Package edu.cmu.tetrad.sem

Class PostnonlinearCausalModel

java.lang.Object

edu.cmu.tetrad.sem.PostnonlinearCausalModel

public class PostnonlinearCausalModel
extends Object

Represents a Post-nonlinear Causal Model (Zhang and Hyvarinen, 2009, 2012).

The form of the recursive model is Xi = f2i(f1i(Pa(Xi)) + Ni)

Zhang, K., & Hyvarinen, A. (2012). On the identifiability of the post-nonlinear causal model. arXiv preprint arXiv:1205.2599.

Chu, T., Glymour, C., & Ridgeway, G. (2008). Search for Additive Nonlinear Time Series Causal Models. Journal of Machine Learning Research, 9(5).

Bühlmann, P., Peters, J., & Ernest, J. (2014). "CAM: Causal Additive Models, high-dimensional order search and penalized regression". The Annals of Statistics.

Peters, J., Mooij, J. M., Janzing, D., & Schölkopf, B. (2014). "Causal Discovery with Continuous Additive Noise Models". Journal of Machine Learning Research.

Hastie, T., & Tibshirani, R. (1986). "Generalized Additive Models".

Hyvarinen, A., & Pajunen, P. (1999). "Nonlinear Independent Component Analysis: Existence and Uniqueness Results"

Constructor Summary

Constructors

Constructor	Description
PostnonlinearCausalModel(Graph graph, int numSamples, org.apache.commons.math3.distribution.RealDistribution noiseDistribution, double rescaleMin, double rescaleMax, int hiddenDimension, double inputScale, double coefLow, double coefHigh, boolean coefSymmetric)	Constructs a PostnonlinearCausalModel object.

Method Summary

Modifier and Type	Method	Description
DataSet	generateData()	Generates synthetic data based on a directed acyclic graph (DAG) with causal relationships and post-nonlinear causal mechanisms.
void	setActivationFunction(Function<Double,Double> activationFunction)	Sets the activation function used in the model.

Methods inherited from class java.lang.Object

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

Constructor Details

PostnonlinearCausalModel

public PostnonlinearCausalModel(Graph graph,
 int numSamples,
 org.apache.commons.math3.distribution.RealDistribution noiseDistribution,
 double rescaleMin,
 double rescaleMax,
 int hiddenDimension,
 double inputScale,
 double coefLow,
 double coefHigh,
 boolean coefSymmetric)

Constructs a PostnonlinearCausalModel object. This model generates synthetic data based on a directed acyclic graph (DAG) with causal relationships, utilizing post-nonlinear causal mechanisms. The model allows for various parameter configurations to control noise, rescaling, dimensionality, and coefficient properties.

Parameters:

graph - The directed acyclic graph (DAG) containing the causal structure for the model. Must be acyclic; otherwise, an exception will be thrown.

numSamples - The number of samples to generate for the synthetic data. Must be positive.

noiseDistribution - The distribution from which noise values are generated. Often a standard distribution, such as Gaussian, but can be user-defined.

rescaleMin - The minimum value for rescaling the data. Must be less than or equal to rescaleMax.

rescaleMax - The maximum value for rescaling the data. Must be greater than or equal to rescaleMin.

hiddenDimension - The dimensionality of the hidden variables affecting the model's behavior.

inputScale - A scaling factor applied to the input variables before applying post-nonlinear operations.

coefLow - The lower bound for randomly selected coefficients used in the model.

coefHigh - The upper bound for randomly selected coefficients used in the model.

coefSymmetric - A boolean flag indicating whether the randomly selected coefficients should be symmetric around zero.

Throws:

IllegalArgumentException - If the provided graph is not acyclic, the number of samples is less than one, or rescaleMin is greater than rescaleMax.

Method Details

generateData

public DataSet generateData()

Generates synthetic data based on a directed acyclic graph (DAG) with causal relationships and post-nonlinear causal mechanisms. The data generation process involves simulating parent-child relationships in the graph, applying noise, rescaling, and applying random piecewise linear transformations.

Returns:

A DataSet object containing the generated synthetic data, with samples and variables defined by the structure of the provided graph and simulation parameters.

setActivationFunction

public void setActivationFunction(Function<Double,Double> activationFunction)

Sets the activation function used in the model. The activation function is a mathematical function that transforms the input and can influence the relationships and behavior within the causal model.

Parameters:

activationFunction - The function to be used as the activation function. It must be a mapping from a Double input to a Double output, representing the non-linear transformation applied within the model.