Learning a directed acyclic graph using a machine learning model loss

A computing device comprising:

• a processor;
• and
• a non-transitory computer-readable medium operably coupled to the processor, the computer-readable medium having computer-readable instructions stored thereon that, when executed by the processor, cause the computing device to
• (A) define a topological order vector, wherein the topological order vector includes an indicator for each variable of a plurality of variables in an order defined such that each variable's parent set is a subset of variables listed in the topological order vector whose order is lower, and wherein the plurality of variables have a non-linear relationship;
• (B) define a target variable and zero or more input variables from the plurality of variables based on the defined topological order vector;
• (C) train a machine learning model with a plurality of observation vectors using the defined target variable and the zero or more input variables, wherein each observation vector of the plurality of observation vectors includes a variable value for each variable of the plurality of variables;
• (D) execute the trained machine learning model with a second plurality of observation vectors using the defined target variable and the zero or more input variables to compute a loss value, wherein each observation vector of the second plurality of observation vectors includes the variable value for each variable of the plurality of variables;
• (E) repeat (B) through (D) a first plurality of times determined based on a number of the plurality of variables to compute the loss value of the topological order defined in (A);
• (F) repeat (A) through (E) a second plurality of times determined based on the number of the plurality of variables, wherein each topological order vector defined in (A) is unique in comparison to other topological order vectors defined in (A);
• (G) repeat (A) through (F) a third plurality of times until a best topological order vector is determined based on a comparison between the loss values computed for each topological order vector in (E);
• (H) output the determined best topological order vector to describe a hierarchical relationship between the plurality of variables;
• and
• (I) learn a Directed Acyclic Graph (DAG) based on the best topological order vector.

A method of learning a topological order of a plurality of variables, the method comprising:

• (A) defining, by a computing device, a topological order vector, wherein the topological order vector includes an indicator for each variable of a plurality of variables in an order defined such that each variable's parent set is a subset of variables listed in the topological order vector whose order is lower, and wherein the plurality of variables have a non-linear relationship;
• (B) defining, by the computing device, a target variable and zero or more input variables from the plurality of variables based on the defined topological order vector;
• (C) training, by the computing device, a machine learning model with a plurality of observation vectors using the defined target variable and the zero or more input variables, wherein each observation vector of the plurality of observation vectors includes a variable value for each variable of the plurality of variables;
• (D) executing, by the computing device, the trained machine learning model with a second plurality of observation vectors using the defined target variable and the zero or more input variables to compute a loss value, wherein each observation vector of the second plurality of observation vectors includes the variable value for each variable of the plurality of variables;
• (E) repeating, by the computing device, (B) through (D) a first plurality of times determined based on a number of the plurality of variables to compute the loss value of the topological order defined in (A);
• (F) repeating, by the computing device, (A) through (E) a second plurality of times determined based on the number of the plurality of variables, wherein each topological order vector defined in (A) is unique in comparison to other topological order vectors defined in (A);
• (G) repeating, by the computing device, (A) through (F) a third plurality of times until a best topological order vector is determined based on a comparison between the loss values computed for each topological order vector in (E);
• (H) outputting, by the computing device, the determined best topological order vector to describe a hierarchical relationship between the plurality of variables, and
• (I) learning, by the computing device, a Directed Acyclic Graph (DAG) based on the best topological order vector.