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Register a new userCausal Inference for Time series Analysis: Problems, Methods and Evaluation
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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.
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Machine learning models have had discernible achievements in a myriad of applications. However, most of these models are black-boxes, and it is obscure how the decisions are made by them. This makes the models unreliable and untrustworthy. To provide insights into the decision making processes of these models, a variety of traditional interpretable models have been proposed. Moreover, to generate more human-friendly explanations, recent work on interpretability tries to answer questions related to causality such as Why does this model makes such decisions? or Was it a specific feature that caused the decision made by the model?. In this work, models that aim to answer causal questions are referred to as causal interpretable models. The existing surveys have covered concepts and methodologies of traditional interpretability. In this work, we present a comprehensive survey on causal interpretable models from the aspects of the problems and methods. In addition, this survey provides in-depth insights into the existing evaluation metrics for measuring interpretability, which can help practitioners understand for what scenarios each evaluation metric is suitable.
Making predictions in a robust way is not easy for nonlinear systems. In this work, a neural network computing framework, i.e., a spatiotemporal convolutional network (STCN), was developed to efficiently and accurately render a multistep-ahead prediction of a time series by employing a spatial-temporal information (STI) transformation. The STCN combines the advantages of both the temporal convolutional network (TCN) and the STI equation, which maps the high-dimensional/spatial data to the future temporal values of a target variable, thus naturally providing the prediction of the target variable. From the observed variables, the STCN also infers the causal factors of the target variable in the sense of Granger causality, which are in turn selected as effective spatial information to improve the prediction robustness. The STCN was successfully applied to both benchmark systems and real-world datasets, all of which show superior and robust performance in multistep-ahead prediction, even when the data were perturbed by noise. From both theoretical and computational viewpoints, the STCN has great potential in practical applications in artificial intelligence (AI) or machine learning fields as a model-free method based only on the observed data, and also opens a new way to explore the observed high-dimensional data in a dynamical manner for machine learning.
Standard causal discovery methods must fit a new model whenever they encounter samples from a new underlying causal graph. However, these samples often share relevant information - for instance, the dynamics describing the effects of causal relations - which is lost when following this approach. We propose Amortized Causal Discovery, a novel framework that leverages such shared dynamics to learn to infer causal relations from time-series data. This enables us to train a single, amortized model that infers causal relations across samples with different underlying causal graphs, and thus makes use of the information that is shared. We demonstrate experimentally that this approach, implemented as a variational model, leads to significant improvements in causal discovery performance, and show how it can be extended to perform well under hidden confounding.
We study the problem of robust time series analysis under the standard auto-regressive (AR) time series model in the presence of arbitrary outliers. We devise an efficient hard thresholding based algorithm which can obtain a consistent estimate of the optimal AR model despite a large fraction of the time series points being corrupted. Our algorithm alternately estimates the corrupted set of points and the model parameters, and is inspired by recent advances in robust regression and hard-thresholding methods. However, a direct application of existing techniques is hindered by a critical difference in the time-series domain: each point is correlated with all previous points rendering existing tools inapplicable directly. We show how to overcome this hurdle using novel proof techniques. Using our techniques, we are also able to provide the first efficient and provably consistent estimator for the robust regression problem where a standard linear observation model with white additive noise is corrupted arbitrarily. We illustrate our methods on synthetic datasets and show that our methods indeed are able to consistently recover the optimal parameters despite a large fraction of points being corrupted.
We introduce new quantities for exploratory causal inference between bivariate time series. The quantities, called penchants and leanings, are computationally straightforward to apply, follow directly from assumptions of probabilistic causality, do not depend on any assumed models for the time series generating process, and do not rely on any embedding procedures; these features may provide a clearer interpretation of the results than those from existing time series causality tools. The penchant and leaning are computed based on a structured method for computing probabilities.
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