Federated learning (FL) for time series forecasting (TSF) enables clients with privacy-sensitive time series (TS) data to collaboratively learn accurate forecasting models, for example, in energy load prediction. Unfortunately, privacy risks in FL persist, as servers can potentially reconstruct clients' training data through gradient inversion attacks (GIA). Although GIA is demonstrated for image classification tasks, little is known about time series regression tasks. In this paper, we first conduct an extensive empirical study on inverting TS data across 4 TSF models and 4 datasets, identifying the unique challenges of reconstructing both observations and targets of TS data. We then propose TS-Inverse, a novel GIA that improves the inversion of TS data by (i) learning a gradient inversion model that outputs quantile predictions, (ii) a unique loss function that incorporates periodicity and trend regularization, and (iii) regularization according to the quantile predictions. Our evaluations demonstrate a remarkable performance of TS-Inverse, achieving at least a 2x-10x improvement in terms of the sMAPE metric over existing GIA methods on TS data. Code repository: https://github.com/Capsar/ts-inverse
Time series are ubiquitous in numerous science and engineering domains, e.g., signal processing, bioinformatics, and astronomy. Previous work has verified the efficacy of symbolic time series representation in a variety of engineering applications due to its storage efficiency and numerosity reduction. The most recent symbolic aggregate approximation technique, ABBA, has been shown to preserve essential shape information of time series and improve downstream applications, e.g., neural network inference regarding prediction and anomaly detection in time series. Motivated by the emergence of high-performance hardware which enables efficient computation for low bit-width representations, we present a new quantization-based ABBA symbolic approximation technique, QABBA, which exhibits improved storage efficiency while retaining the original speed and accuracy of symbolic reconstruction. We prove an upper bound for the error arising from quantization and discuss how the number of bits should be chosen to balance this with other errors. An application of QABBA with large language models (LLMs) for time series regression is also presented, and its utility is investigated. By representing the symbolic chain of patterns on time series, QABBA not only avoids the training of embedding from scratch, but also achieves a new state-of-the-art on Monash regression dataset. The symbolic approximation to the time series offers a more efficient way to fine-tune LLMs on the time series regression task which contains various application domains. We further present a set of extensive experiments performed across various well-established datasets to demonstrate the advantages of the QABBA method for symbolic approximation.
This paper introduces the FinSen dataset that revolutionizes financial market analysis by integrating economic and financial news articles from 197 countries with stock market data. The dataset's extensive coverage spans 15 years from 2007 to 2023 with temporal information, offering a rich, global perspective with 160,000 records on financial market news. Our study leverages causally validated sentiment scores and LSTM models to enhance market forecast accuracy and reliability. Utilizing the FinSen dataset, we introduce an innovative Focal Calibration Loss, reducing Expected Calibration Error (ECE) to 3.34 percent with the DAN 3 model. This not only improves prediction accuracy but also aligns probabilistic forecasts closely with real outcomes, crucial for the financial sector where predicted probability is paramount. Our approach demonstrates the effectiveness of combining sentiment analysis with precise calibration techniques for trustworthy financial forecasting where the cost of misinterpretation can be high. Finsen Data can be found at [this github URL](https://github.com/EagleAdelaide/FinSen_Dataset.git).
Fourier features based positional encoding (PE) is commonly used in machine learning tasks that involve learning high-frequency features from low-dimensional inputs, such as 3D view synthesis and time series regression with neural tangent kernels. Despite their effectiveness, existing PEs require manual, empirical adjustment of crucial hyperparameters, specifically the Fourier features, tailored to each unique task. Further, PEs face challenges in efficiently learning high-frequency functions, particularly in tasks with limited data. In this paper, we introduce sinusoidal PE (SPE), designed to efficiently learn adaptive frequency features closely aligned with the true underlying function. Our experiments demonstrate that SPE, without hyperparameter tuning, consistently achieves enhanced fidelity and faster training across various tasks, including 3D view synthesis, Text-to-Speech generation, and 1D regression. SPE is implemented as a direct replacement for existing PEs. Its plug-and-play nature lets numerous tasks easily adopt and benefit from SPE.
