Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks

The Nonlinear autoregressive exogenous (NARX) model, which predicts the current value of a time series based upon its previous values as well as the current and past values of multiple driving (exogenous) series, has been studied for decades. Despite the fact that various NARX models have been developed, few of them can capture the long-term temporal dependencies appropriately and select the relevant driving series to make predictions. In this paper, we propose a dual-stage attention-based recurrent neural network (DA-RNN) to address these two issues. In the first stage, we introduce an input attention mechanism to adaptively extract relevant driving series (a.k.a., input features) at each time step by referring to the previous encoder hidden state. In the second stage, we use a temporal attention mechanism to select relevant encoder hidden states across all time steps. With this dual-stage attention scheme, our model can not only make predictions effectively, but can also be easily interpreted. Thorough empirical studies based upon the SML 2010 dataset and the NASDAQ 100 Stock dataset demonstrate that the DA-RNN can outperform state-of-the-art methods for time series prediction.

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A dual-stage attention-based recurrent neural network for time series prediction

Survey Kernel methods in system identification, machine learning and function estimation: A survey

The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process regression (GPR), a well-known nonparametric, and interpretable Bayesian model, which suffers from cubic complexity to data size. To improve the scalability while retaining desirable prediction quality, a variety of scalable GPs have been presented. However, they have not yet been comprehensively reviewed and analyzed to be well understood by both academia and industry. The review of scalable GPs in the GP community is timely and important due to the explosion of data size. To this end, this article is devoted to reviewing state-of-the-art scalable GPs involving two main categories: global approximations that distillate the entire data and local approximations that divide the data for subspace learning. Particularly, for global approximations, we mainly focus on sparse approximations comprising prior approximations that modify the prior but perform exact inference, posterior approximations that retain exact prior but perform approximate inference, and structured sparse approximations that exploit specific structures in kernel matrix; for local approximations, we highlight the mixture/product of experts that conducts model averaging from multiple local experts to boost predictions. To present a complete review, recent advances for improving the scalability and capability of scalable GPs are reviewed. Finally, the extensions and open issues of scalable GPs in various scenarios are reviewed and discussed to inspire novel ideas for future research avenues.

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When Gaussian Process Meets Big Data: A Review of Scalable GPs

A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo. We also present stochastic variational inference and online learning approaches for fast learning with long time series.

Variational Gaussian Process State-Space Models

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State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

/pdf/bayesian-inference-and-learning-in-gaussian-process-state-3ezj7s2dfr.pdf

We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully automated procedure that goes from raw data to an identified model. Both pre-processing parameters and GP hyper-parameters are tuned by maximizing the marginal likelihood of the probabilistic model. We obtain a Bayesian model of the system's dynamics which is able to report its uncertainty in regions where the data is scarce. The automated approach, the modeling of uncertainty and its relatively low computational cost make of GP-FNARX a good candidate for applications in robotics and adaptive control.

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Roger Frigola

Papers

Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC

Variational Gaussian Process State-Space Models

Variational Gaussian Process State-Space Models

Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC

Integrated pre-processing for Bayesian nonlinear system identification with Gaussian processes