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