Causality challenge #2: Pot-Luck

Transcription

1 Causality challenge #2: Pot-Luck Isabelle Guyon, Clopinet Constantin Aliferis and Alexander Statnikov, Vanderbilt Univ. André Elisseeff and Jean-Philippe Pellet, IBM Zürich Gregory F. Cooper, Pittsburg University Peter Spirtes, Carnegie Mellon 1

2 * Motivations * Learning causal structure * * Cross-sectional studies * from experiments * without experiments * Equivalent MB * * Longitudinal studies * Bring your own problem(s) * Motivations 2

3 Causality Workbench February 2007: Project starts. Initial funding of the EU Pascal network. August 15, 2007: Two-year grant from the US National Science Foundation. December 15, 2007: Workbench made alive. First causality challenge: causation an prediction. June 3-4, 2008: WCCI 2008, workshop to discuss the results of the first challenge. September 15, 2008: Start pot-luck challenge. Target: NIPS Fall, 2008: Start developing an interactive workbench. 3

4 Why a new challenge? Causality challenge #1 Favor depth Single well defined task Rigor of performance assessment Causality challenge #2 Favor breadth Many different tasks Encourage creativity 4

5 5 5

6 Pot-Luck challenge CYTO: Causal Protein-Signaling Networks in human T cells. Learn a protein signaling network from multicolor flow cytometry data. N=11 proteins, P~800 samples per experimental condition. E=9 conditions. LOCANET: LOcal CAusal NETwork. Find the local causal structure around a given target variable (depth 3 network) in REGED, CINA, SIDO, MARTI. PROMO: Simulated marketing task. Time series of 1000 promotion variables and 100 product sales. Predict a 1000x100 boolean influence matrix, indicating for each (i,j) element whether the i th promotion has a causal influence of the sales of the j th product. Data is provided as time series, with a daily value for each variable for three years. SIGNET: Abscisic Acid Signaling Network. Determine the set of 43 boolean rules that describe the interactions of the nodes within a plant signaling network. 300 separate Boolean pseudodynamic simulations of the true rules. Model inspired by a true biological system. TIED: Target Information Equivalent Dataset. Illustrates a case in which there are many equivalent Markov boundaries. Find them all. real self eval 6 real artif artif self eval artif artif

7 * Motivations * Learning causal structure * * Cross-sectional studies * from experiments * without experiments * Equivalent MB * * Longitudinal studies * Bring your own problem(s) * Learning causal structure 7

8 What is causality? Many definitions. Pragmatic (engineering) view: predicting the consequences of ACTIONS. Distinct from making predictions in a stationary environment. Canonical methodology: designed experiments. Causal discovery from observational data. 8

9 The language of causal Bayesian networks Bayesian network: Graph with random variables X 1, X 2, X n as nodes. Dependencies represented by edges. Allow us to compute P(X 1, X 2, X n ) as Π i P( X i Parents(X i ) ). Edge directions have no meaning. Causal Bayesian network: egde directions indicate causality. 9

10 Small example Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder LUCAS0: natural Coughing Markov boundary Fatigue Car Accident 10

11 Arrows indicate mechanisms If Lung Cancer (LC) is determined by Smoking (S) and Genetics (G), In the language of BN, use the data table: P(LC=1 S=1, G=1)=, P(LC=0 S=1, G=1)= P(LC=1 S=1, G=0)=, P(LC=0 S=1, G=0)= P(LC=1 S=0, G=1)=, P(LC=0 S=0, G=1)= P(LC=1 S=0, G=0)=, P(LC=0 S=0, G=0)= In the language of Structural Equation Models (SEM), use: LC = f(s, G) + noise where usually f is a linear function. 11

12 Common simplifications Assume a Markov process Assume a DAG Assume causal sufficiency (no hidden common cause) Assume stability or faithfulness (no particular parameterization implying dependencies not reflected by the structure) Assume linearity of relationships Assume Gaussianity of PDF s Discard relationships of low statistical significance Focus on a local neighborhood of a target variable Learn unoriented or partially oriented graphs Assume uniqueness of the Markov boundary 12

13 How about time? Cross-sectional study 13

14 14 How about time? Cross-sectional study Longitudinal study

15 * Motivations * Learning causal structure * * Cross-sectional studies * from experiments * without experiments * Equivalent MB * * Longitudinal studies * Bring your own problem(s) * Learning causal structure from cross-sectional studies: CYTO LOCANET TIED 15

16 Causal models as particular generative models Imagine we have prior knowledge about a few alternative plausible causal models (we basically know the architecture). Fit the parameters of the model to data. Select the model based on goodness of fit (score), perhaps penalizing higher complexity models. Could two models have identical scores? 16

17 Key types of causal relationships 1 Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder Coughing Fatigue Direct cause Car Accident 17

