Filling out the missing gaps: Time Series Imputation with Semi-Supervised Learning

Missing data in time series is a challenging issue affecting time series analysis. Missing data occurs due to problems like data drops or sensor malfunctioning. Imputation methods are used to fill in these values, with quality of imputation having a significant impact on downstream tasks like classification. In this work, we propose a semi-supervised imputation method, ST-Impute, that uses both unlabeled data along with downstream task's labeled data. ST-Impute is based on sparse self-attention and trains on tasks that mimic the imputation process. Our results indicate that the proposed method outperforms the existing supervised and unsupervised time series imputation methods measured on the imputation quality as well as on the downstream tasks ingesting imputed time series.

Your time series is worth a binary image: machine vision assisted deep framework for time series forecasting

Time series forecasting (TSF) has been a challenging research area, and various models have been developed to address this task. However, almost all these models are trained with numerical time series data, which is not as effectively processed by the neural system as visual information. To address this challenge, this paper proposes a novel machine vision assisted deep time series analysis (MV-DTSA) framework. The MV-DTSA framework operates by analyzing time series data in a novel binary machine vision time series metric space, which includes a mapping and an inverse mapping function from the numerical time series space to the binary machine vision space, and a deep machine vision model designed to address the TSF task in the binary space. A comprehensive computational analysis demonstrates that the proposed MV-DTSA framework outperforms state-of-the-art deep TSF models, without requiring sophisticated data decomposition or model customization. The code for our framework is accessible at https://github.com/IkeYang/ machine-vision-assisted-deep-time-series-analysis-MV-DTSA-.

Low-count Time Series Anomaly Detection

Low-count time series describe sparse or intermittent events, which are prevalent in large-scale online platforms that capture and monitor diverse data types. Several distinct challenges surface when modelling low-count time series, particularly low signal-to-noise ratios (when anomaly signatures are provably undetectable), and non-uniform performance (when average metrics are not representative of local behaviour). The time series anomaly detection community currently lacks explicit tooling and processes to model and reliably detect anomalies in these settings. We address this gap by introducing a novel generative procedure for creating benchmark datasets comprising of low-count time series with anomalous segments. Via a mixture of theoretical and empirical analysis, our work explains how widely-used algorithms struggle with the distribution overlap between normal and anomalous segments. In order to mitigate this shortcoming, we then leverage our findings to demonstrate how anomaly score smoothing consistently improves performance. The practical utility of our analysis and recommendation is validated on a real-world dataset containing sales data for retail stores.

ICU Mortality Prediction Using Long Short-Term Memory Networks

Extensive bedside monitoring in Intensive Care Units (ICUs) has resulted in complex temporal data regarding patient physiology, which presents an upscale context for clinical data analysis. In the other hand, identifying the time-series patterns within these data may provide a high aptitude to predict clinical events. Hence, we investigate, during this work, the implementation of an automatic data-driven system, which analyzes large amounts of multivariate temporal data derived from Electronic Health Records (EHRs), and extracts high-level information so as to predict in-hospital mortality and Length of Stay (LOS) early. Practically, we investigate the applicability of LSTM network by reducing the time-frame to 6-hour so as to enhance clinical tasks. The experimental results highlight the efficiency of LSTM model with rigorous multivariate time-series measurements for building real-world prediction engines.

OneShotSTL: One-Shot Seasonal-Trend Decomposition For Online Time Series Anomaly Detection And Forecasting

Seasonal-trend decomposition is one of the most fundamental concepts in time series analysis that supports various downstream tasks, including time series anomaly detection and forecasting. However, existing decomposition methods rely on batch processing with a time complexity of O(W), where W is the number of data points within a time window. Therefore, they cannot always efficiently support real-time analysis that demands low processing delay. To address this challenge, we propose OneShotSTL, an efficient and accurate algorithm that can decompose time series online with an update time complexity of O(1). OneShotSTL is more than $1,000$ times faster than the batch methods, with accuracy comparable to the best counterparts. Extensive experiments on real-world benchmark datasets for downstream time series anomaly detection and forecasting tasks demonstrate that OneShotSTL is from 10 to over 1,000 times faster than the state-of-the-art methods, while still providing comparable or even better accuracy.

SAMoSSA: Multivariate Singular Spectrum Analysis with Stochastic Autoregressive Noise

