Predictive engine for generating multivariate predictive responses
A predictive engine includes an optimizer and a predictor. The optimizer is configured to receive an observed dataset having inputs and multivariate responses and determine latent response variables based on the predictive inputs and the multivariate responses. The optimizer is further configured to select latent response variables, measure dependencies between multivariate responses, estimate coefficients that relate the input predictors to determined latent response variables, and correlate dependencies and coefficients with the latent response variables. The predictor is configured to generate a predictive distribution of probabilities for the latent variables, map the probabilities to multivariate responses, generate a predictive distribution of probabilities for the multivariate responses, and determine at least one optimized input from the multivariate responses.
1. A predictive engine for generating optimized multivariate responses, the predictive engine comprising:
an optimizer configured to receive an observed dataset having inputs and multivariate responses;
select latent response variables;
measure dependencies between multivariate responses;
correlate the dependencies with the latent response variables; and
a predictor configured to generate a predictive distribution of probabilities for the latent variables, map the probabilities to multivariate responses, generate a predictive distribution of probabilities for the multivariate responses, and determine at least one optimized input from the multivariate responses.
2. The predictive engine of claim 1 wherein the optimizer is further configured to:
estimate coefficients that relate the input predictors to determined latent response variables; and
correlate the coefficients with the latent response variables.
3. The predictive engine of claim 2 wherein the dependencies are measured by creating a covariance matrix.
4. The predictive engine of claim 2 wherein the dependencies and coefficients are correlated with the latent response variables using joint posterior density distribution.
5. The predictive engine of claim 1 wherein the optimizer is further configured to:
(i) initialize a latent response variable vector with respect to an input predictor and multivariate response vector;
(ii) measure dependency between a latent response variable and a multivariate response;
(iii) estimate a coefficient that relates an input predictor to the latent response variable;
(iv) correlate the dependency measure and the estimate coefficient with the latent response variable; and
(v) select a latent response variable.
6. The predictive engine of claim 5 wherein the dependency measure and the estimate coefficient is correlated with the latent variable using a joint posterior density distribution.
7. The predictive engine of claim 5 wherein steps (ii)-(v) are repeated until convergence.
8. The predictive engine of claim 1 wherein the multivariate responses are one of multivariate binary responses and multivariate categorical responses.
9. The predictive engine of claim 1 wherein the predictive distribution is a posterior predictive distribution.
10. The predictive engine of claim 1 wherein the probabilities are mapped to the multivariate responses by generating a conditional distribution.
11. A method for generating optimized multivariate responses, the method comprising:
receiving an observed dataset having input predictors and multivariate responses;
selecting latent response variables;
measuring dependencies between multivariate responses;
correlating dependencies with the latent response variables;
generating a predictive distribution of probabilities for the latent variables;
mapping the probabilities to multivariate responses, generate a predictive distribution of probabilities for the multivariate responses; and
determining at least one optimized input from the multivariate responses.
12. The method of claim 11 further comprising:
estimating coefficients that relate the input predictors to determined latent response variables; and
correlating coefficients with the latent response variables.
13. The method of claim 11 further comprising:
(i) initializing a latent response variable vector with respect to an input predictor and multivariate response vector;
(ii) measuring dependency between a latent response variable and a multivariate response;
(iii) estimating a coefficient that relates an input predictor to the latent response variable;
(iv) correlating the dependency measure and the estimate coefficient with the latent response variable; and
(v) selecting a latent response variable.
14. The method of claim 13 wherein steps (ii)-(v) are repeated until convergence.
15. A non-transitory computer readable storage medium comprising a set of computer instructions executable by a processor for generating optimized multivariate responses, the computer instructions configured to:
receive an observed dataset having inputs and multivariate responses;
select latent response variables;
measure dependencies between multivariate responses;
correlate the dependencies with the latent response variables;
generate a predictive distribution of probabilities for the latent variables;
map the probabilities to multivariate responses, generate a predictive distribution of probabilities for the multivariate responses; and
determine at least one optimized input from the multivariate responses.
16. The non-transitory computer readable storage medium as recited in claim 15 further including computer instructions configured to:
estimate coefficients that relate the input predictors to determined latent response variables; and
correlate the coefficients with the latent response variables.
17. The non-transitory computer readable storage medium as recited in claim 15 further including computer instructions configured to:
(i) initialize a latent response variable vector with respect to an input predictor and multivariate response vector;
(ii) measure dependency between a latent response variable and a multivariate response;
(iii) estimate a coefficient that relates an input predictor to the latent response variable;
(iv) correlate the dependency measure and the estimate coefficient with the latent response variable; and
(v) select a latent response variable.
18. The non-transitory computer readable storage medium of claim 17 wherein the computer instructions are further configured to:
select latent response variables;
measure dependencies between multivariate responses;
estimate coefficients that relate the input predictors to determined latent response variables; and
correlate dependencies and coefficients with the latent response variables.
19. The non-transitory computer readable storage medium as recited in claim 18 wherein the dependencies are measured by creating a covariance matrix.
20. The non-transitory computer readable storage medium as recited in claim 17 wherein the multivariate responses are one of multivariate binary responses and multivariate categorical responses.