As the conversation around using geoengineering to combat climate change intensifies, it is imperative to engage the public and deeply understand their perspectives on geoengineering research, development, and potential deployment. Through a comprehensive data-driven investigation, this paper explores the types of news that captivate public interest in geoengineering. We delved into 30,773 English-language news articles from the BBC and the New York Times, combined with Google Trends data spanning 2018 to 2022, to explore how public interest in geoengineering fluctuates in response to news coverage of broader climate issues. Using BERT-based topic modeling, sentiment analysis, and time-series regression models, we found that positive sentiment in energy-related news serves as a good predictor of heightened public interest in geoengineering, a trend that persists over time. Our findings suggest that public engagement with geoengineering and climate action is not uniform, with some topics being more potent in shaping interest over time, such as climate news related to energy, disasters, and politics. Understanding these patterns is crucial for scientists, policymakers, and educators aiming to craft effective strategies for engaging with the public and fostering dialogue around emerging climate technologies.
Optical turbulence presents a significant challenge for communication, directed energy, and imaging systems, especially in the atmospheric boundary layer. Effective modeling of optical turbulence strength is critical for the development and deployment of these systems. The lack of standard evaluation tools, especially long-term data sets, modeling tasks, metrics, and baseline models, prevent effective comparisons between approaches and models. This reduces the ease of reproducing results and contributes to over-fitting on local micro-climates. Performance characterized using evaluation metrics provides some insight into the applicability of a model for predicting the strength of optical turbulence. However, these metrics are not sufficient for understanding the relative quality of a model. We introduce the \texttt{otbench} package, a Python package for rigorous development and evaluation of optical turbulence strength prediction models. The package provides a consistent interface for evaluating optical turbulence models on a variety of benchmark tasks and data sets. The \texttt{otbench} package includes a range of baseline models, including statistical, data-driven, and deep learning models, to provide a sense of relative model quality. \texttt{otbench} also provides support for adding new data sets, tasks, and evaluation metrics. The package is available at \url{https://github.com/cdjellen/otbench}.
Traffic forecasting is a complex multivariate time-series regression task of paramount importance for traffic management and planning. However, existing approaches often struggle to model complex multi-range dependencies using local spatiotemporal features and road network hierarchical knowledge. To address this, we propose MultiSPANS. First, considering that an individual recording point cannot reflect critical spatiotemporal local patterns, we design multi-filter convolution modules for generating informative ST-token embeddings to facilitate attention computation. Then, based on ST-token and spatial-temporal position encoding, we employ the Transformers to capture long-range temporal and spatial dependencies. Furthermore, we introduce structural entropy theory to optimize the spatial attention mechanism. Specifically, The structural entropy minimization algorithm is used to generate optimal road network hierarchies, i.e., encoding trees. Based on this, we propose a relative structural entropy-based position encoding and a multi-head attention masking scheme based on multi-layer encoding trees. Extensive experiments demonstrate the superiority of the presented framework over several state-of-the-art methods in real-world traffic datasets, and the longer historical windows are effectively utilized. The code is available at https://github.com/SELGroup/MultiSPANS.
Data-driven, neural network (NN) based anomaly detection and predictive maintenance are emerging research areas. NN-based analytics of time-series data offer valuable insights into past behaviors and estimates of critical parameters like remaining useful life (RUL) of equipment and state-of-charge (SOC) of batteries. However, input time series data can be exposed to intentional or unintentional noise when passing through sensors, necessitating robust validation and verification of these NNs. This paper presents a case study of the robustness verification approach for time series regression NNs (TSRegNN) using set-based formal methods. It focuses on utilizing variable-length input data to streamline input manipulation and enhance network architecture generalizability. The method is applied to two data sets in the Prognostics and Health Management (PHM) application areas: (1) SOC estimation of a Lithium-ion battery and (2) RUL estimation of a turbine engine. The NNs' robustness is checked using star-based reachability analysis, and several performance measures evaluate the effect of bounded perturbations in the input on network outputs, i.e., future outcomes. Overall, the paper offers a comprehensive case study for validating and verifying NN-based analytics of time-series data in real-world applications, emphasizing the importance of robustness testing for accurate and reliable predictions, especially considering the impact of noise on future outcomes.
