTNet) for time series forecasting. MTNet consists of a large memory component, three separate encoders, and an autoregressive component to train jointly. Additionally, the attention mechanism designed enable MTNet to be highly interpretable. We can easily tell which part of the historic data is referenced the most.

Deep convolutional neural networks have become a key element in the recent breakthrough of salient object detection. However, existing CNN-based methods are based on either patch-wise (region-wise) training and inference or fully convolutional networks. Methods in the former category are generally time-consuming due to severe storage and computational redundancies among overlapping patches. To overcome this deficiency, methods in the second category attempt to directly map a raw input image to a predicted dense saliency map in a single network forward pass. Though being very efficient, it is arduous for these methods to detect salient objects of different scales or salient regions with weak semantic information. In this paper, we develop hybrid contrast-oriented deep neural networks to overcome the aforementioned limitations. Each of our deep networks is composed of two complementary components, including a fully convolutional stream for dense prediction and a segment-level spatial pooling stream for sparse saliency inference. We further propose an attentional module that learns weight maps for fusing the two saliency predictions from these two streams. A tailored alternate scheme is designed to train these deep networks by fine-tuning pre-trained baseline models. Finally, a customized fully connected CRF model incorporating a salient contour feature embedding can be optionally applied as a post-processing step to improve spatial coherence and contour positioning in the fused result from these two streams. Extensive experiments on six benchmark datasets demonstrate that our proposed model can significantly outperform the state of the art in terms of all popular evaluation metrics.