Analyzing time series data is crucial to a wide spectrum of applications, including economics, online marketplaces, and human healthcare. In particular, time series classification plays an indispensable role in segmenting different phases in stock markets, predicting customer behavior, and classifying worker actions and engagement levels. These aspects contribute significantly to the advancement of automated decision-making and system optimization in real-world applications. However, there is a large consensus that time series data often suffers from domain shifts between training and test sets, which dramatically degrades the classification performance. Despite the success of (reversible) instance normalization in handling the domain shifts for time series regression tasks, its performance in classification is unsatisfactory. In this paper, we propose \textit{FIC-TSC}, a training framework for time series classification that leverages Fisher information as the constraint. We theoretically and empirically show this is an efficient and effective solution to guide the model converge toward flatter minima, which enhances its generalizability to distribution shifts. We rigorously evaluate our method on 30 UEA multivariate and 85 UCR univariate datasets. Our empirical results demonstrate the superiority of the proposed method over 14 recent state-of-the-art methods.
Determining the ideal architecture for deep learning models, such as the number of layers and neurons, is a difficult and resource-intensive process that frequently relies on human tuning or computationally costly optimization approaches. While Particle Swarm Optimization (PSO) and Large Language Models (LLMs) have been individually applied in optimization and deep learning, their combined use for enhancing convergence in numerical optimization tasks remains underexplored. Our work addresses this gap by integrating LLMs into PSO to reduce model evaluations and improve convergence for deep learning hyperparameter tuning. The proposed LLM-enhanced PSO method addresses the difficulties of efficiency and convergence by using LLMs (particularly ChatGPT-3.5 and Llama3) to improve PSO performance, allowing for faster achievement of target objectives. Our method speeds up search space exploration by substituting underperforming particle placements with best suggestions offered by LLMs. Comprehensive experiments across three scenarios -- (1) optimizing the Rastrigin function, (2) using Long Short-Term Memory (LSTM) networks for time series regression, and (3) using Convolutional Neural Networks (CNNs) for material classification -- show that the method significantly improves convergence rates and lowers computational costs. Depending on the application, computational complexity is lowered by 20% to 60% compared to traditional PSO methods. Llama3 achieved a 20% to 40% reduction in model calls for regression tasks, whereas ChatGPT-3.5 reduced model calls by 60% for both regression and classification tasks, all while preserving accuracy and error rates. This groundbreaking methodology offers a very efficient and effective solution for optimizing deep learning models, leading to substantial computational performance improvements across a wide range of applications.
Supervised time series prediction relies on directly measured target variables, but real-world use cases such as predicting remaining useful life (RUL) involve indirect supervision, where the target variable is labeled as a function of another dependent variable. Trending temporal regression techniques rely on sequential time series inputs to capture temporal patterns, requiring interpolation when dealing with sparsely and irregularly sampled covariates along the timeline. However, interpolation can introduce significant biases, particularly with highly scarce data. In this paper, we address the RUL prediction problem with data scarcity as time series regression under indirect supervision. We introduce a unified framework called parameterized static regression, which takes single data points as inputs for regression of target values, inherently handling data scarcity without requiring interpolation. The time dependency under indirect supervision is captured via a parametrical rectification (PR) process, approximating a parametric function during inference with historical posteriori estimates, following the same underlying distribution used for labeling during training. Additionally, we propose a novel batch training technique for tasks in indirect supervision to prevent overfitting and enhance efficiency. We evaluate our model on public benchmarks for RUL prediction with simulated data scarcity. Our method demonstrates competitive performance in prediction accuracy when dealing with highly scarce time series data.
The release of advanced Large Language Models (LLMs) such as ChatGPT and Copilot is changing the way text is created and may influence the content that we find on the web. This study investigated whether the release of these two popular LLMs coincided with a change in writing style in headlines and links on worldwide news websites. 175 NLP features were obtained for each text in a dataset of 451 million headlines/links. An interrupted time series analysis was applied for each of the 175 NLP features to evaluate whether there were any statistically significant sustained changes after the release dates of ChatGPT and/or Copilot. There were a total of 44 features that did not appear to have any significant sustained change after the release of ChatGPT/Copilot. A total of 91 other features did show significant change with ChatGPT and/or Copilot although significance with earlier control LLM release dates (GPT-1/2/3, Gopher) removed them from consideration. This initial analysis suggests these language models may have had a limited impact on the style of individual news headlines/links, with respect to only some NLP measures.
