CAUSAL DISCOVERY FROM CONDITIONALLY STATIONARY TIME SERIES

Abstract

Causal discovery, i.e., inferring underlying causal relationships from observational data, has been shown to be highly challenging for AI systems. In time series modeling context, traditional causal discovery methods mainly consider constrained scenarios with fully observed variables and/or data from stationary time-series. We develop a causal discovery approach to handle a wide class of non-stationary time-series that are conditionally stationary, where the non-stationary behaviour is modeled as stationarity conditioned on a set of (possibly hidden) state variables. Named State-Dependent Causal Inference (SDCI), our approach is able to recover the underlying causal dependencies, provably with fully-observed states and empirically with hidden states. The latter is confirmed by experiments on synthetic linear system and nonlinear particle interaction data, where SDCI achieves superior performance over baseline causal discovery methods. Improved results over non-causal RNNs on modeling NBA player movements demonstrate the potential of our method and motivate the use causality-driven methods for forecasting.

1. INTRODUCTION

Deep learning has achieved profound success in vision and language modelling tasks (Brown et al., 2020; Nichol et al., 2021) . Still, it remains a grand challenge and a prominent research direction to enable deep neural networks to perform causal discovery and reasoning (Yi et al., 2020; Girdhar & Ramanan, 2020; Sauer & Geiger, 2021) , which is an inherent mechanism in human cognition (Spelke & Kinzler, 2007) . Specifically for analysing time series data, causal discovery involves identifying the underlying temporal causal structure of the observed sequences. Many existing causal discovery approaches for time series assume stationarity (Granger, 1969; Peters et al., 2017; Löwe et al., 2020; Li et al., 2020; Tank et al., 2021) , which is restrictive as sequence data from real-world scenarios are often non-stationary with potential hidden confounders. Recent works introduce a number of different assumptions to tackle causal discovery for non-stationary time series (Zhang et al., 2017; Ghassami et al., 2018; Huang et al., 2019) , but in general, causal discovery on nonstationary time series under mild and realistic assumptions is an open problem. This work aims at addressing this open challenge by proposing a causal discovery algorithm for condionally stationary time series, for which the dynamics of the observed system change depending on a set of "state" variables. This assumption holds for many real-world scenarios, e.g., with people who behave differently and take different decisions depending on underlying factors such as mood, previous experience, and the actions of other agents. The causal discovery task for such conditionally stationary time series poses different challenges depending on the observability of the states, which is classified into 4 different scenarios: 1. Scenario class 1 concerns the simplest case, where the states are observed and their dynamics are independent on other observed time series data (Figure 1a ). 2. In Scenario class 2, the states are unobserved and directly dependent on observed variables. Figure 1b shows an example, where the states of the variables change according to their positions (pink vs purple regions). Another example is to consider an agent moving in a room where different behaviors are observed depending on their location. 3. Scenario class 3 is more challenging: the state depends on earlier events, and thus cannot be directly inferred from observations. E.g., in Figure 1c , particles that change state upon collision. Also in a football game a player acts differently depending on earlier actions of the others. 1

