In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

We present the Open Graph Benchmark (OGB), a diverse set of challenging and realistic benchmark datasets to facilitate scalable, robust, and reproducible graph machine learning (ML) research. OGB datasets are large-scale, encompass multiple important graph ML tasks, and cover a diverse range of domains, ranging from social and information networks to biological networks, molecular graphs, source code ASTs, and knowledge graphs. For each dataset, we provide a unified evaluation protocol using meaningful application-specific data splits and evaluation metrics. In addition to building the datasets, we also perform extensive benchmark experiments for each dataset. Our experiments suggest that OGB datasets present significant challenges of scalability to large-scale graphs and out-of-distribution generalization under realistic data splits, indicating fruitful opportunities for future research. Finally, OGB provides an automated end-to-end graph ML pipeline that simplifies and standardizes the process of graph data loading, experimental setup, and model evaluation. OGB will be regularly updated and welcomes inputs from the community. OGB datasets as well as data loaders, evaluation scripts, baseline code, and leaderboards are publicly available at this https URL .

Open Graph Benchmark: Datasets for Machine Learning on Graphs

The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis-Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.

Riemann manifold Langevin and Hamiltonian Monte Carlo methods

Link prediction is a key problem for network-structured data. Link prediction heuristics use some score functions, such as common neighbors and Katz index, to measure the likelihood of links. They have obtained wide practical uses due to their simplicity, interpretability, and for some of them, scalability. However, every heuristic has a strong assumption on when two nodes are likely to link, which limits their effectiveness on networks where these assumptions fail. In this regard, a more reasonable way should be learning a suitable heuristic from a given network instead of using predefined ones. By extracting a local subgraph around each target link, we aim to learn a function mapping the subgraph patterns to link existence, thus automatically learning a "heuristic" that suits the current network. In this paper, we study this heuristic learning paradigm for link prediction. First, we develop a novel γ-decaying heuristic theory. The theory unifies a wide range of heuristics in a single framework, and proves that all these heuristics can be well approximated from local subgraphs. Our results show that local subgraphs reserve rich information related to link existence. Second, based on the γ-decaying theory, we propose a new method to learn heuristics from local subgraphs using a graph neural network (GNN). Its experimental results show unprecedented performance, working consistently well on a wide range of problems.

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Link prediction based on graph neural networks

Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks' Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning.

Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec.

Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks» Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning.

Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec

Time series are widely used as signals in many classification/regression tasks. It is ubiquitous that time series contains many missing values. Given multiple correlated time series data, how to fill in missing values and to predict their class labels? Existing imputation methods often impose strong assumptions of the underlying data generating process, such as linear dynamics in the state space. In this paper, we propose BRITS, a novel method based on recurrent neural networks for missing value imputation in time series data. Our proposed method directly learns the missing values in a bidirectional recurrent dynamical system, without any specific assumption. The imputed values are treated as variables of RNN graph and can be effectively updated during the backpropagation. BRITS has three advantages: (a) it can handle multiple correlated missing values in time series; (b) it generalizes to time series with nonlinear dynamics underlying; (c) it provides a data-driven imputation procedure and applies to general settings with missing data. We evaluate our model on three real-world datasets, including an air quality dataset, a health-care data, and a localization data for human activity. Experiments show that our model outperforms the state-of-the-art methods in both imputation and classification/regression accuracies.

/pdf/brits-bidirectional-recurrent-imputation-for-time-series-4au4baja03.pdf

BRITS: Bidirectional Recurrent Imputation for Time Series

Estimating the travel time of any path (denoted by a sequence of connected road segments) in a city is of great importance to traffic monitoring, route planning, ridesharing, taxi/Uber dispatching, etc. However, it is a very challenging problem, affected by diverse complex factors, including spatial correlations, temporal dependencies, external conditions (e.g. weather, traffic lights). Prior work usually focuses on estimating the travel times of individual road segments or sub-paths and then summing up these times, which leads to an inaccurate estimation because such approaches do not consider road intersections/traffic lights, and local errors may accumulate. To address these issues, we propose an end-to-end Deep learning framework for Travel Time Estimation called DeepTTE that estimates the travel time of the whole path directly. More specifically, we present a geo-convolution operation by integrating the geographic information into the classical convolution, capable of capturing spatial correlations. By stacking recurrent unit on the geo-convoluton layer, our DeepTTE can capture the temporal dependencies simultaneously. A multi-task learning component is given on the top of DeepTTE, that estimates the travel time of both the entire path and each local path simultaneously during the training phase. The extensive experiments on two large-scale datasets shows our DeepTTE significantly outperforms the state-of-the-art methods.

/pdf/when-will-you-arrive-estimating-travel-time-based-on-deep-1fpvtvakjk.pdf

When Will You Arrive? Estimating Travel Time Based on Deep Neural Networks

The online car-hailing service has gained great popularity all over the world. As more passengers and more drivers use the service, it becomes increasingly more important for the the car-hailing service providers to effectively schedule the drivers to minimize the waiting time of passengers and maximize the driver utilization, thus to improve the overall user experience. In this paper, we study the problem of predicting the real-time car-hailing supply-demand, which is one of the most important component of an effective scheduling system. Our objective is to predict the gap between the car-hailing supply and demand in a certain area in the next few minutes. Based on the prediction, we can balance the supply-demands by scheduling the drivers in advance. We present an end-to-end framework called Deep Supply-Demand (DeepSD) using a novel deep neural network structure. Our approach can automatically discover complicated supply-demand patterns from the car-hailing service data while only requires a minimal amount hand-crafted features. Moreover, our framework is highly flexible and extendable. Based on our framework, it is very easy to utilize multiple data sources (e.g., car-hailing orders, weather and traffic data) to achieve a high accuracy. We conduct extensive experimental evaluations, which show that our framework provides more accurate prediction results than the existing methods.

Jian Li

Papers

Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec.

Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec

BRITS: Bidirectional Recurrent Imputation for Time Series

When Will You Arrive? Estimating Travel Time Based on Deep Neural Networks

DeepSD: Supply-Demand Prediction for Online Car-Hailing Services Using Deep Neural Networks