Causal inference for time series analysis: problems, methods and evaluation

Causal Inference Meets Deep Learning: A Comprehensive Survey

Deep learning relies on learning from extensive data to generate prediction results. This approach may inadvertently capture spurious correlations within the data, leading to models that lack interpretability and robustness. Researchers have developed more profound and stable causal inference methods based on cognitive neuroscience. By replacing the correlation model with a stable and interpretable causal model, it is possible to mitigate the misleading nature of spurious correlations and overcome the limitations of model calculations. In this survey, we provide a comprehensive and structured review of causal inference methods in deep learning. Brain-like inference ideas are discussed from a brain-inspired perspective, and the basic concepts of causal learning are introduced. The article describes the integration of causal inference with traditional deep learning algorithms and illustrates its application to large model tasks as well as specific modalities in deep learning. The current limitations of causal inference and future research directions are discussed. Moreover, the commonly used benchmark datasets and the corresponding download links are summarized.

The Influence of Fatigue, Recovery, and Environmental Factors on the Body Stability of Construction Workers

In the construction industry, falls, slips, and trips (FST) account for 42.3% of all accidents. The primary cause of FST incidents is directly related to the deterioration of workers' body stability. To prevent FST-related accidents, it is crucial to understand the interaction between physical fatigue and body stability in construction workers. Therefore, this study investigates the impact of fatigue on body stability in various construction site environments using Dynamic Time Warping (DTW) analysis. We conducted experiments reflecting six different fatigue levels and four environmental conditions. The analysis process involves comparing changes in DTW values derived from acceleration data obtained through wearable sensors across varying fatigue levels and construction environments. The results reveal the following changes in DTW values across different environments and fatigue levels: for non-obstacle, obstacle, water, and oil conditions, DTW values tend to increase as fatigue levels rise. In our experiments, we observed a significant decrease in body stability against external environments starting from fatigue Levels 3 or 4 (30% and 40% of the maximum failure point). In the non-obstacle condition, the DTW values were 9.4 at Level 0, 12.8 at Level 3, and 23.1 at Level 5. In contrast, for the oil condition, which exhibited the highest DTW values, the values were 10.5 at Level 0, 19.1 at Level 3, and 34.5 at Level 5. These experimental results confirm that the body stability of construction workers is influenced by both fatigue levels and external environmental conditions. Further analysis of recovery time, defined as the time it takes for body stability to return to its original level, revealed an increasing trend in recovery time as fatigue levels increased. This study quantitatively demonstrates through wearable sensor data that, as fatigue levels increase, workers experience decreased body stability and longer recovery times. The findings of this study can inform individual worker fatigue management in the future.

CiGNN: A Causality-Informed and Graph Neural Network Based Framework for Cuffless Continuous Blood Pressure Estimation

Causalityholds profound potentials to dissipate confusion and improve accuracy in cuffless continuous blood pressure (BP) estimation, an area often neglected in current research. In this study, we propose a two-stage framework, CiGNN, that seamlessly integrates causality and graph neural network (GNN) for cuffless continuous BP estimation. The first stage concentrates on the generation of a causal graph between BP and wearable features from the the perspective of causal inference, so as to identify features that are causally related to BP variations. This stage is pivotal for the identification of novel causal features from the causal graph beyond pulse transit time (PTT). We found these causal features empower better tracking in BP changes compared to PTT. For the second stage, a spatio-temporal GNN (STGNN) is utilized to learn from the causal graph obtained from the first stage. The STGNN can exploit both the spatial information within the causal graph and temporal information from beat-by-beat cardiac signals for refined cuffless continuous BP estimation. We evaluated the proposed method with three datasets that include 305 subjects (102 hypertensive patients) with age ranging from 20-90 and BP at different levels, with the continuous Finapres BP as references. The mean absolute difference (MAD) for estimated systolic blood pressure (SBP) and diastolic blood pressure (DBP) were 3.77 mmHg and 2.52 mmHg, respectively, which outperformed comparison methods. In all cases including subjects with different age groups, while doing various maneuvers that induces BP changes at different levels and with or without hypertension, the proposed CiGNN method demonstrates superior performance for cuffless continuous BP estimation. These findings suggest that the proposed CiGNN is a promising approach in elucidating the causal mechanisms of cuffless BP estimation and can substantially enhance the precision of BP measurement.

A query-response causal analysis of reaction events in biochemical reaction networks

