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We study the problem of efficiently scaling ensemble-based deep neural networks for time series (TS) forecasting on a large set of time series. Current state-of-the-art deep ensemble models have high memory and computational requirements, hampering their use to forecast millions of TS in practical scenarios. We propose N-BEATS(P), a global multivariate variant of the N-BEATS model designed to allow simultaneous training of multiple univariate TS forecasting models. Our model addresses the practical limitations of related models, reducing the training time by half and memory requirement by a factor of 5, while keeping the same level of accuracy. We have performed multiple experiments detailing the various ways to train our model and have obtained results that demonstrate its capacity to support zero-shot TS forecasting, i.e., to train a neural network on a source TS dataset and deploy it on a different target TS dataset without retraining, which provides an efficient and reliable solution to forecast at scale even in difficult forecasting conditions.

Analyzing the effect of business cycle on rating transitions has been a subject of great interest these last fifteen years, particularly due to the increasing pressure coming from regulators for stress testing. In this paper, we consider that the dynamics of rating migrations is governed by an unobserved latent factor. Under a point process filtering framework, we explain how the current state of the hidden factor can be efficiently inferred from observations of rating histories. We then adapt the classical Baum-Welsh algorithm to our setting and show how to estimate the latent factor parameters. Once calibrated, we may reveal and detect economic changes affecting the dynamics of rating migration, in real-time. To this end we adapt a filtering formula which can then be used for predicting future transition probabilities according to economic regimes without using any external covariates. We propose two filtering frameworks: a discrete and a continuous version. We demonstrate and compare the efficiency of both approaches on fictive data and on a corporate credit rating database. The methods could also be applied to retail credit loans.

With large quantities of data typically available nowadays, forecasting models that are trained across sets of time series, known as Global Forecasting Models (GFM), are regularly outperforming traditional univariate forecasting models that work on isolated series. As GFMs usually share the same set of parameters across all time series, they often have the problem of not being localised enough to a particular series, especially in situations where datasets are heterogeneous. We study how ensembling techniques can be used with generic GFMs and univariate models to solve this issue. Our work systematises and compares relevant current approaches, namely clustering series and training separate submodels per cluster, the so-called ensemble of specialists approach, and building heterogeneous ensembles of global and local models. We fill some gaps in the existing GFM localisation approaches, in particular by incorporating varied clustering techniques such as feature-based clustering, distance-based clustering and random clustering, and generalise them to use different underlying GFM model types. We then propose a new methodology of clustered ensembles where we train multiple GFMs on different clusters of series, obtained by changing the number of clusters and cluster seeds. Using Feed-forward Neural Networks, Recurrent Neural Networks, and Pooled Regression models as the underlying GFMs, in our evaluation on eight publicly available datasets, the proposed models are able to achieve significantly higher accuracy than baseline GFM models and univariate forecasting methods.

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.

Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, such as quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a $ProbSparse$ Self-attention mechanism, which achieves $O(L \log L)$ in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.

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.

Learning to classify unseen class samples at test time is popularly referred to as zero-shot learning (ZSL). If test samples can be from training (seen) as well as unseen classes, it is a more challenging problem due to the existence of strong bias towards seen classes. This problem is generally known as \emph{generalized} zero-shot learning (GZSL). Thanks to the recent advances in generative models such as VAEs and GANs, sample synthesis based approaches have gained considerable attention for solving this problem. These approaches are able to handle the problem of class bias by synthesizing unseen class samples. However, these ZSL/GZSL models suffer due to the following key limitations: $(i)$ Their training stage learns a class-conditioned generator using only \emph{seen} class data and the training stage does not \emph{explicitly} learn to generate the unseen class samples; $(ii)$ They do not learn a generic optimal parameter which can easily generalize for both seen and unseen class generation; and $(iii)$ If we only have access to a very few samples per seen class, these models tend to perform poorly. In this paper, we propose a meta-learning based generative model that naturally handles these limitations. The proposed model is based on integrating model-agnostic meta learning with a Wasserstein GAN (WGAN) to handle $(i)$ and $(iii)$, and uses a novel task distribution to handle $(ii)$. Our proposed model yields significant improvements on standard ZSL as well as more challenging GZSL setting. In ZSL setting, our model yields 4.5\%, 6.0\%, 9.8\%, and 27.9\% relative improvements over the current state-of-the-art on CUB, AWA1, AWA2, and aPY datasets, respectively.

Time Series Classification (TSC) is an important and challenging problem in data mining. With the increase of time series data availability, hundreds of TSC algorithms have been proposed. Among these methods, only a few have considered Deep Neural Networks (DNNs) to perform this task. This is surprising as deep learning has seen very successful applications in the last years. DNNs have indeed revolutionized the field of computer vision especially with the advent of novel deeper architectures such as Residual and Convolutional Neural Networks. Apart from images, sequential data such as text and audio can also be processed with DNNs to reach state-of-the-art performance for document classification and speech recognition. In this article, we study the current state-of-the-art performance of deep learning algorithms for TSC by presenting an empirical study of the most recent DNN architectures for TSC. We give an overview of the most successful deep learning applications in various time series domains under a unified taxonomy of DNNs for TSC. We also provide an open source deep learning framework to the TSC community where we implemented each of the compared approaches and evaluated them on a univariate TSC benchmark (the UCR/UEA archive) and 12 multivariate time series datasets. By training 8,730 deep learning models on 97 time series datasets, we propose the most exhaustive study of DNNs for TSC to date.

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.