PaperlayerView exact revision on arXiv

Source-linked AI summary

Causal Inference for Time series Analysis: Problems, Methods and Evaluation

Raha Moraffah, Paras Sheth, Mansooreh Karami, Anchit Bhattacharya, Qianru Wang, Anique Tahir, Adrienne Raglin, Huan Liu

arXiv:2102.05829v1cs.LGstat.ML

TL;DR

Time-series causal inference requires methods for estimating intervention effects and discovering causal relations, but existing surveys largely address traditional analysis tasks or specific methods. This paper reviews approaches for both causal tasks and curates datasets and evaluation metrics, concluding that these resources can guide future research and that current methods face data and assumption boundaries.

  • Problem

    Existing time-series surveys emphasize traditional tasks or specific approaches, leaving comprehensive coverage of treatment effect estimation and causal discovery limited.

  • Method

    The paper categorizes and reviews approaches for treatment effect estimation and causal discovery, and compiles evaluation metrics and datasets for both tasks.

  • Results

    The survey provides a comprehensive review and benchmark-oriented list of commonly used datasets and evaluation metrics for time-series causal inference.

  • Takeaways & Limitations

    The compiled metrics and datasets can serve as guidelines and benchmarks for future research on time-series causal inference.

  • Takeaways & Limitations

    Treatment effect methods commonly rely on SUTVA, which excludes interference from other units, while many social settings involve peer influence.

Abstract

from arXiv · show

Time series data is a collection of chronological observations which is generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting, and clustering have been proposed to analyze this type of data. Time series data has been also used to study the effect of interventions over time. Moreover, in many fields of science, learning the causal structure of dynamic systems and time series data is considered an interesting task which plays an important role in scientific discoveries. Estimating the effect of an intervention and identifying the causal relations from the data can be performed via causal inference. Existing surveys on time series discuss traditional tasks such as classification and forecasting or explain the details of the approaches proposed to solve a specific task. In this paper, we focus on two causal inference tasks, i.e., treatment effect estimation and causal discovery for time series data, and provide a comprehensive review of the approaches in each task. Furthermore, we curate a list of commonly used evaluation metrics and datasets for each task and provide in-depth insight. These metrics and datasets can serve as benchmarks for research in the field.

1. INTRODUCTION

The survey frames causal inference for time series around estimating intervention effects and discovering causal relations, then organizes methods and evaluation resources for these tasks.

  • Time series analysis spans classification, clustering, forecasting, intervention-effect estimation, and causal-relation discovery across application domains.
  • The survey focuses on treatment effect estimation and causal discovery as its two causal inference tasks.
  • Treatment effect estimation approaches are categorized as time-invariant effects, time-varying effects, and dynamic regimes.
  • The survey reviews causal treatment effect estimation and causal discovery, then presents datasets and evaluation metrics for assessing proposed frameworks.

2. MODELING TIME SERIES DATA

The survey reviews classical and probabilistic models for representing time-series dynamics, including ARIMA, Bayesian networks, and state-space models.

  • Time series are represented as real-valued variables indexed by discrete timestamps, with X(t) containing k measured variables.
  • ARIMA: ARIMA combines autoregressive, moving-average, and differencing components, with orders p, q, and r estimated alongside model coefficients.
  • ARIMA: AR and MA components suffice for stationary series, while differencing transforms non-stationary data toward stationarity.
  • Dynamic Bayesian Networks: Dynamic Bayesian Networks model evolving random variables through a prior Bayesian network and a two-slice transition network.
  • State-Space Models: Inference and learning procedures include Kalman filtering for state inference and EM-based parameter learning for hidden-variable models.
  • State-Space Models: State-space models use latent states to encode level, trend, and seasonality, with transition and observation models linking states and observations.

2.3 Gaussian Processes

Gaussian processes provide Bayesian nonparametric models for time series, while deep Gaussian processes combine neural feature extraction with Gaussian-process regression.

  • Gaussian processes define joint Gaussian distributions over collections of random variables and are suitable for modeling time series.
  • A Gaussian process is specified by a mean function m(x) and covariance function k(x, x′), with Gaussian noise included in the observation model.
  • Deep Gaussian processes use neural networks to extract non-stationary features before a sparse Gaussian-process layer performs regression in latent space.
  • Stochastic Gradient Hamiltonian Monte Carlo has been proposed for inference in deep Gaussian processes with non-Gaussian, multimodal posteriors.

2.4 Neural Networks

The survey describes recurrent, convolutional, and generative models for sequential data, emphasizing architectures that preserve temporal ordering and capture long-range dependencies.

