Package edu.cmu.tetrad.search

Class IdaCheck

java.lang.Object

edu.cmu.tetrad.search.IdaCheck

public class IdaCheck
extends Object

This calculates total effects and absolute total effects for an MPDAG G for all pairs distinct (x, y) of variables, where the total effect is obtained by regressing y on x ∪ S and reporting the regression coefficient. Here, S ranges over sets consisting of possible parents of x in G--that is, a set consisting of the parents of x in G plus some combination of the neighbors for x in G, and excluding any children of x in G. Absolute total effects are calculated as the abolute values of the total effects; the minimum values for these across possible parent sets is reported as suggested in this paper:

Maathuis, Marloes H., Markus Kalisch, and Peter Bühlmann. "Estimating high-dimensional intervention effects from observational data." The Annals of Statistics 37.6A (2009): 3133-3164.

Additionally, if a linear SEM model is supplied over the same variables, a minimum squared distance is calculated of each coefficient in this IM from the interval of total effects (min to max) for the pair (x, y) for each directed edge x->y in the SEM IM. If the true total effect falls within the interval [min, max], we give a distance of 0; otherwise, we give the distance to the nearest endpoint. This distance is then squared.

We also report the averages of each statistic across all pairs of distinct nodes in the dataset.

Version:

$Id: $Id

Author:

josephramsey

See Also:

• Ida

Constructor Summary

Constructors

Constructor	Description
IdaCheck(Graph graph, DataSet dataSet, SemIm trueSemIm)	Constructs a new IDA check for the given MPDAG and data set.

Method Summary

Modifier and Type	Method	Description
double	getAverageSquaredDistance(List<OrderedPair<Node>> pairs)	Returns the average of the squared distances between the true total effects and the IDA effect ranges the list of node pairs indicated.
double	getAvgMaxSquaredDiffEstTrue(List<OrderedPair<Node>> pairs)	Returns the average of the squared differences between the maximum total effects and the true total effects for the list of node pairs indicated.
double	getAvgMinSquaredDiffEstTrue(List<OrderedPair<Node>> pairs)	Returns the average of the squared differences between the minimum total effects and the true total effects for the list of node pairs indicated.
double	getIdaMinEffect(Node x, Node y)	Gets the signed minimum absolute total effect value between two nodes.
double	getMaxTotalEffect(Node x, Node y)	Returns the maximum total effect value between two nodes.
double	getMinTotalEffect(Node x, Node y)	Gets the minimum total effect value between two nodes.
List<Node>	getNodes()	Returns a list of nodes.
List<OrderedPair<Node>>	getOrderedPairs()	Retrieves a list of OrderedPair objects representing all possible pairs of distinct nodes in the graph.
double	getSquaredDistance(OrderedPair<Node> pair)	Calculates the squared distance of the true total effect to the [min, max] IDA effect range of the given (x, y) node pair, for x predicting y.
double	getSquaredMaxTrueDist(OrderedPair<Node> pair)	Returns the squared difference between the maximum total effect and the true total effect for the given pair of nodes.
double	getSquaredMinTrueDistance(OrderedPair<Node> pair)	Returns the squared difference between the minimum total effect and the true total effect for the given pair of nodes.
double	getTrueTotalEffect(OrderedPair<Node> pair)	Calculates the true total effect between two nodes in the graph.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

IdaCheck

public IdaCheck(Graph graph,
 DataSet dataSet,
 SemIm trueSemIm)

Constructs a new IDA check for the given MPDAG and data set.

Parameters:

graph - the MPDAG.

dataSet - the data set.

trueSemIm - the true SEM IM.

Method Details

getTrueTotalEffect

public double getTrueTotalEffect(OrderedPair<Node> pair)

Calculates the true total effect between two nodes in the graph.

Parameters:

pair - the ordered pair of nodes for which the total effect is calculated.

Returns:

the true total effect between the two nodes.

getNodes

public List<Node> getNodes()

Returns a list of nodes.

Returns:

the list of nodes.

getOrderedPairs

public List<OrderedPair<Node>> getOrderedPairs()

Retrieves a list of OrderedPair objects representing all possible pairs of distinct nodes in the graph.

Returns:

a list of OrderedPair objects.

getMinTotalEffect

public double getMinTotalEffect(Node x,
 Node y)

Gets the minimum total effect value between two nodes.

Parameters:

x - the first node.

y - the second node.

Returns:

the minimum total effect value between the two nodes.

Throws:

IllegalArgumentException - if the nodes x and y are the same.

getMaxTotalEffect

public double getMaxTotalEffect(Node x,
 Node y)

Returns the maximum total effect value between two nodes.

Parameters:

x - the first node.

y - the second node.

Returns:

the maximum total effect value between the two nodes.

Throws:

IllegalArgumentException - if the nodes x and y are the same.

getIdaMinEffect

public double getIdaMinEffect(Node x,
 Node y)

Gets the signed minimum absolute total effect value between two nodes.

Parameters:

x - the first node.

y - the second node.

Returns:

the signed minimum absolute total effect value between the two nodes.

Throws:

IllegalArgumentException - if the nodes x and y are the same.

getSquaredDistance

public double getSquaredDistance(OrderedPair<Node> pair)

Calculates the squared distance of the true total effect to the [min, max] IDA effect range of the given (x, y) node pair, for x predicting y. If the true effect falls within [min, max], the method returns 0. Otherwise, the squared distance to the nearest endpoint of the [min, max] range is returned.

Parameters:

pair - the pair of nodes.

Returns:

the squared distance between the two nodes.

getAverageSquaredDistance

public double getAverageSquaredDistance(List<OrderedPair<Node>> pairs)

Returns the average of the squared distances between the true total effects and the IDA effect ranges the list of node pairs indicated.

Parameters:

pairs - the list of node pairs.

Returns:

the average of the squared distances between the true total effects and the IDA effect ranges.

getSquaredMinTrueDistance

public double getSquaredMinTrueDistance(OrderedPair<Node> pair)

Returns the squared difference between the minimum total effect and the true total effect for the given pair of nodes.

Parameters:

pair - the pair of nodes.

Returns:

the squared difference between the minimum total effect and the true total effect.

getAvgMinSquaredDiffEstTrue

public double getAvgMinSquaredDiffEstTrue(List<OrderedPair<Node>> pairs)

Returns the average of the squared differences between the minimum total effects and the true total effects for the list of node pairs indicated.

Parameters:

pairs - the list of node pairs.

Returns:

the average of the squared differences between the minimum total effects and the true total effects.

getSquaredMaxTrueDist

public double getSquaredMaxTrueDist(OrderedPair<Node> pair)

Returns the squared difference between the maximum total effect and the true total effect for the given pair of nodes.

Parameters:

pair - the pair of nodes.

Returns:

the squared difference between the maximum total effect and the true total effect.

getAvgMaxSquaredDiffEstTrue

public double getAvgMaxSquaredDiffEstTrue(List<OrderedPair<Node>> pairs)

Returns the average of the squared differences between the maximum total effects and the true total effects for the list of node pairs indicated.

Parameters:

pairs - the list of node pairs.

Returns:

the average of the squared differences between the maximum total effects and the true total effects.