18 Key types of causal relationships 2 Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder Coughing Fatigue Indirect cause (chain) AN LC S Car Accident 18

19 Key types of causal relationships 3 Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder Coughing Fatigue Confounder (fork) YF LC S Car Accident 19

20 How this might look in data Lung cancer Yellow Fingers 20

21 How this might look in data Lung cancer Non-smoking Smoking Simpson s paradox YF LC S Yellow Fingers 21

22 Markov equivalence X 1 Y X 2 X 1 P(X 1, X 2, Y) X 2 Y = P(X 1 X 2, Y) P(Y X 2 ) P(X 2 ) X 1 X 2 Y P(X 1, X 2, Y) = P(Y X 2, X 1 ) P(X 2 X 1 ) P(X 1 ) X 1 X 2 Y P(X 1, X 2, Y) = P(X 1 X 2, Y) P(X 2 Y) P(Y) 22

23 Key types of causal relationships 4 Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder Coughing Fatigue Collider (V-structure) AL LC C Car Accident 23

24 How this might look in data Lung cancer Allergy 24

25 How this might look in data Lung cancer Coughing=1 Coughing=0 Allergy 25

26 No Markov equivalence Colliders (V-structures) : X 1 Y X 2 X 1 Y X 2 P(X 1, X 2, Y) = P(X 2 X 1,Y) P(X 1 ) P(Y) 26

27 Structural methods 1. Build unoriented graph (using conditional independencies). 2. Orient colliders. 3. Add more arrows by constraint propagation without creating new colliders

28 * Motivations * Learning causal structure * * Cross-sectional studies * from experiments * without experiments * Equivalent MB * * Longitudinal studies * Bring your own problem(s) * towards CYTO: using experiments to learn the causal structure 28

29 Manipulating a single variable 1 Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder Coughing Fatigue Direct cause Car Accident Smoking manipulated (disconnected from its direct causes): remains predictive of LC. 29

30 Manipulating a single variable 2 Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder Coughing Fatigue Indirect cause Car Accident Anxiety manipulated: remains predictive of Lung Cancer. 30

31 Manipulating a single variable 3 Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Consequence of common cause (correlated, but not cause) Allergy Coughing Lung Cancer Fatigue Attention Disorder Car Accident Yellow Fingers manipulated: no longer predictive of LC. 31

32 Manipulating a single variable 4 Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics? Allergy Lung Cancer Attention Disorder Coughing Fatigue Direct cause Car Accident Genetics manipulated: remains predictive of LC and AD. 32

33 Manipulating a single variable 5 Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder Coughing Fatigue Direct cause Car Accident Attention disorder manipulated: no longer predictive of Genetics. 33

34 The CYTO problem CD CD28 LFA-1 Zap70 L A LckT VAV SLP-76 PI3K 10 6 RAS PKC 4 Cytohesin JAB-1 Activators PLCg PIP3 Akt 1. a-cd3 2. a-cd28 3. ICAM-2 4. PMA 8 PIP2 7 PKA 5 Raf 5. b2camp Inhibitors 6. G AKT inh MAPKKK MEK4/7 MAPKKK MEK3/6 Mek1/2 Erk1/ Psitect 9. U LY JNK p38 34 Karen Sachs et al

35 * Motivations * Learning causal structure * * Cross-sectional studies * from experiments * without experiments * Equivalent MB * * Longitudinal studies * Bring your own problem(s) * towards LOCANET: learning the causal structure without experiments to predict the consequences of future actions. 35

36 What if we cannot experiment? Experiments may be infeasible, costly or unethical Using only observations we may want to predict the effect of new policies. Policies may consist in manipulating several variables. 36

37 Manipulating a few variables Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder LUCAS1: manipulated Coughing Markov boundary Fatigue Car Accident 37

38 Manipulating all variables Anxiety Peer Pressure Born an Even Day Yellow Fingers Smoking Genetics Allergy Lung Cancer Attention Disorder LUCAS2: manipulated Coughing Markov boundary Fatigue Car Accident 38

39 Causality challenge #1: causation and prediction Task: Predict the target (e.g., Lung cancer) in unmanipulated or manipulated test data. Goals: Introduce ML people to causal discovery problems. Investigate ties between causation and prediction. Findings: Participants used either causal or non-causal feature selection. Good causal discovery (feature set containing the manipulated MB) correlated with good predictions. However, some participants using non-causal feature selection obtained good prediction results. 39

40 Causality challenge #2: The LOCANET problem Task: Find the local causal structure around a given target variable (depth 3 network) in REGED, CINA, SIDO, MARTI. Goal: Analyze more finely to which extent causal discovery methods recover the causal structure and how this affects predicting the target values. 40

41 * Motivations * Learning causal structure * * Cross-sectional studies * from experiments * without experiments * Equivalent MB * * Longitudinal studies * Bring your own problem(s) * TIED Equivalent Markov boundaries 41

