Class PostnonlinearSem

java.lang.Object

edu.cmu.tetrad.sem.PostnonlinearSem

public class PostnonlinearSem
extends Object

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

The form of the recursive model is X_i = f_{2,i}( f_{1,i}(Pa(X_i)) + N_i ), where N_i is an exogenous noise term independent across variables.

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
PostnonlinearSem(Graph graph, int numSamples, org.apache.commons.math3.distribution.RealDistribution noiseDistribution, int hiddenDimension, double inputScale)	Constructs a PostnonlinearCausalModel object.

Method Summary

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

Methods inherited from class Object

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

Constructor Details

PostnonlinearSem

public PostnonlinearSem(Graph graph,
 int numSamples,
 org.apache.commons.math3.distribution.RealDistribution noiseDistribution,
 int hiddenDimension,
 double inputScale)

Constructs a PostnonlinearCausalModel object. This model generates synthetic data based on a directed acyclic graph (DAG) with causal relationships, utilizing post-nonlinear causal mechanisms of the form X_i = f_{2,i}( f_{1,i}(Pa(X_i)) + N_i ).

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.

hiddenDimension - The dimensionality of the hidden layer in the MLPs approximating f1 and f2.

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

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 the directed acyclic graph (DAG) with post-nonlinear causal mechanisms. The data generation process involves simulating parent-child relationships in the graph, applying noise, optional rescaling, and then applying an invertible post-nonlinear distortion.

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.