The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In this study, we apply advanced network-based information filtering techniques to design a novel deep neural network unit characterized by a sparse higher-order graphical architecture built over the homological structure of underlying data. We demonstrate its effectiveness in two application domains which are traditionally challenging for deep learning: tabular data and time series regression problems. Results demonstrate the advantages of this novel design which can tie or overcome the results of state-of-the-art machine learning and deep learning models using only a fraction of parameters.
The aim of Predictive Maintenance, within the field of Prognostics and Health Management (PHM), is to identify and anticipate potential issues in the equipment before these become critical. The main challenge to be addressed is to assess the amount of time a piece of equipment will function effectively before it fails, which is known as Remaining Useful Life (RUL). Deep Learning (DL) models, such as Deep Convolutional Neural Networks (DCNN) and Long Short-Term Memory (LSTM) networks, have been widely adopted to address the task, with great success. However, it is well known that this kind of black box models are opaque decision systems, and it may be hard to explain its outputs to stakeholders (experts in the industrial equipment). Due to the large number of parameters that determine the behavior of these complex models, understanding the reasoning behind the predictions is challenging. This work presents a critical and comparative revision on a number of XAI methods applied on time series regression model for PM. The aim is to explore XAI methods within time series regression, which have been less studied than those for time series classification. The model used during the experimentation is a DCNN trained to predict the RUL of an aircraft engine. The methods are reviewed and compared using a set of metrics that quantifies a number of desirable properties that any XAI method should fulfill. The results show that GRAD-CAM is the most robust method, and that the best layer is not the bottom one, as is commonly seen within the context of Image Processing.
Rapid global urbanization is a double-edged sword, heralding promises of economical prosperity and public health while also posing unique environmental and humanitarian challenges. Smart and connected communities (S&CCs) apply data-centric solutions to these problems by integrating artificial intelligence (AI) and the Internet of Things (IoT). This coupling of intelligent technologies also poses interesting system design challenges regarding heterogeneous data fusion and task diversity. Transformers are of particular interest to address these problems, given their success across diverse fields of natural language processing (NLP), computer vision, time-series regression, and multi-modal data fusion. This begs the question whether Transformers can be further diversified to leverage fusions of IoT data sources for heterogeneous multi-task learning in S&CC trade spaces. In this paper, a Transformer-based AI system for emerging smart cities is proposed. Designed using a pure encoder backbone, and further customized through interchangeable input embedding and output task heads, the system supports virtually any input data and output task types present S&CCs. This generalizability is demonstrated through learning diverse task sets representative of S&CC environments, including multivariate time-series regression, visual plant disease classification, and image-time-series fusion tasks using a combination of Beijing PM2.5 and Plant Village datasets. Simulation results show that the proposed Transformer-based system can handle various input data types via custom sequence embedding techniques, and are naturally suited to learning a diverse set of tasks. The results also show that multi-task learners increase both memory and computational efficiency while maintaining comparable performance to both single-task variants, and non-Transformer baselines.