42 Equivalent Markov boundaries Y Markov boundary Many almost identical measurements of the same (hidden) variable can lead to many statistically undistinguishable Markov boundaries. 42

43 Target Information Equivalence (TIE) Two disjoint subsets of variables V 1 and V 2 are Target Information Equivalent (TIE) with respect to target Y iff: V 1 Y V 2 Y V 1 Y V 2 V 2 Y V 1 Alexander Statnikov & Constantin Aliferis 43

44 TIE Data (TIED) Exact equivalence X 1 X 2 X 3 X 11 Y Small example of the type of relationships implemented in TIED. The following TIE relations hold in the data: TIE Y (X 1, X 2 ) TIE Y (X 1, X 3 ) TIE Y (X 1, X 11 ) TIE Y (X 2, X 3 ) TIE Y (X 2, X 11 ) TIE Y (X 3, X 11 ) TIE X11 (X 1, X 2 ) TIE X11 (X 1, X 3 ) TIE X11 (X 2, X 3 ) Notice that variables X 1, X 2, X 3, X 11, and Y are not deterministically related. Alexander Statnikov & Constantin Aliferis 44

45 * Motivations * Learning causal structure * * Cross-sectional studies * from experiments * without experiments * Equivalent MB * * Longitudinal studies * Bring your own problem(s) * Learning causal structure from longitudinal studies: SIGNET PROMO 45

46 SIGNET: a plant signaling network Plants loose water and take in carbone dioxide through microscopic pores. During drought, plant hormone abiscisic acid (ABA) inhibits pore opening (important for the genetic engineering of new drought resistant plants). Unraveling the ABA signal transduction network took years of research. A recent dynamic model synthesizes many findings (Li, Assmann, Albert, PLOS, 2006). The model is used by Jenkins and Soni to generate artificial data. The problem is to reconstruct the network from the data. 46

47 Abscisic Acid Signaling Network Li, Assmann, Albert, PLOS,

48 SIGNET: sample data time Boolean model; asynchronous updates - 43 nodes simulations Example of asynchronous updates for a 4-node network: 48

49 PROMO: simulated marketing task 100 products 1000 promotions 3 years of daily data Goal: quantify the effect of promotions on sales Jean-Philippe Pellet products 49 promotions

50 PROMO: schematically The difficulties include: - non iid samples - seasonal effects - promotions are binary, sales are continuous - the problem is more quantifying the relationships than determining the causal skeleton 1000 other

51 * Motivations * Learning causal structure * * Cross-sectional studies * from experiments * without experiments * Equivalent MB * * Longitudinal studies * Bring your own problem * Pot-luck challenge: Bring your own problem 51

52 From NIPS 2006 workshop 1. Predict the consequences of a manipulation (similar to a usual predictive modeling task, but the test data is no longer distributed in the same way as the training data; the system undergoes a manipulation to produce the test data). 2. Determine what manipulations are needed to reach a desired system state with maximum probability (e.g., select variables and propose values to achieve a certain value of a response/target variable, with perhaps a cost per variable). 3. Propose system queries to acquire more training data, i.e. design experiments, with perhaps an associated cost per variable and per sample and perhaps with constraints on variables, which cannot be controllable. 4. Determine all causal relationships between variables. 5. Determine a local causal region around a response/target variable (causal adjacency). 6. Determine the source cause(s) for a response/target variable. 7. Determine for all variables whether they are, with respect to a response/target variable: cause, effect, consequence of a common cause, cause of a common effect, or unrelated. 8. Predict the existence of unmeasured variables (not part of the set of variables provided in the data), which are potential confounders (are common causes of an observed variable and the target). 9. Predict which variables called relevant by feature selection algorithms are potentially causally irrelevant because their correlation to the target is the result of an experimental artifact (e.g., sampling bias or systematic error). 10. Determine a causal order of all variables. 11. Determine a causal direction in time series data in which one variable is causing the other. 12. Determine the direction of time in a time series (mostly of fundamental rather than practical interest). 13. Incorporate prior knowledge in causal discovery. 14. Predict counterfactuals. 52

53 September 15, 2008: challenge start. October 15, 2008: deadline for (optional) submission of milestone challenge results. October 24, 2008: workshop abstracts due. November 12, 2008: challenge ends (last day to submit challenge results). November 21, 2008: JMLR proceedings paper submission deadline. December 12, 2008: challenge results publicly released; workshop. 53

54 Prizes Four prizes (free NIPS workshop entrance or $200). Best solution to one or more problems: 3 prizes. Best problem:1 prize. All competitors must submit a 6-page paper. Criteria: performance/usefulness, novelty/originality, sanity, insight, reproducibility, clarity. 54