Causal Discovery from Subsampled Time Series with Proxy Variables (2023-05-09T00:00:00.000000Z)

TL;DR

A constraint-based algorithm that can identify the entire causal structure from subsampled time series, without any parametric constraint is proposed, which is nonparametric and can achieve full causal identification.

Abstract

Inferring causal structures from time series data is the central interest of many scientific inquiries. A major barrier to such inference is the problem of subsampling, i.e., the frequency of measurement is much lower than that of causal influence. To overcome this problem, numerous methods have been proposed, yet either was limited to the linear case or failed to achieve identifiability. In this paper, we propose a constraint-based algorithm that can identify the entire causal structure from subsampled time series, without any parametric constraint. Our observation is that the challenge of subsampling arises mainly from hidden variables at the unobserved time steps. Meanwhile, every hidden variable has an observed proxy, which is essentially itself at some observable time in the future, benefiting from the temporal structure. Based on these, we can leverage the proxies to remove the bias induced by the hidden variables and hence achieve identifiability. Following this intuition, we propose a proxy-based causal discovery algorithm. Our algorithm is nonparametric and can achieve full causal identification. Theoretical advantages are reflected in synthetic and real-world experiments.

Authors

Mingzhou Liu

2 papers

Xinwei Sun

2 papers

Yizhou Wang

2 papers

TL;DR

Abstract

Authors

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Specifically,

Since A(t 1 ) and B(t 2 ) are adjacent in the MAG, there is an inducing path p = A(t 1 ), V 1

B(t + k), Z(t + 1), Z(t + k) have the causal graph shown in Fig. 8. • A(t) → Z(t + 1)

Vi(t1 + k) → Vi+1(t1 + k + 1) means Vi(t1 + k) can not be a collider

A(t) → V1(t + 1) means we have A(t) → V1(t + k) in the MAG. V1 is the ancestor of B

B), since V1 is the ancestor of Zi, we have Zi ∈ De(B), which contradicts with the definition of the vertex set Z

In this case, except for the above analysis, we need to extra show that every path p = A(t) → B(t + 1), V 1

B(t + k), then A(t) ∈ An(B(t + k))

such that time(V j ) ≤ t. Then, there is a vertex V j on the path such that V j (t) → V j+1 (t + 1) → V j+2 (t + 2) → ⋯. If the path between V j (t) and Z i (t + k) is a directed one

B(t + k) can not be the ancestor of A(t) according to the causal precedence assumption

We prove this by showing that A(t) ↔ B(t + k) can not be true. Prove by contradiction. Suppose that we have A(t) ↔ B(t + k) in the MAG, then there is an inducing path p = A(t), V 1

As a result,there is a vertex V j on p between V i (t − τ ) and B(t + k) such that time(V j ) = t and time

In the following, we will show neither of these paths exist

In this case, the path must be A(t) → V 1 (t + 1) → V 2 (t + 2) → ⋯. If the path between V 1 (t1) and Z i (t + k) is a directed one, we have V 1 (t + 1) ∈ Z(t + 1), because of the following facts

• Z(t + 1) → Z(t + k). By Asm. A.2 the self causation edge always exists

• Z(t + 1) → B(t + k). By definition B is not the ancestor of any vertex in Z

In other words, we have time(V i ) = t + 1, .., t + k − 1. We show that in this case, we have A(t) ∈ An(B(t + k)) in the full time DAG

For the path that ∀ V i ,t < time ( V i ) < t + k

time ( V i ) ≤ t + τ

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