Cross-sectional prediction is common in many domains such as healthcare, including forecasting tasks using electronic health records, where different patients form a cross-section. We focus on the task of constructing valid prediction intervals (PIs) in time series regression with a cross-section. A prediction interval is considered valid if it covers the true response with (a pre-specified) high probability. We first distinguish between two notions of validity in such a setting: cross-sectional and longitudinal. Cross-sectional validity is concerned with validity across the cross-section of the time series data, while longitudinal validity accounts for the temporal dimension. Coverage guarantees along both these dimensions are ideally desirable; however, we show that distribution-free longitudinal validity is theoretically impossible. Despite this limitation, we propose Conformal Prediction with Temporal Dependence (CPTD), a procedure that is able to maintain strict cross-sectional validity while improving longitudinal coverage. CPTD is post-hoc and light-weight, and can easily be used in conjunction with any prediction model as long as a calibration set is available. We focus on neural networks due to their ability to model complicated data such as diagnosis codes for time series regression, and perform extensive experimental validation to verify the efficacy of our approach. We find that CPTD outperforms baselines on a variety of datasets by improving longitudinal coverage and often providing more efficient (narrower) PIs.
Accurate real-time traffic forecast is critical for intelligent transportation systems (ITS) and it serves as the cornerstone of various smart mobility applications. Though this research area is dominated by deep learning, recent studies indicate that the accuracy improvement by developing new model structures is becoming marginal. Instead, we envision that the improvement can be achieved by transferring the "forecasting-related knowledge" across cities with different data distributions and network topologies. To this end, this paper aims to propose a novel transferable traffic forecasting framework: Domain Adversarial Spatial-Temporal Network (DASTNet). DASTNet is pre-trained on multiple source networks and fine-tuned with the target network's traffic data. Specifically, we leverage the graph representation learning and adversarial domain adaptation techniques to learn the domain-invariant node embeddings, which are further incorporated to model the temporal traffic data. To the best of our knowledge, we are the first to employ adversarial multi-domain adaptation for network-wide traffic forecasting problems. DASTNet consistently outperforms all state-of-the-art baseline methods on three benchmark datasets. The trained DASTNet is applied to Hong Kong's new traffic detectors, and accurate traffic predictions can be delivered immediately (within one day) when the detector is available. Overall, this study suggests an alternative to enhance the traffic forecasting methods and provides practical implications for cities lacking historical traffic data.
Machine learning can be enhanced through the integration of external knowledge. This method, called knowledge informed machine learning, is also applicable within the field of Prognostics and Health Management (PHM). In this paper, the various methods of knowledge informed machine learning, from a PHM context, are reviewed with the goal of helping the reader understand the domain. In addition, a knowledge informed machine learning technique is demonstrated, using the common IMS and PRONOSTIA bearing data sets, for remaining useful life (RUL) prediction. Specifically, knowledge is garnered from the field of reliability engineering which is represented through the Weibull distribution. The knowledge is then integrated into a neural network through a novel Weibull-based loss function. A thorough statistical analysis of the Weibull-based loss function is conducted, demonstrating the effectiveness of the method on the PRONOSTIA data set. However, the Weibull-based loss function is less effective on the IMS data set. The results, shortcomings, and benefits of the approach are discussed in length. Finally, all the code is publicly available for the benefit of other researchers.
Machine learning, with its advances in deep learning has shown great potential in analyzing time series. In many scenarios, however, additional information that can potentially improve the predictions is available. This is crucial for data that arise from e.g., sensor networks that contain information about sensor locations. Then, such spatial information can be exploited by modeling it via graph structures, along with the sequential (time series) information. Recent advances in adapting deep learning to graphs have shown potential in various tasks. However, these methods have not been adapted for time series tasks to a great extent. Most attempts have essentially consolidated around time series forecasting with small sequence lengths. Generally, these architectures are not well suited for regression or classification tasks where the value to be predicted is not strictly depending on the most recent values, but rather on the whole length of the time series. We propose TISER-GCN, a novel graph neural network architecture for processing, in particular, these long time series in a multivariate regression task. Our proposed model is tested on two seismic datasets containing earthquake waveforms, where the goal is to predict maximum intensity measurements of ground shaking at each seismic station. Our findings demonstrate promising results of our approach -- with an average MSE reduction of 16.3% - compared to the best performing baselines. In addition, our approach matches the baseline scores by needing only half the input size. The results are discussed in depth with an additional ablation study.
