Causal discovery in non-stationary time series data is crucial for understanding complex systems but remains challenging due to evolving relationships over time. This paper presents a novel two-stage approach for causal discovery in non-stationary multivariate time series data. The first stage employs a Temporal Attention Forecasting Network (TAFNet), a modified Transformer architecture, to capture complex temporal dependencies and generate informative attention matrices. The second stage utilizes these matrices in an iterative process for Granger causality discovery, refining the predicted causal graph while improving forecasting accuracy. The proposed method addresses the limitations of existing approaches and provides a more complete understanding of causal relationships in non-stationary systems. Extensive experiments demonstrate the method’s superior performance compared to state-of-the-art approaches, particularly in handling non-linear relationships and scaling to high-dimensional data.

For many spatio-temporal applications, building regression models that can reproduce the true data distribution is often as important as building models with high prediction accuracy. For example, knowing the future distribution of daily temperature and precipitation can help scientists determine their long-term trends and assess their potential impact on human and natural systems. As conventional methods are designed to minimize residual errors, the shape of their predicted distribution may not be consistent with their actual distribution. To overcome this challenge, this paper presents a novel, distribution-preserving multi-task learning framework for multi-location prediction of spatio-temporal data. The framework employs a non-parametric density estimation approach with L2-distance to measure the divergence between the predicted and true distribution of the data. Experimental results using climate data from more than 1500 weather stations in the United States show that the proposed framework reduces the distribution error for more than 78% of the stations without degrading the prediction accuracy significantly.

When using statistical models (such as a classifier) in a streaming environment, there is often a need to detect and adapt to concept drifts to mitigate any deterioration in the model's predictive performance over time. Unfortunately, the ability of popular concept drift approaches in detecting these drifts in the relationship of the response and predictor variable is often dependent on the distribution characteristics of the data streams, as well as its sensitivity on parameter tuning. This paper presents Hierarchical Linear Four Rates (HLFR), a framework that detects concept drifts for different data stream distributions (including imbalanced data) by leveraging a hierarchical set of hypothesis tests in an online setting. The performance of HLFR is compared to benchmark approaches using both simulated and real-world datasets spanning the breadth of concept drift types. HLFR significantly outperforms benchmark approaches in terms of accuracy, G-mean, recall, delay in detection and adaptability across the various datasets.

Common statistical prediction models often require and assume stationarity in the data. However, in many practical applications, changes in the relationship of the response and predictor variables are regularly observed over time, resulting in the deterioration of the predictive performance of these models. This paper presents Linear Four Rates (LFR), a framework for detecting these concept drifts and subsequently identifying the data points that belong to the new concept (for relearning the model). Unlike conventional concept drift detection approaches, LFR can be applied to both batch and stream data; is not limited by the distribution properties of the response variable (e.g., datasets with imbalanced labels); is independent of the underlying statistical-model; and uses user-specified parameters that are intuitively comprehensible. The performance of LFR is compared to benchmark approaches using both simulated and commonly used public datasets that span the gamut of concept drift types. The results show LFR significantly outperforms benchmark approaches in terms of recall, accuracy and delay in detection of concept drifts across datasets.

Regression-based approaches are widely used in climate modeling to capture the relationship between a climate variable of interest and a set of predictor variables. These approaches are often designed to minimize the overall prediction errors. However, some climate modeling applications emphasize more on fitting the distribution properties of the observed data. For example, histogram equalization techniques such as quantile mapping have been successfully used to debias outputs from computer-simulated climate models to obtain more realistic projections of future climate scenarios. In this paper, we show the limitations of current regression-based approaches in terms of preserving the distribution of observed climate data and present a multi-objective regression framework that simultaneously fits the distribution properties and minimizes the prediction error. The framework is highly flexible and can be applied to linear, nonlinear, and conditional quantile models. The paper demonstrates the effectiveness of the framework in modeling the daily minimum and maximum temperature as well as precipitation for climate stations in the Great Lakes region. The framework showed marked improvement over traditional regression-based approaches in all 14 climate stations evaluated.

Zero-inflated time series data are commonly encountered in many applications, including climate and ecological modeling, disease monitoring, manufacturing defect detection, and traffic monitoring. Such data often leads to poor model fitting using standard regression methods because they tend to underestimate the frequency of zeros and the magnitude of non-zero values. This paper presents an integrated framework that simultaneously performs classification and regression to accurately predict future values of a zero-inflated time series. A regression model is initially applied to predict the value of the time series. The regression output is then fed into a classification model to determine whether the predicted value should be adjusted to zero. Our regression and classification models are trained to optimize a joint objective function that considers both classification errors on the time series and regression errors on data points that have non-zero values. We demonstrate the effectiveness of our framework in the context of its application to a precipitation downscaling problem for climate impact assessment studies.