Determining variable attribution between instances of discrete series models

Abstract

A method of determining the effect that changes in input variables have on changes in the output of a time series model, between two instances of time, produces variable attributions that satisfy the Shapley fairness properties of efficiency, symmetry, linearity, and null player.

1 . A method of determining an effect, on a time series model prediction, of a change in a value of a first dynamic variable of a plurality of dynamic variables between a first instance in time and a second instance in time, the method comprising:
 generating, using the one or more processors, combinations of values for two or more dynamic variables of the plurality of dynamic variables of the time series model by setting each dynamic variable of the two or more dynamic variables to either a first value corresponding to the first instance in time or a second value corresponding to the second instance in time, wherein the two or more dynamic variables comprises the first dynamic variable;   for each combination of values of the combinations of values, generating, using the time series model, a first model prediction of the time series model using the first value of the first dynamic variable and a second model prediction of the time series model using the second value of the first dynamic variable;   for each combination of values of the combinations of values, assigning, using the one or more processors, a weight to a difference between the first model prediction and the second model prediction;   determining, using the one or more processors, a sum of the effect of the change in the first dynamic variable and effects of changes in each of the two or more dynamic variables, wherein the sum of the effect of the change is equal to a total change in model prediction between the first instance in time and the second instance in time;   determining, using the one or more processors, a sum of any of the two or more dynamic variables' effects, in each of multiple time series models, wherein the sum of any of the two or more dynamic variables' effects is equal to an effect of that dynamic variable for the sum of the multiple time series models; and   based on the determined sum of the effect and the sum of any of the two or more dynamic variables' effect, determining, using the one or more processors, the effect of the change of the values corresponding to the first instance in time and the second instance in time for the first dynamic variable.   
     
     
         2 . The method of  claim 1 , wherein the time series model further includes one or more static variables that do not change between the first instance in time and the second instance in time and the method further comprises:
 excluding, from the generating of the combinations of values, the one or more static variables that do not change between the first instance in time and the second instance in time.   
     
     
         3 . The method of  claim 1 , wherein the first model prediction comprises a predicted in a time series model of pooled debt securities. 
     
     
         4 . The method of  claim 1 , further comprising displaying a representation of the effect of the change of values corresponding to the first instance in time and the second instance in time of the first dynamic variable in conjunction with one or more effects of another dynamic variable of the two or more dynamic variables. 
     
     
         5 . The method of  claim 1 , further comprising:
 for each combination of values of the combinations of values, determining the effect of the change in the first dynamic variable corresponding to the first instance in time and the second instance in time as being equal to an effect of a change in another dynamic variable of the two or more dynamic variables based on a difference between a first model prediction of the time series model using a first value corresponding to the first instance in time for the other dynamic variable and a second model prediction of the time series model using a second value corresponding to the second instance in time for the other dynamic variable.   
     
     
         6 . The method of  claim 1 , further comprising:
 determining the effect of the first dynamic variable is zero when a change in the first dynamic variable produces zero change in the model prediction of the time series model.   
     
     
         7 . The method of  claim 1 , wherein the time series model prediction is implemented using a machine-learning model. 
     
     
         8 . A system for determining an effect, on a time series model prediction, of a change in a value of a first dynamic variable of a plurality of dynamic variables between a first instance in time and a second instance in time, the system comprising:
 a memory configured to store operations; and   a processor coupled to the memory and configured to perform the operations comprising:
 generating combinations of values for two or more dynamic variables of the plurality of dynamic variables of the time series model by setting each dynamic variable of the two or more dynamic variables to either a first value corresponding to the first instance in time or a second value corresponding to the second instance in time, wherein the two or more dynamic variables comprises the first dynamic variable; 
 for each combination of values of the combinations of values, generating a first model prediction of the time series model using the first value of the first dynamic variable and a second model prediction of the time series model using the second value of the first dynamic variable; 
 for each combination of values of the combinations of values, assigning a weight to a difference between the first model prediction and the second model prediction; 
 determining a sum of the effect of the change in the first dynamic variable and effects of changes in each of the two or more dynamic variables, wherein the sum of the effect of the change is equal to a total change in model prediction between the first instance in time and the second instance in time; 
 determining a sum of any of the two or more dynamic variables' effects, in each of multiple time series models, wherein the sum of any of the two or more dynamic variables' effects is equal to an effect of that dynamic variable for the sum of the multiple time series models; and 
 based on the determined sum of the effect and the sum of any of the two or more dynamic variables' effect, determining, using the one or more processors, the effect of the change of the values corresponding to the first instance in time and the second instance in time for the first dynamic variable 
   
     
     
         9 . The system of  claim 8 , wherein the time series model further includes one or more static variables that do not change between the first instance in time and the second instance in time and the operations further comprise:
 excluding, from the generating of all combinations, static variables that do not change between the first instance and the second instance.   
     
