Generating a probabilistic graphical model with causal information

1. A computer-implemented method of generating a probabilistic graphical model with causal information, said graphical model containing a causal relationship between a first variable and a second variable, the method comprising:

receiving data at a processor, said data showing a correlation between the first variable and the second variable, wherein the first variable and the second variable are observed variables;

generating a graphical representation of the data defined by the first variable and the second variable;

modifying the graphical representation to replace a direct causal relationship between the first variable and the second variable with a latent common cause between the first variable and the second variable;

determining a manifold in the modified graphical representation;

deriving a third variable from the manifold, the third variable describing the manifold, wherein the third variable is a parametrization of the latent common cause;

applying a causal discovery algorithm to the modified graphical representation to determine the causal relationship between the first and third variables and the second and third variables, the causal discovery algorithm being able to determine if the first variable causes the third variable, the third variable causes the first variable, the second variable causes the third variable, and the third variable causes the second variable, comprising:

determining a first one or more values quantifying the asymmetry in the causal relationship between the first variable and the third variable; and

determining a second one or more values quantifying the asymmetry in the casual relationship between the third variable and the second variable;

determining the structure of the causal relationship between the first and second variables, comprising:

calculating a heuristic based on the first one or more values and the second one or more values;

in response to the heuristic being below a decision threshold, determining that the third variable causes the first and second variables and that the third variable is not caused by the first or second variables;

in response to the third variable causing the first and second variables and the third variable not being caused by the first or second variables, determining that a latent variable is the cause of the first and second variables, wherein the latent variable is an unobserved variable; and

outputting a graphical model with the determined causal structure, said causal structure indicating the direction of edges in a graphical representation of said graphical model, the graphical model utilized for triage or diagnosis, wherein the graphical model comprises, in response to

the latent variable being determined to be the cause of the first and second variables, the first node, the second node, a third node representing the latent variable, a directed edge from the third node to the first node, and a directed edge from the third node to the second node.

2. The computer-implemented method according to claim 1 , wherein the manifold is described by a single third variable and determining a manifold reduces the dimensionality of the graphical representation from two dimensions to one dimension.

3. The computer-implemented method according to claim 1 , wherein determining the structure of the causal relationship comprises determining that the first variable causes the second variable if the third variable causes the first and second variables, the third variable is caused by the first variable, but where the third variable is not caused by the second variable.

4. The computer-implemented method according to claim 1 , wherein determining the structure of the causal relationship comprises determining that the second variable causes the first variable if the third variable causes the first and second variables, the third variable is caused by the second variable, but where the third variable is not caused by the first variable.

5. The computer-implemented method according to claim 1 , wherein the causal discovery algorithm determines whether a variable causes another variable by evaluating asymmetry between the variables.

6. The computer-implemented method according to claim 5 , wherein the causal discover algorithm is KCDC or an additive noise model.

7. The computer-implemented method according to claim 1 , wherein the first and second variables are binary variables and wherein noise is added to the binary variables prior to the determination of the manifold.

8. The computer-implemented method according to claim 1 , wherein the manifold is determined using a non-linear algorithm.

9. The computer-implemented method according to claim 8 , wherein the algorithm is selected from Isomap, PCA, or ICA.

10. The computer-implemented method according to claim 1 , wherein the probabilistic graphical model is a medical probabilistic graphical model.

11. The computer-implemented method according to claim 10 , wherein the medical probabilistic graphical model comprises diseases, symptoms, and risk factors as variables.

12. A computer-implemented method of determining a response to a user inputted query, using a probabilistic graphical model, the method comprising:

receiving a user inputted query;

identifying a node in said probabilistic graphical model “PGM” related to said query, said PGM being stored in a memory of a computer; and

performing inference on said PGM to provide a response to said user, wherein, said graphical model contains a causal relationship between a first variable and a second variable, the PGM being constructed by:

receiving data at a processor, said data showing a correlation between the first variable and the second variable, wherein the first variable and the second variable are observed variables;

generating a graphical representation of the data defined by the first variable and the second variable;

modifying the graphical representation to replace a direct causal relationship between the first variable and the second variable with a latent common cause between the first variable and the second variable;

determining a manifold in the modified graphical representation;

deriving a third variable from the manifold, the third variable describing the manifold, wherein the third variable is a parametrization of the latent common cause;

applying a causal discovery algorithm to the modified graphical representation to determine the causal relationship between the first and third variables and the second and third variable, the causal discovery algorithm being able to determine if the first variable causes the third variable, the third variable causes the first variable, the second variable causes the third variable, and the third variable causes the second variable, comprising:

determining a first one or more values quantifying the asymmetry in the causal relationship between the first variable and the third variable;

determining a second one or more values quantifying the asymmetry in the casual relationship between the third variable and the second variable;

determining the structure of the causal relationship between the first and second variables, comprising

calculating a heuristic based on the first one or more values and the second one or more values;

in response to the heuristic being below a decision threshold, determining that the third variable causes the first and second variables and that the third variable is not caused by the first or second variables;

in response to the third variable causing the first and second variables and the third variable not being caused by the first or second variables, determining that a latent variable is the cause of the first and second variables, wherein the latent variable is an unobserved variable; and

outputting a graphical model with the determined causal structure, said causal structure indicating the direction of edges in a graphical representation of said graphical model, the graphical model utilized for triage or diagnosis, wherein the graphical model comprises, in response to

the latent variable being determined to be the cause of the first and second variables, the first node, the second node, a third node representing the latent variable, a directed edge from the third node to the first node, and a directed edge from the third node to the second node.

13. A system adapted to generate a probabilistic graphical model with causal information, said graphical model containing the causal relationship between a first variable and a second variable, the system comprising a processor and a memory, the processor being adapted to:

receive data from a database, said data showing a correlation between the first variable and the second variable, wherein the first variable and the second variable are observed variables;

generate a graphical representation of the data defined by the first variable and the second variable;

modify the graphical representation to replace a direct causal relationship between the first variable and the second variable with a latent common cause between the first variable and the second variable;

determine a manifold in the modified graphical representation;

derive a third variable from the manifold, the third variable describing the manifold, wherein the third variable is a parametrization of the latent common cause;

apply a causal discovery algorithm to the modified graphical representation to determine the causal relationship between the first and third variables and the second and third variable, the causal discovery algorithm being able to determine if the first variable causes the third variable, the third variable causes the first variable, the second variable causes the third variable, and the third variable causes the second variable, comprising:

determining a first one or more values quantifying the asymmetry in the causal relationship between the first variable and the third variable;

determining a second one or more values quantifying the asymmetry in the casual relationship between the third variable and the second variable;

determine the structure of the causal relationship between the first and second variables, comprising:

calculating a heuristic based on the first one or more values and the second one or more values;

in response to the heuristic being below a decision threshold, determining that the third variable causes the first and second variables and that the third variable is not caused by the first or second variables;

in response to the third variable causing the first and second variables and the third variable not being caused by the first or second variables, determining that a latent variable is the cause of the first and second variables, wherein the latent variable is an unobserved variable; and

output a graphical model with the determined causal structure, the graphical model utilized for triage or diagnosis, wherein the graphical model comprises, in response to

the latent variable being determined to be the cause of the first and second variables, the first node, the second node, a third node representing the latent variable, a directed edge from the third node to the first node, and a directed edge from the third node to the second node.

14. A non-transitory carrier medium carrying computer-readable instructions being adapted to cause a computer to perform a method for determining the causal relationship between a first variable and a second variable, the method comprising:

receiving data, said data showing a correlation between the first variable and the second variable, wherein the first variable and the second variable are observed variables;

generating a graphical representation of the data defined by the first variable and the second variable;

modifying the graphical representation to replace a direct causal relationship between the first variable and the second variable with a latent common cause between the first variable and the second variable;

determining a manifold in the modified graphical representation;

deriving a third variable from the manifold, the third variable describing the manifold, wherein the third variable is a parametrization of the latent common cause;

applying a causal discovery algorithm to the modified graphical representation to determine the causal relationship between the first and third variables and the second and third variable, the causal discovery algorithm being able to determine if the first variable causes the third variable, the third variable causes the first variable, the second variable causes the third variable, and the third variable causes the second variable, comprising:

determining a first one or more values quantifying the asymmetry in the causal relationship between the first variable and the third variable;

determining a second one or more values quantifying the asymmetry in the casual relationship between the third variable and the second variable;

determining the structure of the causal relationship between the first and second variables, comprising:

calculating a heuristic based on the first one or more values and the second one or more values;

in response to the heuristic being below a decision threshold, determining that the third variable causes the first and second variables and that the third variable is not caused by the first or second variables;

in response to the third variable causing the first and second variables and the third variable not being caused by the first or second variables, determining that a latent variable is the cause of the first and second variables, wherein the latent variable is an unobserved variable; and

outputting a graphical model with the determined causal structure, the graphical model utilized for triage or diagnosis, wherein the graphical model comprises, in response to

the latent variable being determined to be the cause of the first and second variables, the first node, the second node, a third node representing the latent variable, a directed edge from the third node to the first node, and a directed edge from the third node to the second node.