This manuscript proposes to extend the information set of time-series regression trees with latent stationary factors extracted via state-space methods. In doing so, this approach generalises time-series regression trees on two dimensions. First, it allows to handle predictors that exhibit measurement error, non-stationary trends, seasonality and/or irregularities such as missing observations. Second, it gives a transparent way for using domain-specific theory to inform time-series regression trees. Empirically, ensembles of these factor-augmented trees provide a reliable approach for macro-finance problems. This article highlights it focussing on the lead-lag effect between equity volatility and the business cycle in the United States.
Analyzing better time series with limited human effort is of interest to academia and industry. Driven by business scenarios, we organized the first Automated Time Series Regression challenge (AutoSeries) for the WSDM Cup 2020. We present its design, analysis, and post-hoc experiments. The code submission requirement precluded participants from any manual intervention, testing automated machine learning capabilities of solutions, across many datasets, under hardware and time limitations. We prepared 10 datasets from diverse application domains (sales, power consumption, air quality, traffic, and parking), featuring missing data, mixed continuous and categorical variables, and various sampling rates. Each dataset was split into a training and a test sequence (which was streamed, allowing models to continuously adapt). The setting of time series regression, differs from classical forecasting in that covariates at the present time are known. Great strides were made by participants to tackle this AutoSeries problem, as demonstrated by the jump in performance from the sample submission, and post-hoc comparisons with AutoGluon. Simple yet effective methods were used, based on feature engineering, LightGBM, and random search hyper-parameter tuning, addressing all aspects of the challenge. Our post-hoc analyses revealed that providing additional time did not yield significant improvements. The winners' code was open-sourced https://www.4paradigm.com/competition/autoseries2020.
Graph Gaussian Processes (GGPs) provide a data-efficient solution on graph structured domains. Existing approaches have focused on static structures, whereas many real graph data represent a dynamic structure, limiting the applications of GGPs. To overcome this we propose evolving-Graph Gaussian Processes (e-GGPs). The proposed method is capable of learning the transition function of graph vertices over time with a neighbourhood kernel to model the connectivity and interaction changes between vertices. We assess the performance of our method on time-series regression problems where graphs evolve over time. We demonstrate the benefits of e-GGPs over static graph Gaussian Process approaches.
An increasing body of research focuses on using neural networks to model time series. A common assumption in training neural networks via maximum likelihood estimation on time series is that the errors across time steps are uncorrelated. However, errors are actually autocorrelated in many cases due to the temporality of the data, which makes such maximum likelihood estimations inaccurate. In this paper, in order to adjust for autocorrelated errors, we propose to learn the autocorrelation coefficient jointly with the model parameters. In our experiments, we verify the effectiveness of our approach on time series forecasting. Results across a wide range of real-world datasets with various state-of-the-art models show that our method enhances performance in almost all cases. Based on these results, we suggest empirical critical values to determine the severity of autocorrelated errors. We also analyze several aspects of our method to demonstrate its advantages. Finally, other time series tasks are also considered to validate that our method is not restricted to only forecasting.
In this work we propose for the first time a transformer-based framework for unsupervised representation learning of multivariate time series. Pre-trained models can be potentially used for downstream tasks such as regression and classification, forecasting and missing value imputation. By evaluating our models on several benchmark datasets for multivariate time series regression and classification, we show that not only does our modeling approach represent the most successful method employing unsupervised learning of multivariate time series presented to date, but also that it exceeds the current state-of-the-art performance of supervised methods; it does so even when the number of training samples is very limited, while offering computational efficiency. Finally, we demonstrate that unsupervised pre-training of our transformer models offers a substantial performance benefit over fully supervised learning, even without leveraging additional unlabeled data, i.e., by reusing the same data samples through the unsupervised objective.