Accurate forecasting of the U.K. gross value added (GVA) is fundamental for measuring the growth of the U.K. economy. A common nonstationarity in GVA data, such as the ABML series, is its increase in variance over time due to inflation. Transformed or inflation-adjusted series can still be challenging for classical stationarity-assuming forecasters. We adopt a different approach that works directly with the GVA series by advancing recent forecasting methods for locally stationary time series. Our approach results in more accurate and reliable forecasts, and continues to work well even when the ABML series becomes highly variable during the COVID pandemic.
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Typical deep visual recognition models are capable of performing the one task they were trained on. In this paper, we tackle the extremely difficult problem of combining completely distinct models with different initializations, each solving a separate task, into one multi-task model without any additional training. Prior work in model merging permutes one model to the space of the other then adds them together. While this works for models trained on the same task, we find that this fails to account for the differences in models trained on disjoint tasks. Thus, we introduce "ZipIt!", a general method for merging two arbitrary models of the same architecture that incorporates two simple strategies. First, in order to account for features that aren't shared between models, we expand the model merging problem to additionally allow for merging features within each model by defining a general "zip" operation. Second, we add support for partially zipping the models up until a specified layer, naturally creating a multi-head model. We find that these two changes combined account for a staggering 20-60% improvement over prior work, making the merging of models trained on disjoint tasks feasible.
The analysis of large-scale time-series network data, such as social media and email communications, remains a significant challenge for graph analysis methodology. In particular, the scalability of graph analysis is a critical issue hindering further progress in large-scale downstream inference. In this paper, we introduce a novel approach called "temporal encoder embedding" that can efficiently embed large amounts of graph data with linear complexity. We apply this method to an anonymized time-series communication network from a large organization spanning 2019-2020, consisting of over 100 thousand vertices and 80 million edges. Our method embeds the data within 10 seconds on a standard computer and enables the detection of communication pattern shifts for individual vertices, vertex communities, and the overall graph structure. Through supporting theory and synthesis studies, we demonstrate the theoretical soundness of our approach under random graph models and its numerical effectiveness through simulation studies.
The Transformer is a highly successful deep learning model that has revolutionised the world of artificial neural networks, first in natural language processing and later in computer vision. This model is based on the attention mechanism and is able to capture complex semantic relationships between a variety of patterns present in the input data. Precisely because of these characteristics, the Transformer has recently been exploited for time series forecasting problems, assuming a natural adaptability to the domain of continuous numerical series. Despite the acclaimed results in the literature, some works have raised doubts about the robustness and effectiveness of this approach. In this paper, we further investigate the effectiveness of Transformer-based models applied to the domain of time series forecasting, demonstrate their limitations, and propose a set of alternative models that are better performing and significantly less complex. In particular, we empirically show how simplifying Transformer-based forecasting models almost always leads to an improvement, reaching state of the art performance. We also propose shallow models without the attention mechanism, which compete with the overall state of the art in long time series forecasting, and demonstrate their ability to accurately predict time series over extremely long windows. From a methodological perspective, we show how it is always necessary to use a simple baseline to verify the effectiveness of proposed models, and finally, we conclude the paper with a reflection on recent research paths and the opportunity to follow trends and hypes even where it may not be necessary.
Wind energy is a widely distributed, recyclable and environmentally friendly energy source that plays an important role in mitigating global warming and energy shortages. Wind energy's uncertainty and fluctuating nature makes grid integration of large-scale wind energy systems challenging. Medium-term wind power forecasts can provide an essential basis for energy dispatch, so accurate wind power forecasts are essential. Much research has yielded excellent results in recent years. However, many of them require additional experimentation and analysis when applied to other data. In this paper, we propose a novel short-term forecasting framework by tree-structured parzen estimator (TPE) and decomposition algorithms. This framework defines the TPE-VMD-TFT method for 24-h and 48-h ahead wind power forecasting based on variational mode decomposition (VMD) and time fusion transformer (TFT). In the Engie wind dataset from the electricity company in France, the results show that the proposed method significantly improves the prediction accuracy. In addition, the proposed framework can be used to other decomposition algorithms and require little manual work in model training.
Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques to smooth the signal, sparse regression to identify the relevant parameters, and bootstrap confidence intervals to quantify the uncertainty of the estimates. We evaluate our method on well-known ordinary differential equations with an ensemble of random initial conditions, time series of increasing length, and varying signal-to-noise ratios. Our algorithm consistently identifies three-dimensional systems, given moderately-sized time series and high levels of signal quality relative to background noise. By accurately discovering dynamical systems automatically, our methodology has the potential to impact the understanding of complex systems, especially in fields where data are abundant, but developing mathematical models demands considerable effort.
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.
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.
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.
We examine the problem of question answering over knowledge graphs, focusing on simple questions that can be answered by the lookup of a single fact. Adopting a straightforward decomposition of the problem into entity detection, entity linking, relation prediction, and evidence combination, we explore simple yet strong baselines. On the popular SimpleQuestions dataset, we find that basic LSTMs and GRUs plus a few heuristics yield accuracies that approach the state of the art, and techniques that do not use neural networks also perform reasonably well. These results show that gains from sophisticated deep learning techniques proposed in the literature are quite modest and that some previous models exhibit unnecessary complexity.
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