Package edu.cmu.tetrad.search

Class Fask

java.lang.Object
edu.cmu.tetrad.search.Fask
All Implemented Interfaces:
IGraphSearch
public final class Fask extends Object implements IGraphSearch

Implements the FASK (Fast Adjacency Skewness) algorithm, which makes decisions for adjacency and orientation using a combination of conditional independence testing, judgments of nonlinear adjacency, and pairwise orientation due to non-Gaussianity. The reference is this:

Sanchez-Romero, R., Ramsey, J. D., Zhang, K., Glymour, M. R., Huang, B., and Glymour, C. (2019). Estimating feedforward and feedback effective connections from fMRI time series: Assessments of statistical methods. Network Neuroscience, 3(2), 274-30

Some adjustments have been made in some ways from that version, and some additional pairwise options have been added from this reference:

Hyvärinen, A., and Smith, S. M. (2013). Pairwise likelihood ratios for estimation of non-Gaussian structural equation models. Journal of Machine Learning Research, 14(Jan), 111-152.

This method (and the Hyvarinen and Smith methods) make the assumption that the data are generated by a linear, non-Gaussian causal process and attempts to recover the causal graph for that process. They do not attempt to recover the parametrization of this graph; for this a separate estimation algorithm would be needed, such as linear regression regressing each node onto its parents. A further assumption is made, that there are no latent common causes of the algorithm. This is not a constraint on the pairwise orientation methods, since they orient with respect only to the two variables at the endpoints of an edge and so are happy with all other variables being considered latent with respect to that single edge. However, if the built-in adjacency search is used (FAS-Stable), the existence of latents will throw this method off.

As was shown in the Hyvarinen and Smith paper above, FASK works quite well even if the graph contains feedback loops in most configurations, including 2-cycles. 2-cycles can be detected fairly well if the FASK left-right rule is selected and the 2-cycle threshold set to about 0.1--more will be detected (or hallucinated) if the threshold is set higher. As shown in the Sanchez-Romero reference above, 2-cycle detection of the FASK algorithm using this rule is quite good.

Some edges may be undiscoverable by FAS-Stable; to recover more of these edges, a test related to the FASK left-right rule is used, and there is a threshold for this test. A good default for this threshold (the "skew edge threshold") is 0.3. For more of these edges, set this threshold to a lower number.

It is assumed that the data are arranged so the each variable forms a column and that there are no missing values. The data matrix is assumed to be rectangular. To this end, the Tetrad DataSet class is used, which enforces this.

Note that orienting a DAG for a linear, non-Gaussian model using the Hyvarinen and Smith pairwise rules is alternatively known in the literature as Pairwise LiNGAM--see Hyvärinen, A., and Smith, S. M. (2013). Pairwise likelihood ratios for estimation of non-Gaussian structural equation models. Journal of Machine Learning Research, 14(Jan), 111-152. We include some of these methods here for comparison.

Parameters:

faskAdjacencyMethod: 1 # this run FAS-Stable (the one used in the paper). See Algorithm 2.

depth: -1. # control the size of the conditional set in the independence tests, setting this to a small integer may reduce the running time, but can also result in false positives. -1 means that it will check "all" possible sizes.

test: sem-bic-test # test for FAS adjacency

score: sem-bic-score

semBicRule: 1 # to set the Chickering Rule, used in the original Fask

penaltyDiscount: 2 # if using sem-bic as independence test (as in the paper). In the paper this is referred as c. Check step 1 and 10 in Algorithm 2 FAS stable.

skewEdgeThreshold: 0.3 # See description of Fask algorithm, and step 11 in Algorithm 1 FASK. Threshold to add edges that may have been non-inferred because there was a positive/negative cycle that result in a non-zero observed relation.

faskLeftRightRule: 1 # this run FASK v1, the original FASK from the paper

faskDelta: -0.3 # See step 1 and 11 in Algorithm 4 (this is the value set in the paper)

twoCycleScreeningThreshold: 0 # not used in the original paper implementation. Added afterwards. You can set it to 0.3, for example, to use it as a filter to run Algorithm 3 2-cycle detection, which may take some time to run.

orientationAlpha: 0.1 # this was referred in the paper as TwoCycle Alpha or just alpha, the lower it is, the lower the chance of inferring a two cycle. Check steps 17 to 28 in Algorithm 3: 2 Cycle Detection Rule.

structurePrior: 0 # prior on the number of parents. Not used in the paper implementation.

So a run of command line would look like this:

java -jar -Xmx10G causal-cmd-1.4.1-jar-with-dependencies.jar --delimiter tab --data-type continuous --dataset concat_BOLDfslfilter_60_FullMacaque.txt --prefix Fask_Test_MacaqueFull --algorithm fask --faskAdjacencyMethod 1 --depth -1 --test sem-bic-test --score sem-bic-score --semBicRule 1 --penaltyDiscount 2 --skewEdgeThreshold 0.3 --faskLeftRightRule 1 --faskDelta -0.3 --twoCycleScreeningThreshold 0 --orientationAlpha 0.1 -structurePrior 0

This class is configured to respect knowledge of forbidden and required edges, including knowledge of temporal tiers.

