Directed acyclic graph machine learning system

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
• compute a sum of square and cross products (SSCP) matrix from variable values of a plurality of variables defined for a plurality of observation vectors, wherein the SSCP matrix has a dimension of Nv×Nv, where Nv is a number of the plurality of variables;
• initialize a topological order vector that defines a topological order for the plurality of variables;
• compute an initial loss value using the initialized topological order vector and the computed SSCP matrix;
• learn a directed acyclic graph by
• (A) selecting a neighbor determination method;
• (B) determining a next topological order vector using the selected neighbor determination method;
• (C) computing a loss value using the determined next topological order vector and the computed SSCP matrix;
• (D) repeating (B) and (C) until each topological order vector is determined in (B) based on the selected neighbor determination method;
• (E) determining a best topological order vector from each determined next topological order vector based on having a minimum value for the computed loss value;
• and
• (F) computing an adjacency matrix using the determined best topological order vector and the computed SSCP matrix, wherein the adjacency matrix has the dimension of Nv×Nv, wherein values in the computed adjacency matrix indicate whether a variable is a parent of another variable;
• and
• (G) output the computed adjacency matrix, wherein data in the computed adjacency matrix defines the directed acyclic graph based on the plurality of observation vectors, wherein the directed acyclic graph describes relationships among the plurality of variables.

A method of learning a directed acyclic graph, the method comprising:

• computing, by a computing device, a sum of square and cross products (SSCP) matrix from variable values of a plurality of variables defined for a plurality of observation vectors, wherein the SSCP matrix has a dimension of Nv×Nv, where Nv is a number of the plurality of variables;
• initializing, by the computing device, a topological order vector that defines a topological order for the plurality of variables;
• computing, by the computing device, an initial loss value using the initialized topological order vector and the computed SSCP matrix;
• learning, by the computing device, a directed acyclic graph by
• (A) selecting, by the computing device, a neighbor determination method;
• (B) determining, by the computing device, a next topological order vector using the selected neighbor determination method;
• (C) computing, by the computing device, a loss value using the determined next topological order vector and the computed SSCP matrix;
• (D) repeating, by the computing device, (B) and (C) until each topological order vector is determined in (B) based on the selected neighbor determination method;
• (E) determining, by the computing device, a best topological order vector from each determined next topological order vector based on having a minimum value for the computed loss value;
• and
• (F) computing, by the computing device, an adjacency matrix using the determined best topological order vector and the computed SSCP matrix, wherein the adjacency matrix has the dimension of Nv×Nv, wherein values in the computed adjacency matrix indicate whether a variable is a parent of another variable;
• and
• (G) outputting, by the computing device, the computed adjacency matrix, wherein data in the computed adjacency matrix defines the directed acyclic graph based on the plurality of observation vectors, wherein the directed acyclic graph describes relationships among the plurality of variables.