Multivariate responses using classification and regression trees systems and methods
AssigneeGE Capital Commercial Finance, Inc.
InventorTim K. Keyes
Life of this patent
Estimating the term…
Abstract
The present invention is a method of allowing inclusion of more than one variable in a Classification and Regression Tree (CART) analysis. The method includes predicting y using p exploratory variables, where y is a multivariate, continuous response vector, describing a probability density function at “parent” and “child” nodes using a multivariate normal distribution, which is a function of y, and defining a split function where “child” node distributions are individualized, compared to the parent node. In one embodiment a system is configured to implement the multivariate CART analysis for predicting behavior in a non-performing loan portfolio.
Claims19
A method of allowing inclusion of more than one variable in a classification and regression tree analysis for valuing a portfolio of non-performing loans and predicting future performance of the portfolio of non-performing loans using p explanatory variables, said method comprising the steps of:
- defining a first “parent” node representing the portfolio of non-performing loans;
- defining a split function to determine whether to create “child” nodes by generating a probability density function of the p explanatory variables at a corresponding parent node using a multivariate normal distribution;
- creating “child” nodes when a split function value for the corresponding parent node and child nodes indicates that the parent node is statistically non-homogeneous with respect to at least one of the p variables, wherein statistical non-homogeneity is determined by comparing the split function value for the corresponding parent and child nodes, and wherein statistical non-homogeneity indicates a greater predictive value included within at least one of the created child nodes as compared to the corresponding parent node;
- repeating said steps of defining a split function and creating “child” nodes until the parent node is statistically homogeneous;
- calculating y based on the p explanatory variables and the defined split functions, wherein y is a multivariate response vector representing a predicted recovery amount and a predicted timing value, the predicted recovery amount including at least one amount predicted to be recovered for each non-performing loan included within the portfolio of non-performing loans, the predicted timing value including at least one value predicting when each predicted recovery amount will be recovered, wherein the calculation is performed by a computer;
- and
- determining a value of the portfolio of non-performing loans based on the calculated y.
A system for performing multivariate classification and regression tree analysis for valuing a portfolio of non-performing loans using p explanatory variables, said system comprising:
- at least one computer having a user interface for enabling a user to input information relating to the portfolio of non-performing loans;
- a server in communication with the at least one computer, said server configured to read input information relating to the portfolio of non-performing loans, said server further configured to perform the steps of:
- defining a first “parent” node representing the portfolio of non-performing loans,
- defining a split function to determine whether to create “child” nodes by generating a probability density function of the p explanatory variables at a corresponding parent node using a multivariate normal distribution,
- creating “child” nodes when a split function value for the corresponding parent node and child nodes indicates that the parent node is statistically non-homogeneous with respect to at least one of the p variables, wherein statistical non-homogeneity is determined by comparing the split function value for the corresponding parent and child nodes, and wherein statistical non-homogeneity indicates a greater predictive value included within at least one of the created child nodes as compared to the corresponding parent node,
- repeating said steps of defining a split function and creating “child” nodes until the parent node is statistically homogeneous,
- calculating y based on the p explanatory variables and the defined split functions, wherein y is a multivariate response vector representing a predicted recovery amount and a predicted timing value, the predicted recovery amount including at least one amount predicted to be recovered for each non-performing loan included within the portfolio of non-performing loans, the predicted timing value including at least one value predicting when each predicted recovery amount will be recovered, and
- determining a value of the portfolio of non-performing loans based on the calculated y;
- and
- a network connecting said computer to said server.
Dependencies are inferred from the claim text.