Author:
josephramsey, rubensanchez
See Also:

  • Constructor Details

    • Fask

      public Fask(DataSet dataSet, Score score, IndependenceTest test)
      Constructor.
      Parameters:
      dataSet - A continuous dataset over variables V.
      test - An independence test over variables V. (Used for FAS.)

  • Method Details

    • search

      public Graph search()
      Runs the search on the concatenated data, returning a graph, possibly cyclic, possibly with two-cycles. Runs the fast adjacency search (FAS, Spirtes et al., 2000) followed by a modification of the robust skew rule (Pairwise Likelihood Ratios for Estimation of Non-Gaussian Structural Equation Models, Smith and Hyvarinen), together with some heuristics for orienting two-cycles.
      Specified by:
      search in interface IGraphSearch
      Returns:
      the graph. Some edges may be undirected (though it shouldn't be many in most cases) and some adjacencies may be two-cycles.

    • getB

      public double[][] getB()
      Returns the coefficient matrix for the search. If the search has not yet run, runs it, then estimates coefficients of each node given its parents using linear regression and forms the B matrix of coefficients from these estimates. B[i][j] != 0 means i->j with that coefficient.
      Returns:
      This matrix as a double[][] array.

    • getLrScores

      public double[][] getLrScores()
      Returns a matrix of left-right scores for the search. If lr = getLrScores(), then lr[i][j] is the left right scores leftRight(data[i], data[j]);
      Returns:
      This matrix as a double[][] array.

    • getDepth

      public int getDepth()
      Returns:
      The depth of search for the Fast Adjacency Search (FAS).

    • setDepth

      public void setDepth(int depth)
      Parameters:
      depth - The depth of search for the Fast Adjacency Search (S). The default is -1. Unlimited. Making this too high may result in statistical errors.

    • getElapsedTime

      public long getElapsedTime()
      Returns:
      The elapsed time in milliseconds.

    • getKnowledge

      public Knowledge getKnowledge()
      Returns:
      the current knowledge.

    • setKnowledge

      public void setKnowledge(Knowledge knowledge)
      Parameters:
      knowledge - Knowledge of forbidden and required edges.

    • setExternalGraph

      public void setExternalGraph(Graph externalGraph)
      Sets the external graph to use. This graph will be used as a set of adjacencies to be included in the graph is the "external graph" options is selected. It doesn't matter what the orientations of the graph are; the graph will be reoriented using the left-right rule selected.
      Parameters:
      externalGraph - This graph.

    • setSkewEdgeThreshold

      public void setSkewEdgeThreshold(double skewEdgeThreshold)
      Sets the skew-edge threshold.
      Parameters:
      skewEdgeThreshold - This threshold.

    • setTwoCycleScreeningCutoff

      public void setTwoCycleScreeningCutoff(double twoCycleScreeningCutoff)
      Sets the cutoff for two-cycle screening.
      Parameters:
      twoCycleScreeningCutoff - This cutoff.

    • setOrientationAlpha

      public void setOrientationAlpha(double orientationAlpha)
      Sets the orientation alpha.
      Parameters:
      orientationAlpha - This alpha.

    • setLeftRight

      public void setLeftRight(Fask.LeftRight leftRight)
      Sets the left-right rule used
      Parameters:
      leftRight - This rule.
      See Also:

    • setAdjacencyMethod

      public void setAdjacencyMethod(Fask.AdjacencyMethod adjacencyMethod)
      Sets the adjacency method used.
      Parameters:
      adjacencyMethod - This method.
      See Also:

    • setDelta

      public void setDelta(double delta)
      Sets the delta to use.
      Parameters:
      delta - This delta.

    • setEmpirical

      public void setEmpirical(boolean empirical)
      Sets whether the empirical option is selected.
      Parameters:
      empirical - True, if so.

    • leftRight

      public double leftRight(double[] x, double[] y)
      A left/right judgment for double[] arrays (data) as input.
      Parameters:
      x - The data for the first variable.
      y - The data for the second variable.
      Returns:
      The left-right judgment, which is negative if X<-Y, positive if X->Y, and 0 if indeterminate.

    • faskLeftRightV2

      public static double faskLeftRightV2(double[] x, double[] y, boolean empirical, double delta)

    • faskLeftRightV1

      public static double faskLeftRightV1(double[] x, double[] y, boolean empirical, double delta)

    • robustSkew

      public static double robustSkew(double[] x, double[] y, boolean empirical)

    • skew

      public static double skew(double[] x, double[] y, boolean empirical)

    • g

      public static double g(double x)

    • correctSkewness

      public static double[] correctSkewness(double[] data, double sk)