The well-established practice of time series analysis involves estimating deterministic, non-stationary trend and seasonality components followed by learning the residual stochastic, stationary components. Recently, it has been shown that one can learn the deterministic non-stationary components accurately using multivariate Singular Spectrum Analysis (mSSA) in the absence of a correlated stationary component; meanwhile, in the absence of deterministic non-stationary components, the Autoregressive (AR) stationary component can also be learnt readily, e.g. via Ordinary Least Squares (OLS). However, a theoretical underpinning of multi-stage learning algorithms involving both deterministic and stationary components has been absent in the literature despite its pervasiveness. We resolve this open question by establishing desirable theoretical guarantees for a natural two-stage algorithm, where mSSA is first applied to estimate the non-stationary components despite the presence of a correlated stationary AR component, which is subsequently learned from the residual time series. We provide a finite-sample forecasting consistency bound for the proposed algorithm, SAMoSSA, which is data-driven and thus requires minimal parameter tuning. To establish theoretical guarantees, we overcome three hurdles: (i) we characterize the spectra of Page matrices of stable AR processes, thus extending the analysis of mSSA; (ii) we extend the analysis of AR process identification in the presence of arbitrary bounded perturbations; (iii) we characterize the out-of-sample or forecasting error, as opposed to solely considering model identification. Through representative empirical studies, we validate the superior performance of SAMoSSA compared to existing baselines. Notably, SAMoSSA's ability to account for AR noise structure yields improvements ranging from 5% to 37% across various benchmark datasets.

Non-Parametric and Regularized Dynamical Wasserstein Barycenters for Time-Series Analysis

We consider probabilistic time-series models for systems that gradually transition among a finite number of states, in contrast to the more commonly considered case where such transitions are abrupt or instantaneous. We are particularly motivated by applications such as human activity analysis where the observed time-series contains segments representing distinct activities such as running or walking as well as segments characterized by continuous transition among these states. Accordingly, the dynamical Wasserstein barycenter (DWB) model introduced in Cheng et al. in 2021 [1] associates with each state, which we call a pure state, its own probability distribution, and models these continuous transitions with the dynamics of the barycentric weights that combine the pure state distributions via the Wasserstein barycenter. This is in contrast to methods that model these transitions with a mixture of the pure state distributions. Here, focusing on the univariate case where Wasserstein distances and barycenters can be computed in closed form, we extend [1] by discussing two challenges associated with learning a DWB model and two improvements. First, we highlight the issue of uniqueness in identifying the model parameters. Secondly, we discuss the challenge of estimating a dynamically evolving distribution given a limited number of samples. The uncertainty associated with this estimation may cause a model's learned dynamics to not reflect the gradual transitions characteristic of the system. The first improvement introduces a regularization framework that addresses this uncertainty by imposing temporal smoothness on the dynamics of the barycentric weights while leveraging the understanding of the non-uniqueness of the problem. Our second improvement lifts the Gaussian assumption on the pure states distributions in [1] by proposing a quantile-based non-parametric representation.

Comfort Foods and Community Connectedness: Investigating Diet Change during COVID-19 Using YouTube Videos on Twitter

Unprecedented lockdowns at the start of the COVID-19 pandemic have drastically changed the routines of millions of people, potentially impacting important health-related behaviors. In this study, we use YouTube videos embedded in tweets about diet, exercise and fitness posted before and during COVID-19 to investigate the influence of the pandemic lockdowns on diet and nutrition. In particular, we examine the nutritional profile of the foods mentioned in the transcript, description and title of each video in terms of six macronutrients (protein, energy, fat, sodium, sugar, and saturated fat). These macronutrient values were further linked to demographics to assess if there are specific effects on those potentially having insufficient access to healthy sources of food. Interrupted time series analysis revealed a considerable shift in the aggregated macronutrient scores before and during COVID-19. In particular, whereas areas with lower incomes showed decrease in energy, fat, and saturated fat, those with higher percentage of African Americans showed an elevation in sodium. Word2Vec word similarities and odds ratio analysis suggested a shift from popular diets and lifestyle bloggers before the lockdowns to the interest in a variety of healthy foods, communal sharing of quick and easy recipes, as well as a new emphasis on comfort foods. To the best of our knowledge, this work is novel in terms of linking attention signals in tweets, content of videos, their nutrients profile, and aggregate demographics of the users. The insights made possible by this combination of resources are important for monitoring the secondary health effects of social distancing, and informing social programs designed to alleviate these effects.

Singular spectrum analysis of time series data from low frequency radiometers, with an application to SITARA data

Understanding the temporal characteristics of data from low frequency radio telescopes is of importance in devising suitable calibration strategies. Application of time series analysis techniques to data from radio telescopes can reveal a wealth of information that can aid in calibration. In this paper, we investigate singular spectrum analysis (SSA) as an analysis tool for radio data. We show the intimate connection between SSA and Fourier techniques. We develop the relevant mathematics starting with an idealised periodic dataset and proceeding to include various non-ideal behaviours. We propose a novel technique to obtain long-term gain changes in data, leveraging the periodicity arising from sky drift through the antenna beams. We also simulate several plausible scenarios and apply the techniques to a 30-day time series data collected during June 2021 from SITARA - a short-spacing two element interferometer for global 21-cm detection. Applying the techniques to real data, we find that the first reconstructed component - the trend - has a strong anti-correlation with the local temperature suggesting temperature fluctuations as the most likely origin for the observed variations in the data. We also study the limitations of the calibration in the presence of diurnal gain variations and find that such variations are the likely impediment to calibrating SITARA data with SSA.