Talk Outline Granger Causality Baseline methods: SIN in addition to VAR

Talk Outline Granger Causality Baseline methods: SIN in addition to VAR www.phwiki.com

Talk Outline Granger Causality Baseline methods: SIN in addition to VAR

Ross, Woody, News Director has reference to this Academic Journal, PHwiki organized this Journal Temporal Causal Modeling with Graphical Granger Methods Andrew Arnold (Carnegie Mellon University) Yan Liu (IBM T.J. Watson Research) Naoki Abe (IBM T.J. Watson Research) SIGKDD 07 August 13, 2007 Talk Outline Introduction in addition to motivation Overview of Granger causality Graphical Granger methods Exhaustive Granger Lasso Granger SIN Granger Vector auto-regression (VAR) Experimental results A Motivating Example: Key Per as long as mance Indicator Data (KPI) in Corporate Index Management [S&P] Time Variables

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KPI Case Study: Temporal Causal Modeling as long as Identifying Levers of Corporate Per as long as mance How can we leverage in as long as mation in temporal data to assist causal modeling in addition to inference Key idea: A cause necessarily precedes its effects Time Variables 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 in addition to only if: regressing as long as y in terms of past values of both y in addition to x is statistically significantly better than regressing y on past values of y only Assumption: no common latent causes Variable Space Expansion & Feature Space Mapping

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] Exhaustive Granger vs. Lasso Granger Baseline methods: SIN in addition to VAR SIN VAR

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 per as long as mance analysis R in addition to omly 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 Experiment 1A: Per as long as mance vs. Factors – R in addition to om sampling all factors – Experiment 1’s Efficiency

Experiment 1B: Per as long as mance vs. Factors – Fixing other factors – Experiment 1C: Per as long as mance vs. Factors – Detail: Parametric Conditioning – Experiment 2: Learned Graphs

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

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