1. Temporal Causal Modeling with Graphical Granger Methods
SIGKDD 07
August 13, 2007
Andrew Arnold (Carnegie Mellon University)
Yan Liu (IBM T.J. Watson Research)
Naoki Abe (IBM T.J. Watson Research)

2. Talk Outline Introduction and motivation Overview of Granger causality
Graphical Granger methods
Exhaustive Granger
Lasso Granger
SIN Granger
Vector auto-regression (VAR)
Experimental results

3. A Motivating Example: Key Performance Indicator Data (KPI) in Corporate Index Management [S&P]
Variables
Company
HAL
Year
1999
2000
2001
Quarter 4 1 2 3
Revenue ($M)
6.24
6.54
5.82
3.89
4.1
4.41
3.6
Revenue-to-RD
Revenue-to-RD CAGR
Innovation Index
Innovation Index CAGR
CapEx to Revenue
compound annual growth rate
Time

4. KPI Case Study: Temporal Causal Modeling for Identifying Levers of Corporate Performance
How can we leverage information in temporal data to assist causal modeling and inference ?
Key idea: A cause necessarily precedes its effects…
Variables
Company
HAL
Year
1999
2000
2001
Quarter 4 1 2 3
Revenue ($M)
6.24
6.54
5.82
3.89
4.1
4.41
3.6
Revenue-to-RD
Revenue-to-RD CAGR
Innovation Index
Innovation Index CAGR
CapEx to Revenue
compound annual growth rate
Time

5. Granger Causality Granger causality
Introduced by the Nobel prize winning economist, Clive Granger [Granger ‘69]
Definition: a time series x is said to “Granger cause” another time series y, if and only if:
regressing for y in terms of past values of both y and x
is statistically significantly better than regressing y on past values of y only
Assumption: no common latent causes

6. Variable Space Expansion & Feature Space Mapping
Fewer edges
Fewer variables

7. Graphical Granger Methods
Exhaustive Granger
Test all possible univariate Granger models independently
Lasso Granger
Use L1-normed regression to choose sparse multivariate regression models
[Meinshausen & Buhlmann, ‘06]
SIN Granger
Do matrix inversion to find correlations between features across time
[Drton & Perlman, ‘04]
Vector auto-regression (VAR)
Fit data to linear-normal time series model
[Gilbert, ‘95]
Too many variables.
How can we condense.

8. Exhaustive Granger vs. Lasso Granger
Too many variables.
How can we condense.

9. Baseline methods: SIN and VAR

10. Empirical Evaluation of Competing Methods
Evaluation by simulation
Sample data from synthetic (linear normal) causal model
Learn using a number of competing methods
Compare learned graphs to original model
Measure similarity of output graph to original graph in terms of
Precision of predicted edges
Recall of predicted edges
F1 of predicted edges
Parameterize performance analysis
Randomly sample graphs from parameter space
Lag; Features; Affinity; Noise; Samples per feature; Samples per feature per lag
Conditioning to see interaction effects
E.g. Effect of # features when samples_per_feature_per_lag is small vs large

11. Experiment 1A: Performance vs. Factors - Random sampling all factors -

12. Experiment 1’s Efficiency

13. Experiment 1B: Performance vs. Factors - Fixing other factors -13 13

14. Experiment 1C: Performance vs
Experiment 1C: Performance vs. Factors - Detail: Parametric Conditioning -

15. Experiment 2: Learned Graphs

16. Experiment 3: Real World Data Output Graphs on the Corporate KPI Data