  • RNNs and LSTMs generate sequences by processing recurrent dependencies, while RBM variants extend generative modeling to sequential data.
  • Convolutional Models: WaveNet models sequence probabilities with dilated causal convolutions that use past inputs and expand receptive fields with depth.
  • Convolutional Models: Causal convolutions prevent predictions from depending on future timesteps, preserving the temporal direction of sequence modeling.
  • Generative Models: GAN-based models such as C-RNN-GAN generate continuous sequential data by modeling the sequence’s joint probability distribution.

3. CAUSAL INFERENCE

The section introduces causal inference quantities for treatment effects and summarizes assumptions needed for causal estimation and discovery, especially with observational time-series data.

  • Treatment-effect estimands: Potential outcomes compare treatment and control states to define individual causal effects and population-level average treatment effects.The individual effect is δYa = Ya=1 − Ya=0; the average treatment effect is non-zero when treatment affects the outcome mean.
  • Treatment-effect estimands: Sample average treatment effect targets study units directly and avoids assuming that sampled units represent a larger population.Selection bias can make population-based averages unrepresentative of the specific study sample.
  • Treatment-effect estimands: Conditional average treatment effect measures treatment effects for covariate-defined sub-populations when individual responses are heterogeneous.CATE uses covariates X and their values x to characterize treatment effects across sub-populations.
  • Treatment-effect estimands: The average treatment effect of the treated focuses on individuals who participate in treatment rather than the full population.ATT is defined for the treated sub-population.
  • Identification assumptions: Randomized-trial estimators require additional identifiability conditions when researchers use observational aggregate outcomes.The section lists consistency, positivity, and conditional exchangeability among the relevant conditions.
  • Identification assumptions: Causal discovery for time series is presented with assumptions including causal stationarity, causal sufficiency, the causal Markov condition, and faithfulness.These assumptions constrain the process, its common causes, its graph-based distribution, and conditional independences.

4. CAUSALITY AND TIME SERIES ANALYSIS

The paper organizes causal inference for time series around treatment-effect estimation and causal discovery, then discusses how methods for both tasks can be evaluated.

  • Scope and organization: The review classifies treatment-effect approaches by time-setting and causal-discovery frameworks by model type.It discusses state-of-the-art approaches in each category.
  • Scope and organization: The paper also provides datasets and evaluation metrics to guide assessment of frameworks for both causal-inference tasks.These materials are presented as extensive evaluation guidelines.
  • Scope and organization: The two central tasks are causal treatment-effect estimation and causal discovery for time-series data.The section frames both as the main topics of the subsequent review.

4.1 Causal TreatmentEffectEstimationonTime Series

Treatment-effect estimation for time series compares observed outcomes with counterfactual outcomes across fixed, interrupted, and time-varying treatment settings. The reviewed methods use designs such as DiD, ITS, structural time-series models, and longitudinal treatment models.

  • Counterfactual treatment effects: Researchers estimate intervention effects by comparing observed treatment outcomes with counterfactual outcomes that represent what would have happened without treatment.The difference can be reported with ITE, ATE, or ATT measures.
  • Time-invariant treatment effects: Difference-in-differences uses control-group changes as a counterfactual under a common-trends or parallel-trends assumption.Its regression form includes treatment-group, time-period, and interaction terms, with the interaction coefficient representing the DiD effect.
  • Time-invariant treatment effects: The DiD illustration contrasts observed treatment-group outcomes with a counterfactual control-based trajectory after intervention.In the hypothetical tobacco-control example, consumption fell markedly after the program.
  • Time-invariant treatment effects: Causal Impact learns pre-intervention treatment-control relationships and predicts the post-intervention counterfactual using state-space models.The method generalizes DiD and structural time-series modeling for discrete interventions.
  • Time-invariant treatment effects: Interrupted Time Series estimates intervention effects from one series when the intervention begins at a known time and post-intervention outcomes can be measured.Segmented regression estimates immediate level changes and changes in post-intervention trends relative to the pre-intervention period.
  • Time-varying treatment effects: Time-varying treatment methods include marginal structural, structural nested, Bayesian nonparametric, factor-model, and deep-learning approaches.These approaches address longitudinal treatment effects, continuous treatments, flexible disease trajectories, or hidden multi-cause confounding.

4.2 Causal Discovery for Time Series

Causal discovery for time series seeks causal relations among dynamic variables using Granger, conditional-independence, structural-equation, and deep-learning approaches.