The stochastic kinetics of biochemical reaction networks is described by a chemical master equation (CME) and the underlying laws of mass action. Assuming network-free simulations of the rule-based models of biochemical reaction networks (BRNs), this paper departs from the usual analysis of network dynamics as the time-dependent distributions of chemical species counts, and instead considers statistically evaluating the sequences of reaction events generated from the stochastic simulations. The reaction event-time series can be used for reaction clustering, identifying rare events, and recognizing the periods of increased or steady-state activity. However, the main aim of this paper is to device an effective method for identifying causally and anti-causally related sub-sequences of reaction events using their empirical probabilities. This allows discovering some of the causal dynamics of BRNs as well as uncovering their short-term deterministic behaviors. In particular, it is proposed that the reaction sub-sequences that are conditionally nearly certain or nearly uncertain can be considered as being causally related. Moreover, since the time-ordering of reaction events is locally irrelevant, the reaction sub-sequences can be transformed into the reaction sets or multi-sets. The distance metrics can be then used to define the equivalences among the reaction events. The proposed method for identifying the causally related reaction sub-sequences has been implemented as a computationally efficient query-response mechanism. The method was evaluated for five models of genetic networks in seven defined numerical experiments. The models were simulated in BioNetGen using the open-source network-free simulator NFsim. This simulator had to be modified first to allow recording the traces of reaction events, and it is available in the Github repository, ploskot/nfsim_1.20. The generated event time-series were analyzed with Python and Matlab scripts. The whole process of data generation, analysis and visualization has been nearly fully automated using shell scripts. This demonstrates the opportunities for substantially increasing the research productivity by creating automated data generation and processing pipelines.

Inferring connectivity of an oscillatory network via the phase dynamics reconstruction

We review an approach for reconstructing oscillatory networks' undirected and directed connectivity from data. The technique relies on inferring the phase dynamics model. The central assumption is that we observe the outputs of all network nodes. We distinguish between two cases. In the first one, the observed signals represent smooth oscillations, while in the second one, the data are pulse-like and can be viewed as point processes. For the first case, we discuss estimating the true phase from a scalar signal, exploiting the protophase-to-phase transformation. With the phases at hand, pairwise and triplet synchronization indices can characterize the undirected connectivity. Next, we demonstrate how to infer the general form of the coupling functions for two or three oscillators and how to use these functions to quantify the directional links. We proceed with a different treatment of networks with more than three nodes. We discuss the difference between the structural and effective phase connectivity that emerges due to high-order terms in the coupling functions. For the second case of point-process data, we use the instants of spikes to infer the phase dynamics model in the Winfree form directly. This way, we obtain the network's coupling matrix in the first approximation in the coupling strength.

Search-and-rescue in the Central Mediterranean Route does not induce migration: Predictive modeling to answer causal queries in migration research

State- and private-led search-and-rescue are hypothesized to foster irregular migration (and thereby migrant fatalities) by altering the decision calculus associated with the journey. We here investigate this 'pull factor' claim by focusing on the Central Mediterranean route, the most frequented and deadly irregular migration route towards Europe during the past decade. Based on three intervention periods-(1) state-led Mare Nostrum, (2) private-led search-and-rescue, and (3) coordinated pushbacks by the Libyan Coast Guard-which correspond to substantial changes in laws, policies, and practices of search-and-rescue in the Mediterranean, we are able to test the 'pull factor' claim by employing an innovative machine learning method in combination with causal inference. We employ a Bayesian structural time-series model to estimate the effects of these three intervention periods on the migration flow as measured by crossing attempts (i.e., time-series aggregate counts of arrivals, pushbacks, and deaths), adjusting for various known drivers of irregular migration. We combine multiple sources of traditional and non-traditional data to build a synthetic, predicted counterfactual flow. Results show that our predictive modeling approach accurately captures the behavior of the target time-series during the various pre-intervention periods of interest. A comparison of the observed and predicted counterfactual time-series in the post-intervention periods suggest that pushback policies did affect the migration flow, but that the search-and-rescue periods did not yield a discernible difference between the observed and the predicted counterfactual number of crossing attempts. Hence we do not find support for search-and-rescue as a driver of irregular migration. In general, this modeling approach lends itself to forecasting migration flows with the goal of answering causal queries in migration research.

Time series causal relationships discovery through feature importance and ensemble models

Inferring causal relationships from observational data is a key challenge in understanding the interpretability of Machine Learning models. Given the ever-increasing amount of observational data available in many areas, Machine Learning algorithms used for forecasting have become more complex, leading to a less understandable path of how a decision is made by the model. To address this issue, we propose leveraging ensemble models, e.g., Random Forest, to assess which input features the trained model prioritizes when making a forecast and, in this way, establish causal relationships between the variables. The advantage of these algorithms lies in their ability to provide feature importance, which allows us to build the causal network. We present our methodology to estimate causality in time series from oil field production. As it is difficult to extract causal relations from a real field, we also included a synthetic oil production dataset and a weather dataset, which is also synthetic, to provide the ground truth. We aim to perform causal discovery, i.e., establish the existing connections between the variables in each dataset. Through an iterative process of improving the forecasting of a target's value, we evaluate whether the forecasting improves by adding information from a new potential driver; if so, we state that the driver causally affects the target. On the oil field-related datasets, our causal analysis results agree with the interwell connections already confirmed by tracer information; whenever the tracer data are available, we used it as our ground truth. This consistency between both estimated and confirmed connections provides us the confidence about the effectiveness of our proposed methodology. To our knowledge, this is the first time causal analysis using solely production data is employed to discover interwell connections in an oil field dataset.

