Stable data-driven discovery of a symbolic expression

A computer system comprising:

• a memory;
• and
• a processor system implemented with a machine learning system communicatively coupled to the memory;
• the processor system configured to perform a method comprising:
• receiving a set of data, wherein the set of data comprises data of at least one explanatory variable and data of at least one response variable;
• receiving an input that identifies one or more relevant explanatory variables;
• determining, using the machine learning system, a symbolic expression that represents the received set of data and includes the identified one or more relevant explanatory variables such that the controller learns a relationship between the at least one explanatory variable and the at least one response variable;
• generating an output data that corresponds to a symbolic expression that represents the relationship between the at least one explanatory variable and the at least one response variable, wherein the symbolic expression is responsive to the identified one or more relevant explanatory variables, and the symbolic expression comprises a mathematically stable expression, the stable expression defined by the output data of the symbolic expression and a value of each internal state of the symbolic expression being limited within bounds,
• wherein the symbolic expression corresponds to an expression of minimal complexity, and
• wherein the output data that is based on the symbolic expression having the minimal complexity does not deviate from the received data of the response variables beyond a threshold.

A computer program product comprising a non-transitory computer-readable storage medium having program instructions embodied therewith, the program instructions readable by a processor system implemented with a machine learning system to cause the processor system to:

• receive a set of data, wherein the set of data comprises data of at least one explanatory variable and data of at least one response variable;
• receive an input that identifies one or more relevant explanatory variables;
• determining, using the machine learning system, a symbolic expression that represents the received set of data and includes the identified one or more relevant explanatory variables such that the controller learns, a relationship between the at least one explanatory variable and the at least one response variable;
• and
• generate an output data that corresponds to a symbolic expression that represents the relationship between the at least one explanatory variable and the at least one response variable, wherein the symbolic expression is responsive to the identified one or more relevant explanatory variables, and the symbolic expression comprises a mathematically stable expression, the stable expression defined by the output data of the symbolic expression and a value of each internal state of the symbolic expression being limited within bounds,
• wherein the symbolic expression corresponds to an expression of minimal complexity, and
• wherein the output data that is based on the symbolic expression having the minimal complexity does not deviate from the received data of the response variables beyond a threshold.

A computer-implemented method comprising:

• receiving, by a symbolic expression discovery engine implemented with a machine learning system, a set of data, wherein the set of data comprises data of at least one explanatory variable and data of at least one response variable;
• receiving, by the symbolic expression discovery engine, an input that identifies one or more relevant explanatory variables;
• determining, using the machine learning system, a symbolic expression that represents the received set of data and includes the identified one or more relevant explanatory variables such that the controller learns a relationship between the at least one explanatory variable and the at least one response variable;
• and
• generating, by the symbolic expression discovery engine, an output data that corresponds to a symbolic expression that represents the relationship between the at least one explanatory variable and the at least one response variable, wherein the symbolic expression is responsive to the identified one or more relevant explanatory variables, and the symbolic expression comprises a mathematically stable expression, the stable expression defined by the output data of the symbolic expression and a value of each internal state of the symbolic expression being limited within bounds,
• wherein the symbolic expression corresponds to an expression of minimal complexity, and
• wherein the output data that is based on the symbolic expression having the minimal complexity does not deviate from the received data of the response variables beyond a threshold.

A symbolic expression discovery engine system comprising:

• a plurality of interconnected processor elements defining a machine learning system, wherein connections between the processor elements are configured with numerical weights that correspond to a strength or weakness of a given connection, and the plurality of interconnected processor elements being configured to perform a method comprising:
• receiving a set of data, wherein the set of data comprises data of at least one explanatory variable and data of at least one response variable;
• receiving an input that identifies one or more relevant explanatory variables;
• determining, using the machine learning system, a symbolic expression that represents the received set of data and includes the identified one or more relevant explanatory variables such that the machine learning system learns a relationship between the at least one explanatory variable and the at least one response variable;
• and
• generating an output data that corresponds to a symbolic expression that represents the relationship between the at least one explanatory variable and the at least one response variable, wherein the symbolic expression is responsive to the identified one or more relevant explanatory variables, and the symbolic expression comprises a mathematically stable expression, the stable expression defined by the output data of the symbolic expression and a value of each internal state of the symbolic expression being limited within bound,
• wherein the symbolic expression corresponds to an expression of minimal complexity, and
• wherein the output data that is based on the symbolic expression having the minimal complexity does not deviate from the received data of the response variables beyond a threshold.