  • Motivation: Causal discovery identifies relations among phenomena and helps analyze how manipulating one phenomenon affects others.The paper motivates this task as important across scientific fields.
  • Granger causality and conditional independence: Granger causality declares Y informative for X when Y’s past improves prediction of X beyond X’s own past and other available information.Vector autoregressive models represent lagged effects through coefficient matrices.
  • Granger causality and conditional independence: Reviewed Granger and conditional-independence methods address shared lag structures, high-dimensional short series, variable lags, latent variables, and contemporaneous links.Examples include modified BTS, dynamic time warping, FCI, PCMCI, and PCMCI+ frameworks.
  • Granger causality and conditional independence: A mutual-information approach incrementally constructs causal information and outputs a graph whose edge weights represent leading times.Leading time is the difference between cause and effect occurrence times.
  • Structural equation models: Structural equation approaches include LiNGAM-based models that use non-Gaussianity to estimate causal structure from observational data.Time-series extensions can estimate instantaneous and lagged effects through autoregressive modeling, residual computation, and LiNGAM analysis.
  • Deep-learning methods: Deep-learning methods use nonlinear architectures such as MLPs, RNNs, and customized GRUs to model lagged and inter-series dependencies.Group-lasso penalties can shrink input weights to zero while the recurrent models discover nonlinear dependencies.

5. PERFORMANCE EVALUATION

The evaluation section surveys datasets for traditional time-series analysis and for causal treatment-effect estimation and causal discovery. It emphasizes that causal evaluation requires metadata and structures absent from many traditional datasets.

  • Causal time-series evaluation uses datasets and metrics matched to the model type being evaluated.
  • Traditional time-series datasets cover tasks such as classification and forecasting but may lack causal metadata.
  • The UCR archive contains more than 120 classification datasets with class labels for each item.
  • Time Series Datasets: Causal treatment-effect estimation may require treatment and control groups, while causal discovery may require confounder variables.
  • Treatment Effect Estimation Datasets: Treatment-effect datasets include ICU patient records, advertisement campaigns, geographic experiments, economic regions, tobacco-control data, air-quality data, and monetary-policy data.
  • Causal Discovery Datasets: Causal-discovery datasets span economic, health, environmental, neural, motion-capture, and traffic applications.

3 MSE

The supplied passage defines TP and FP as the basic quantities used for performance evaluation.

  • TP denotes True Positive.
  • FP denotes False Positive.
  • The passage introduces TP and FP as evaluation quantities.

6 Precision

The supplied passage defines TP and FN, which are quantities used in classification-based evaluation.

  • TP denotes True Positive.
  • FN denotes False Negative.
  • The passage introduces TP and FN as evaluation quantities.

7 Recall

The supplied passages present F1-Score in terms of precision and recall and distinguish time-dependent errors for null and alternative hypotheses.

  • F1-Score is defined using precision P and recall R.
  • The displayed definition gives F1 as 2PR.
  • Time-dependent errors are denoted separately for the null and alternative hypotheses.

9 F-Test

The paper reviews F-tests and other metrics for evaluating causal discovery and treatment-effect estimation in time series. Causal discovery metrics assess recovered relationships, while treatment-effect metrics compare estimated effects with ground truth.

  • Treatment Effect Estimation Metrics: Treatment-effect evaluation compares inferred effect series with ground truth using metrics including MSE, F-test, and t-test.The F-test examines treatment-effect heterogeneity through treated-to-control variance ratios, while the t-test can assess cause significance within a time range.
  • Causal Discovery Metrics: Structural Hamming Distance counts missing edges, extra edges, and incorrect directions when comparing a discovered causal graph with ground truth.It measures the graph changes required to transform one graph into the other.
  • Causal Discovery Metrics: True and false positive rates evaluate predicted adjacencies and arrowheads against the corresponding ground-truth graph.The rates use predicted and ground-truth adjacency matrices to calculate edge-recovery ratios.
  • Causal Discovery Metrics: AUROC, AUPR, F-score, precision, recall, and MSE are also used to evaluate causal relationships inferred by time-series models.AUROC summarizes TPR against FPR, AUPR summarizes precision-recall performance, and MSE can compare transition matrices with ground truth.
  • F-Test: F-tests assess causal discovery by testing whether lagged driving-variable coefficients in an unrestricted VAR model are jointly zero.The procedure constructs restricted and unrestricted equations and estimates their parameters using Ordinary Least Squares.

6. CONCLUSION AND FUTURE WORK

The paper surveys causal treatment-effect estimation and causal discovery for time series, organizing existing approaches and compiling datasets and metrics for evaluation. It identifies peer influence and continuous treatments as important directions for treatment-effect research.

  • Conclusion: The survey categorizes traditional time-series modeling and reviews approaches for treatment-effect estimation and causal discovery.Each causal task is classified by the types of approaches proposed to solve it.
  • Conclusion: The paper compiles datasets and evaluation metrics that can guide future research on causal time-series methods.The review presents these resources as tools for assessing frameworks across the covered tasks.
  • Future Work: Many treatment-effect methods assume SUTVA, but social relationships can influence treatment participation and outcomes.The paper specifically identifies friends, families, and acquaintances as potential sources of peer influence.
  • Future Work: Existing methods commonly model treatments as discrete events, leaving continuous-time and continuous-valued treatments as an open direction.Dialysis and intravenous diuretics are given as examples of treatments delivered continuously over time.
Loading 2102.05829v1…