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
Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and Regularized Factor-based (SSRF) framework that systematically addresses high-dimensional predictor sets through a structured four-step procedure integrating both static and dynamic forecasting mechanisms. The static approach selects predictors via marginal correlation screening and scales them using univariate predictive slopes, while the dynamic method screens and scales predictors based on time series regression incorporating lagged predictors. PCA then extracts latent factors from the scaled predictors, followed by LASSO regularization to refine predictive accuracy. In the simulation study, we validate the effectiveness of SSRF and identify its parameter adjustment strategies in high-dimensional data settings. An empirical analysis of macroeconomic indices in China demonstrates that the SSRF method generally outperforms several commonly used forecasting techniques in out-of-sample predictions.
We propose a novel online Gaussian process (GP) model that is capable of capturing long-term memory in sequential data in an online regression setting. Our model, Online HiPPO Sparse Variational Gaussian Process Regression (OHSGPR), leverages the HiPPO (High-order Polynomial Projection Operators) framework, which is popularized in the RNN domain due to its long-range memory modeling capabilities. We interpret the HiPPO time-varying orthogonal projections as inducing variables with time-dependent orthogonal polynomial basis functions, which allows the SGPR inducing points to memorize the process history. We show that the HiPPO framework fits naturally into the interdomain GP framework and demonstrate that the kernel matrices can also be updated online in a recurrence form based on the ODE evolution of HiPPO. We evaluate our method on time series regression tasks, showing that it outperforms the existing online GP method in terms of predictive performance and computational efficiency
Smart grid, through networked smart meters employing the non-intrusive load monitoring (NILM) technique, can considerably discern the usage patterns of residential appliances. However, this technique also incurs privacy leakage. To address this issue, we propose an innovative scheme based on adversarial attack in this paper. The scheme effectively prevents NILM models from violating appliance-level privacy, while also ensuring accurate billing calculation for users. To achieve this objective, we overcome two primary challenges. First, as NILM models fall under the category of time-series regression models, direct application of traditional adversarial attacks designed for classification tasks is not feasible. To tackle this issue, we formulate a novel adversarial attack problem tailored specifically for NILM and providing a theoretical foundation for utilizing the Jacobian of the NILM model to generate imperceptible perturbations. Leveraging the Jacobian, our scheme can produce perturbations, which effectively misleads the signal prediction of NILM models to safeguard users' appliance-level privacy. The second challenge pertains to fundamental utility requirements, where existing adversarial attack schemes struggle to achieve accurate billing calculation for users. To handle this problem, we introduce an additional constraint, mandating that the sum of added perturbations within a billing period must be precisely zero. Experimental validation on real-world power datasets REDD and UK-DALE demonstrates the efficacy of our proposed solutions, which can significantly amplify the discrepancy between the output of the targeted NILM model and the actual power signal of appliances, and enable accurate billing at the same time. Additionally, our solutions exhibit transferability, making the generated perturbation signal from one target model applicable to other diverse NILM models.
The success of large language models (LLMs) for time series has been demonstrated in previous work. Utilizing a symbolic time series representation, one can efficiently bridge the gap between LLMs and time series. However, the remaining challenge is to exploit the semantic information hidden in time series by using symbols or existing tokens of LLMs, while aligning the embedding space of LLMs according to the hidden information of time series. The symbolic time series approximation (STSA) method called adaptive Brownian bridge-based symbolic aggregation (ABBA) shows outstanding efficacy in preserving salient time series features by modeling time series patterns in terms of amplitude and period while using existing tokens of LLMs. In this paper, we introduce a method, called LLM-ABBA, that integrates ABBA into large language models for various downstream time series tasks. By symbolizing time series, LLM-ABBA compares favorably to the recent state-of-the-art (SOTA) in UCR and three medical time series classification tasks. Meanwhile, a fixed-polygonal chain trick in ABBA is introduced to \kc{avoid obvious drifting} during prediction tasks by significantly mitigating the effects of cumulative error arising from misused symbols during the transition from symbols to numerical values. In time series regression tasks, LLM-ABBA achieves the new SOTA on Time Series Extrinsic Regression (TSER) benchmarks. LLM-ABBA also shows competitive prediction capability compared to recent SOTA time series prediction results. We believe this framework can also seamlessly extend to other time series tasks.
