Discovery and Visualization of Nonstationary Causal Models

Post date: Sep 21, 2016 5:26:38 PM

Sep 21

By Kun Zhang, Biwei Huang, Jiji Zhang, Bernhard Schoelkopf and Clark Glymour

Paper deals with non-stationarities that may be captures by latent confounders:

- attention

- policy changes

- credit risk

Ignoring the dependency on time may lead to either spurious relations or missing relations.

Can we use the distribution shifts in time to enhance the causal discovery.

The method is to use a switching variable T (time) or C. In the paper this is called “indicator” or “surrogate”.

1) The skeleton of the model is recovered using C (or T) as an extra variable. Algorithm 1, section 3.2.

2) Orientations:

Do this using V structures like regularly done.

Use V structures involving C or T, e.g. T-> V1 <- V2

Assumption: the causal structure does not change (the directions do no switch), but an edge can become zero. The model allows to modulate edges.

Argument: the direction that is “better” is the simplest in information theoretic sense.

Eq. 14

compute < log P(V1|V2) / < P(V1|V2) >over_Csegments >over_datasets

Empirical value of the KL divergence

For the correct causal direction, this measure should be zero

If for both directions the measure is high, there is a counfounder.

We decide for the direction of the smaller Delta.

Oct 5

Non stationarity allows us to identify causal models

C variable is the time index, we use it as surrogate variable

We use C for conditional independence tests

We have a SEM

V = f(parents, some functions of C modeling the non-stationarities, noise)

For example each variable is a stock

Non stationarity helps identify the causal direction

Independently but not identically distributed

We are interested in the instantaneous causal directions

We are using time to unravel the instantaneous causal directions

The cause and the effect given the cause change independently

A visualization method is obtained with kernel embedding and kernel PCA