     
         10 . The system of  claim 8 , wherein the first model prediction comprises a predicted in a time series model of pooled debt securities. 
     
     
         11 . The system of  claim 8  further comprising an output device, wherein the operations further comprise displaying a representation of the effect of the change of values corresponding to the first instance in time and the second instance in time of the first dynamic variable in conjunction with one or more effects of another dynamic variable of the two or more dynamic variables. 
     
     
         12 . The system of  claim 8 , wherein the operations further comprise:
 for each combination of values of the combinations of values, determining the effect of the change in the first dynamic variable corresponding to the first instance in time and the second instance in time as being equal to an effect of a change in another dynamic variable of the two or more dynamic variables based on a difference between a first model prediction of the time series model using a first value corresponding to the first instance in time for the other dynamic variable and a second model prediction of the time series model using a second value corresponding to the second instance in time for the other dynamic variable.   
     
     
         13 . The system of  claim 8 , wherein the operations further comprise:
 determining the effect of the first dynamic variable is zero when a change in the first dynamic variable produces zero change in the model prediction of the time series model.   
     
     
         14 . The system of  claim 8 , wherein the time series model prediction is implemented using a machine-learning model. 
     
     
         15 . A non-transitory computer-readable storage device storing instructions, execution of which, by one or more processors, causes the one or more processors to perform a method of determining an effect, on a time series model prediction, of a change in a value of a first dynamic variable of a plurality of dynamic variables between a first instance in time and a second instance in time, the method comprising:
 generating combinations of values for two or more dynamic variables of the plurality of dynamic variables of the time series model by setting each dynamic variable of the two or more dynamic variables to either a first value corresponding to the first instance in time or a second value corresponding to the second instance in time, wherein the two or more dynamic variables comprises the first dynamic variable;   for each combination of values of the combinations of values, generating a first model prediction of the time series model using the first value of the first dynamic variable and a second model prediction of the time series model using the second value of the first dynamic variable;   for each combination of values of the combinations of values, assigning a weight to a difference between the first model prediction and the second model prediction;   determining a sum of the effect of the change in the first dynamic variable and effects of changes in each of the two or more dynamic variables, wherein the sum of the effect of the change is equal to a total change in model prediction between the first instance in time and the second instance in time;   determining a sum of any of the two or more dynamic variables' effects, in each of multiple time series models, wherein the sum of any of the two or more dynamic variables' effects is equal to an effect of that dynamic variable for the sum of the multiple time series models; and   based on the determined sum of the effect and the sum of any of the two or more dynamic variables' effect, determining, using the one or more processors, the effect of the change of the values corresponding to the first instance in time and the second instance in time for the first dynamic variable.   
     
     
         16 . The non-transitory computer-readable storage device of  claim 15 , wherein the time series model further includes one or more static variables that do not change between the first instance in time and the second instance in time and the method further comprising:
 excluding, from the generating of all combinations, static variables that do not change between the first instance and the second instance.   
     
     
         17 . The non-transitory computer-readable storage device of  claim 15 , wherein the first model prediction comprises a predicted in a time series model of pooled debt securities. 
     
     
         18 . The non-transitory computer-readable storage device of  claim 15 , wherein the method further comprising displaying a representation of the effect of the change of values corresponding to the first instance in time and the second instance in time of the first dynamic variable in conjunction with one or more effects of another dynamic variable of the two or more dynamic variables. 
     
     
         19 . The non-transitory computer-readable storage device of  claim 15 , wherein the method further comprising:
 for each combination of values of the combinations of values, determining the effect of the change in the first dynamic variable corresponding to the first instance in time and the second instance in time as being equal to an effect of a change in another dynamic variable of the two or more dynamic variables based on a difference between a first model prediction of the time series model using a first value corresponding to the first instance in time for the other dynamic variable and a second model prediction of the time series model using a second value corresponding to the second instance in time for the other dynamic variable.   
     
     
         20 . The non-transitory computer-readable storage device of  claim 15 , wherein the method further comprising:
 determining the effect of the first dynamic variable is zero when a change in the first dynamic variable produces zero change in the model prediction of the time series model.