Decision theoretic approach to targeted solicitation by maximizing expected profit increases

Abstract

A decision theoretic approach to targeted solicitation, by maximizing expected profit increases, is disclosed. A decision theoretic model is used to identify a sub-population of a population to solicit, where the model is constructed to maximize an expected increase in profits. A decision tree in particular can be used as the model. The decision tree has paths from a root node to a number of leaf nodes. The decision tree has a split on a solicitation variable in every path from the root node to each leaf node. The solicitation variable has two values, a first value corresponding to a solicitation having been made, and a second value corresponding to a solicitation not having been made.

1 . A method for soliciting a sub-population of a population comprising: 
 identifying the sub-population to solicit by using a decision theoretic model, the decision theoretic model constructed to maximize an expected increase in profits; and,    soliciting the sub-population identified.    
     
     
         2 . The method of  claim 1 , wherein using the decision theoretic model comprises using a decision tree, the decision tree having a plurality of paths from a root node to a plurality of leaf nodes, each of the plurality of paths having a split on a solicitation variable having a first value corresponding to solicitation and a second value corresponding to non-solicitation.  
     
     
         3 . The method of  claim 2 , wherein the decision tree is constructed such that the split on the solicitation variable of each of the plurality of paths is a last split.  
     
     
         4 . The method of  claim 2 , wherein the decision tree is constructed such that the split on the solicitation variable of each of the plurality of paths is a first split.  
     
     
         5 . The method of  claim 2 , wherein each of the plurality of leaf nodes provides a value for a probability conditional on at least a purchase variable having a first value corresponding to purchase and a second value corresponding to non-purchase.  
     
     
         6 . The method of  claim 2 , wherein identifying the sub-population to solicit comprises: 
 constructing the decision tree from a sample of the population using a predetermined scoring criterion, each of the plurality of leaf nodes of the tree providing a value for a probability conditional on at least the purchase variable; and,    applying the decision tree against the population to identify the sub-population to solicit to maximize the expected increase in profits.    
     
     
         7 . The method of  claim 6 , wherein identifying the sub-population to solicit further initially comprises performing an experiment using the sample of the population to obtain values for the sample of the population for each of the solicitation variable and a purchase variable, the purchase variable having a first value corresponding to purchase and a second value corresponding to non-purchase.  
     
     
         8 . The method of  claim 1 , wherein soliciting the sub-population identified comprises mailing a solicitation to each of a plurality of members of the sub-population.  
     
     
         9 . The method of  claim 1 , wherein soliciting the sub-population identified comprises e-mailing a solicitation to each of a plurality of members of the sub-population.  
     
     
         10 . The method of  claim 1 , wherein soliciting the sub-population identified comprises calling each of a plurality of members of the sub-population.  
     
     
         11 . A method for constructing a decision theoretic model to identify a sub-population of a population to solicit to maximize an expected increase in profits, comprising: 
 performing an experiment using a sample of the population to obtain values for the sample of the population for each of a solicitation variable and a purchase variable, the solicitation variable having a first value corresponding to solicitation and a second value corresponding to non-solicitation, and the purchase variable having a first value corresponding to purchase and a second value corresponding to non-purchase;    constructing a decision tree as the decision theoretic model from the sample using a predetermined scoring criterion, the decision tree having a plurality of paths from a root node to a plurality of leaf nodes, each of the plurality of paths having a split on the solicitation variable, and each of the plurality of leaf nodes providing a value for a probability conditional on at least the purchase variable; and, applying the decision tree against the population to identify the sub-population to solicit to maximize the expected increase in profits.    
     
     
         12 . The method of  claim 11 , wherein performing the experiment comprises: 
 dividing the sample of the population into a non-solicitation group and a solicitation group;    setting the solicitation variable to the first value for each of a plurality of members of the solicitation group and to the second value for each of a plurality of members of the non-solicitation group;    soliciting the solicitation group; and,    setting the purchase variable to the first value for each of the plurality of members of the solicitation and the non-solicitation groups that made a purchase and to the second value for each of the plurality of members of the solicitation and the non-solicitation groups that did not make the purchase.    
     
     
         13 . The method of  claim 11 , wherein construction the decision tree comprises using a greedy approach.  
     
     
         14 . The method of  claim 11 , wherein the predetermined scoring criterion is a holdout criterion.  
     
     
         15 . The method of  claim 11 , wherein the predetermined scoring criterion is a cross-validation holdout criterion.  
     
     
         16 . The method of  claim 11 , wherein the predetermined scoring criterion is a marginal likelihood criterion.  
     
     
         17 . The method of  claim 11 , wherein the predetermined scoring criterion is an adjusted marginal likelihood criterion.  
     
     
         18 . The method of  claim 11 , wherein the split on the solicitation variable of each of the plurality of paths is a last split.  
     
     
         19 . The method of  claim 18 , wherein constructing the decision tree comprises: 
 initializing the decision tree with an initial single leaf node as the root node;    using the greedy approach to construct the decision tree with no splits on the solicitation variable, the decision tree after construction using the greedy approach having a plurality of interim leaf nodes; and,    performing a split on the solicitation variable at each of the plurality of interim leaf nodes to generate the plurality of leaf nodes.    
     
     
         20 . The method of  claim 11 , wherein the split on the solicitation variable of each of the plurality of paths is a first split at the root node.  
     
     
         21 . The method of  claim 20 , wherein constructing the decision tree comprises: 
 initializing the decision tree with the first split at the root node on the solicitation variable; and,    using a greedy approach to finish constructing the decision tree.    
     
     
         22 . The method of  claim 11 , further comprising soliciting the sub-population identified.  
     
     
         23 . The method of  claim 11 , wherein the method is performed by execution of a computer program by a processor from a computer-readable medium.  
     
     
         24 . A method for constructing a decision theoretic model to identify a sub-population of a population to solicit to maximize an expected increase in profits, comprising: 
 performing an experiment using a sample of the population to obtain values for the sample of the population for each of a solicitation variable and a purchase variable, the solicitation variable having a first value corresponding to solicitation and a second value corresponding to non-solicitation, and the purchase variable having a first value corresponding to purchase and a second value corresponding to non-purchase;    constructing a decision tree as the decision theoretic model from the sample using a greedy approach and a marginal likelihood scoring criterion, the decision tree having a plurality of paths from a root node to a plurality of leaf nodes, each of the plurality of paths having a last split on the solicitation variable, and each of the plurality of leaf nodes providing a value for a probability conditional on at least the purchase variable; and,    applying the decision tree against the population to identify the sub-population to solicit to maximize the expected increase in profits.    
     
     
         25 . The method of  claim 24 , wherein performing the experiment comprises: 
 dividing the sample of the population into a non-solicitation group and a solicitation group;    setting the solicitation variable to the first value for each of a plurality of members of the solicitation group and to the second value for each of a plurality of members of the non-solicitation group;    soliciting the solicitation group; and,    setting the purchase variable to the first value for each of the plurality of members of the solicitation and the non-solicitation groups that made a purchase and to the second value for each of the plurality of members of the solicitation and the non-solicitation groups that did not make the purchase.    
     
     
         26 . The method of  claim 24 , further comprising soliciting the sub-population identified by one of: calling each of a plurality of members of the sub-population, mailing a solicitation to each of the plurality of members of the sub-population, and e-mailing the solicitation to each of the plurality of members of the sub-population.  
     
     
         27 . The method of  claim 24 , wherein the method is performed by execution of a computer program by a processor from a computer-readable medium.