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.
As one of the most popular and effective methods in model compression, knowledge distillation (KD) attempts to transfer knowledge from single or multiple large-scale networks (i.e., Teachers) to a compact network (i.e., Student). For the multiteacher scenario, existing methods either assign equal or fixed weights for different teacher models during distillation, which can be inefficient as teachers might perform variously or even oppositely on different training samples. To address this issue, we propose a novel reinforced knowledge distillation method with negatively correlated teachers which are generated via negative correlation learning. The negatively correlated teachers would encourage teachers to learn different aspects of data and thus the ensemble of them can be more comprehensive and suitable for multiteacher KD. Subsequently, a reinforced KD algorithm is proposed to dynamically employ proper teachers for different training instances via dueling double deep Q-network (DDQN). Our proposed method complements the existing KD procedure on teacher generation and selection. Extensive experimental results on two real-world time series regression tasks clearly demonstrate that the proposed approach could achieve superior performance over state-of-the-art (SOTA) methods. The PyTorch implementation of our proposed approach is available at https://github.com/xuqing88/RL-KD-for-time-series-regression.
We analyze the methodological approach and validity of interpretation of using national-level time-series regression analyses relating epidemic outcomes to policies that estimate many models involving permutations of analytic choices (i.e., a "multiverse" approach). Specifically, we evaluate the possible biases and pitfalls of interpretation of a multiverse approach to the context of government responses to epidemics using the example of COVID-19 and a recently published peer-reviewed paper by Bendavid and Patel (2024) along with the subsequent commentary that the two authors published discussing and interpreting the implications of their work. While we identify multiple potential errors and sources of biases in how the specific analyses were undertaken that are also relevant for other studies employing similar approaches, our most important finding involves constructing a counterexample showing that causal model specification-agnostic multiverse analyses can be incorrectly used to suggest that no consistent effect can be discovered in data especially in cases where most specifications estimated with the data are far from causally valid. Finally, we suggest an alternative approach involving hypothesis-drive specifications that explicitly account for infectiousness across jurisdictions in the analysis as well as the interconnected ways that policies and behavioral responses may evolve within and across these jurisdictions.
We use cutting-edge mixed integer optimization (MIO) methods to develop a framework for detection and estimation of structural breaks in time series regression models. The framework is constructed based on the least squares problem subject to a penalty on the number of breakpoints. We restate the $l_0$-penalized regression problem as a quadratic programming problem with integer- and real-valued arguments and show that MIO is capable of finding provably optimal solutions using a well-known optimization solver. Compared to the popular $l_1$-penalized regression (LASSO) and other classical methods, the MIO framework permits simultaneous estimation of the number and location of structural breaks as well as regression coefficients, while accommodating the option of specifying a given or minimal number of breaks. We derive the asymptotic properties of the estimator and demonstrate its effectiveness through extensive numerical experiments, confirming a more accurate estimation of multiple breaks as compared to popular non-MIO alternatives. Two empirical examples demonstrate usefulness of the framework in applications from business and economic statistics.
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}.
This paper explores the application of Sample Entropy (SampEn) as a sophisticated tool for quantifying and predicting volatility in international oil price returns. SampEn, known for its ability to capture underlying patterns and predict periods of heightened volatility, is compared with traditional measures like standard deviation. The study utilizes a comprehensive dataset spanning 27 years (1986-2023) and employs both time series regression and machine learning methods. Results indicate SampEn's efficacy in predicting traditional volatility measures, with machine learning algorithms outperforming standard regression techniques during financial crises. The findings underscore SampEn's potential as a valuable tool for risk assessment and decision-making in the realm of oil price investments.
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.
These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional dependent data which is relevant to covariance matrix structures as well as to dependent time series sequences. Second, we present main aspects of the asymptotic theory related to time series regression models with many covariates. Third, we discuss various applications of statistical learning methodologies for time series analysis purposes.