Inferring Causal Factors of Core Affect Dynamics on Social Participation through the Lens of the Observer

A core endeavour in current affective computing and social signal processing research is the construction of datasets embedding suitable ground truths to foster machine learning methods. This practice brings up hitherto overlooked intricacies. In this paper, we consider causal factors potentially arising when human raters evaluate the affect fluctuations of subjects involved in dyadic interactions and subsequently categorise them in terms of social participation traits. To gauge such factors, we propose an emulator as a statistical approximation of the human rater, and we first discuss the motivations and the rationale behind the approach.The emulator is laid down in the next section as a phenomenological model where the core affect stochastic dynamics as perceived by the rater are captured through an Ornstein-Uhlenbeck process; its parameters are then exploited to infer potential causal effects in the attribution of social traits. Following that, by resorting to a publicly available dataset, the adequacy of the model is evaluated in terms of both human raters' emulation and machine learning predictive capabilities. We then present the results, which are followed by a general discussion concerning findings and their implications, together with advantages and potential applications of the approach.

A dynamic causal modeling of the second outbreak of COVID-19 in Italy

While the vaccination campaign against COVID-19 is having its positive impact, we retrospectively analyze the causal impact of some decisions made by the Italian government on the second outbreak of the SARS-CoV-2 pandemic in Italy, when no vaccine was available. First, we analyze the causal impact of reopenings after the first lockdown in 2020. In addition, we also analyze the impact of reopening schools in September 2020. Our results provide an unprecedented opportunity to evaluate the causal relationship between the relaxation of restrictions and the transmission in the community of a highly contagious respiratory virus that causes severe illness in the absence of prophylactic vaccination programs. We present a purely data-analytic approach based on a Bayesian methodology and discuss possible interpretations of the results obtained and implications for policy makers.

Disentangling personalized treatment effects from “time-of-the-day” confounding in mobile health studies

Ideally, a patient’s response to medication can be monitored by measuring changes in performance of some activity. In observational studies, however, any detected association between treatment (“on-medication” vs “off-medication”) and the outcome (performance in the activity) might be due to confounders. In particular, causal inferences at the personalized level are especially vulnerable to confounding effects that arise in a cyclic fashion. For quick acting medications, effects can be confounded by circadian rhythms and daily routines. Using the time-of-the-day as a surrogate for these confounders and the performance measurements as captured on a smartphone, we propose a personalized statistical approach to disentangle putative treatment and “time-of-the-day” effects, that leverages conditional independence relations spanned by causal graphical models involving the treatment, time-of-the-day, and outcome variables. Our approach is based on conditional independence tests implemented via standard and temporal linear regression models. Using synthetic data, we investigate when and how residual autocorrelation can affect the standard tests, and how time series modeling (namely, ARIMA and robust regression via HAC covariance matrix estimators) can remedy these issues. In particular, our simulations illustrate that when patients perform their activities in a paired fashion, positive autocorrelation can lead to conservative results for the standard regression approach (i.e., lead to deflated true positive detection), whereas negative autocorrelation can lead to anticonservative behavior (i.e., lead to inflated false positive detection). The adoption of time series methods, on the other hand, leads to well controlled type I error rates. We illustrate the application of our methodology with data from a Parkinson’s disease mobile health study.

The impact of extreme weather on student online learning participation

In March 2020, the COVID-19 pandemic forced over 1 billion learners to shift from face-to-face instruction to online learning. Seven months after it began, this transition became even more challenging for Filipino online learners. Eight typhoons struck the Philippines from October to November 2020. Two of these typhoons caused widespread flooding, utilities interruptions, property destruction, and loss of life. We examine how these severe weather conditions affected online learning participation of Filipino students pursuing their undergraduate and graduate studies. We used CausalImpact analysis to explore September 2020 to January 2021 data collected from the Moodle Learning Management System data of one university in the Philippines. We found that overall student online participation was significantly negatively affected by typhoons. However, the effect on participation in Assignments and Quizzes was not significant. These findings suggested that students continued to participate in activities that have a direct bearing on their final grades, rather than activities that had no impact on their course outcomes.

Causal Discovery in Manufacturing: A Structured Literature Review

Industry 4.0 radically alters manufacturing organization and management, fostering collection and analysis of increasing amounts of data. Advanced data analytics, such as machine learning (ML), are essential for implementing Industry 4.0 and obtaining insights regarding production, better decision support, and enhanced manufacturing quality and sustainability. ML outperforms traditional approaches in many cases, but its complexity leads to unclear bases for decisions. Thus, acceptance of ML and, concomitantly, Industry 4.0, is hindered due to increasing requirements of fairness, accountability, and transparency, especially in sensitive-use cases. ML does not augment organizational knowledge, which is highly desired by manufacturing experts. Causal discovery promises a solution by providing insights on causal relationships that go beyond traditional ML’s statistical dependency. Causal discovery has a theoretical background and been successfully applied in medicine, genetics, and ecology. However, in manufacturing, only experimental and scattered applications are known; no comprehensive overview about how causal discovery can be applied in manufacturing is available. This paper investigates the state and development of research on causal discovery in manufacturing by focusing on motivations for application, common application scenarios and approaches, impacts, and implementation challenges. Based on the structured literature review, four core areas are identified, and a research agenda is proposed.

Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance.