COMPACT REPRESENTATION OF MULTIVARIATE POSTERIOR PROBABILITY DISTRIBUTION FROM SIMULATED SAMPLES

• US 20140279819A1
• Filed: 03/18/2014
• Published: 09/18/2014
• Est. Priority Date: 03/15/2013
• Status: Active Grant

• Current Assignee: SAS Institute Incorporated
• Original Assignee: SAS Institute Incorporated
• Inventors: Macaro, Christian, Chvosta, Jan, Little, Mark Roland
• Granted Patent: US 9,672,193 B2
• Time in Patent Office: Days
• US Class Current: 706/52
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06N 7/01 Probabilistic graphical models, e.g. probabilistic networks

Abstract

Various embodiments are directed to techniques for selecting a subset of a set of simulated samples. A computer-program product including instructions to cause a computing device to order a plurality of UPDFs by UPDF value, wherein the plurality of UPDFs is associated with a chain of draws of a set of simulated samples, wherein each draw comprises multiple parameters and the UPDF values map to parameter values of the parameters; select a subset of the plurality of UPDFs based on the subset of the plurality of UPDFs having UPDF values within a range corresponding to a range of parameter values to include in a subset of the set of simulated samples; and transmit an indication of a draw comprising parameters having parameter values to include in the subset of the set of simulated samples, wherein the indication identifies the draw by associated UPDF. Other embodiments are described and claimed.

Claims

1. A computer-program product tangibly embodied in a non-transitory machine-readable storage medium, the computer-program product including instructions operable to cause a computing device to perform operations including:

order a plurality of un-normalized probability density functions (UPDFs) by a UPDF value of each UPDF, wherein the plurality of UPDFs is associated with a chain of draws of a set of simulated samples, wherein each draw comprises multiple parameters, and wherein the UPDF values of the plurality of UPDFs map to the parameter values of the of the chain of draws;

select a subset of the plurality of UPDFs based on the subset of the plurality of UPDFs having UPDF values within a range of UPDF values that corresponds to a specified range of parameter values to include in a subset of the set of simulated samples; and

transmit to another computing device an indication of at least one draw of the chain comprising parameters having values to include in the subset of the set of simulated samples, wherein the indication identifies the at least one draw by referring to at least one UPDF of the plurality of UPDFs associated with the at least one draw.

2. The computer-program product of claim 1, the computing device caused to perform operations including receive the UPDF values of the plurality of UPDFs from the other computing device, wherein the UPDF values are generated by the other computing device from at least a posterior probability distribution derived by the computing device.

3. The computer-program product of claim 1, wherein:

the other computing device is one of a plurality of computing devices operated in parallel to each generate a portion of the chain and a portion of the plurality of UPDFs from a posterior probability distribution; and

the computing device is caused to perform operations including;

receive a portion of the plurality of UPDFs from each computing device of the plurality of computing devices; and

transmit at least a portion of the indication of at least one draw of the chain to each computing device of the plurality of computing devices.

4. The computer-program product of claim 3, the computing device caused to perform operations including:

receive parameter values of a draw of the chain from each computing device of the plurality of computing devices; and

generate the subset of the set of simulated samples from the parameter values.

5. The computer-program product of claim 1, the computing device caused to perform operations including:

generate a portion of the chain and a portion of the plurality of UPDFs from a posterior probability distribution derived by a Bayesian analysis; and

select parameter values of parameters of a draw of the portion of the chain to include in the subset of the set of simulated samples based on an association of the draw with a UPDF of the subset of the plurality of UPDFs.

6. The computer-program product of claim 1, the computing device caused to perform operations including:

receive an indication of the specified range of parameter values from a viewing device; and

transmit the subset of the set of simulated samples to the viewing device.

7. A computer-implemented method comprising:

ordering, on a computing device, a plurality of un-normalized probability density functions (UPDFs) by a UPDF value of each UPDF, wherein the plurality of UPDFs is associated with a chain of draws of a set of simulated samples, wherein each draw comprises multiple parameters, and wherein the UPDF values of the plurality of UPDFs map to the multivariate parameter values of the parameters of the chain of draws;

selecting, on the computing device, a subset of the plurality of UPDFs based on the subset of the plurality of UPDFs having UPDF values within a range of UPDF values that corresponds to a specified range of parameter values to include in a subset of the set of simulated samples; and

transmitting, from the computing device, to another computing device an indication of at least one draw of the chain comprising parameters having values to include in the subset of the set of simulated samples, wherein the indication identifies the at least one draw by referring to at least one UPDF of the plurality of UPDFs associated with the at least one draw.

8. The computer-implemented method of claim 7, comprising receiving, at the computing device, the UPDF values of the plurality of UPDFs from the other computing device, wherein the UPDF values are generated by the other computing device from at least a posterior probability distribution derived by the computing device.

9. The computer-implemented method of claim 7, wherein:

the other computing device is one of a plurality of computing devices operated in parallel to each generate a portion of the chain and a portion of the plurality of UPDFs from a posterior probability distribution; and

the method comprises;

receiving, at the computing device, a portion of the plurality of UPDFs from each computing device of the plurality of computing devices; and

transmitting, from the computing device, at least a portion of the indication of at least one draw of the chain to each computing device of the plurality of computing devices.

10. The computer-implemented method of claim 9, wherein:

receiving, at the computing device, parameter values of a draw of the chain from each computing device of the plurality of computing devices; and

generating, on the computing device, the subset of the set of simulated samples from the parameter values.

11. The computer-implemented method of claim 7, wherein:

generating, on the computing device, a portion of the chain and a portion of the plurality of UPDFs from a posterior probability distribution derived by a Bayesian analysis; and

selecting, on the computing device, parameter values of parameters of a draw of the portion of the chain to include in the subset of the set of simulated samples based on an association of the draw with a UPDF of the subset of the plurality of UPDFs.

12. The computer-implemented method of claim 7, comprising:

receiving an indication of the specified range of parameter values from a viewing device; and

transmitting the subset of the set of simulated samples to the viewing device.

13. An apparatus comprising:

a processor component;

a ranking component for execution by the processor component to;

order a plurality of un-normalized probability density functions (UPDFs) by a UPDF value of each UPDF, wherein the plurality of UPDFs is associated with a chain of draws of a set of simulated samples, wherein each draw comprises multiple parameters, and wherein the UPDF values of the plurality of UPDFs map to the multivariate parameter values of the parameters of the chain of draws; and

select a subset of the plurality of UPDFs based on the subset of the plurality of UPDFs having UPDF values within a range of UPDF values that corresponds to a specified range of parameter values to include in a subset of the set of simulated samples; and

a communications component for execution by the processor component to transmit to another computing device an indication of at least one draw of the chain comprising parameters having values to include in the subset of the set of simulated samples, wherein the indication identifies the at least one draw by referring to at least one UPDF of the plurality of UPDFs associated with the at least one draw.

14. The apparatus of claim 13, wherein the communications component receives the UPDF values of the plurality of UPDFs from the other computing device, wherein the UPDF values are generated by the other computing device from at least a posterior probability distribution derived by the computing device.

15. The apparatus of claim 13, wherein:

the other computing device is one of a plurality of computing devices operated in parallel to each generate a portion of the chain and a portion of the plurality of UPDFs from a posterior probability distribution; and

the communications component receives a portion of the plurality of UPDFs from each computing device of the plurality of computing devices, and transmits at least a portion of the indication of at least one draw of the chain to each computing device of the plurality of computing devices.

16. The apparatus of claim 15, wherein:

the communications component receives parameter values of a draw of the chain from each computing device of the plurality of computing devices; and

the apparatus comprises a simulation component for execution by the processor component to generate the subset of the set of simulated samples from the parameter values.

17. The apparatus of claim 13, comprising:

a simulation component for execution by the processor component to generate a portion of the chain and a portion of the plurality of UPDFs from a posterior probability distribution derived by a Bayesian analysis; and

a selection component for execution by the processor component to select parameter values of parameters of a draw of the portion of the chain to include in the subset of the set of simulated samples based on an association of the draw with a UPDF of the subset of the plurality of UPDFs.

18. The apparatus of claim 13, wherein the communications component receives an indication of the specified range of parameter values from a viewing device, and transmits the subset of the set of simulated samples to the viewing device.

19. A computer-program product tangibly embodied in a non-transitory machine-readable storage medium, the computer-program product including instructions operable to cause a computing device to perform operations including:

generate a portion of a set of simulated samples from a posterior probability distribution, wherein the set of simulated samples comprises a chain of draws of parameters;

generate a portion of a set of un-normalized probability density functions (UPDFs), wherein each UPDF of the set of UPDFs is associated with one of the draws of the chain;

select at least one draw of the chain to include in a subset of the set of simulated samples based on an indication of the at least one chain as included in the subset, wherein the indication specifies the at least one draw by at least one UPDF of the set of UPDFs, and wherein the at least one UPDF is associated with the at least one draw; and

transmit parameter values of the at least one draw to a requesting device based on the indication.

20. The computer-program product of claim 19, the computing device caused to perform operations including receive the indication of the at least one chain as included in the subset from the requesting device.

21. The computer-program product of claim 20, the computing device caused to perform operations including:

coordinate with another computing device to derive the posterior probability distribution in parallel with the other computing device deriving the posterior probability distribution;

generate the portion of the set of simulated samples in parallel with the other computing device generating another portion of the set of simulated samples; and

generate the portion of the set of UPDFs in parallel with the other computing device generating another portion of the set of UPDFs.

22. The computer-program product of claim 21, the computing device caused to perform operations including coordinate with the other computing device to perform a Bayesian analysis to derive the posterior probability distribution from at least a prior probability distribution in parallel with the other computing device performing the Bayesian analysis to derive the posterior probability distribution from at least the prior probability distribution.

23. The computer-program product of claim 22, the computing device caused to perform operations including distribute at least the prior probability distribution to at least the other computing device.

24. The computer-program product of claim 19, the computing device caused to perform operations including:

receive at least one other draw of the chain from the other computing device, wherein the at least one other draw is selected to include in the subset based on another indication of the at least one other chain as included in the subset, wherein the other indication specifies the at least one other draw by at least one other UPDF of the set of UPDFs, and wherein the at least one other UPDF is associated with the at least one other draw; and

combine parameters values of the at least one draw with parameter values of the at least one other draw, wherein transmitting the parameter values of the at least one draw to the requesting device comprises transmitting the parameters of the at least one other draw to the requesting device.

25. A computer-implemented method comprising:

generating, at a computing device, a portion of a set of simulated samples from a posterior probability distribution, wherein the set of simulated samples comprises a chain of draws of parameters;

generating, at the computing device, a portion of a set of un-normalized probability density functions (UPDFs), wherein each UPDF of the set of UPDFs is associated with one of the draws of the chain;

select, at the computing device, at least one draw of the chain to include in a subset of the set of simulated samples based on an indication of the at least one chain as included in the subset, wherein the indication specifies the at least one draw by at least one UPDF of the set of UPDFs, and wherein the at least one UPDF is associated with the at least one draw; and

transmitting, from the computing device, parameter values of the at least one draw to a requesting device based on the indication.

26. The computer-implemented method of claim 25, comprising receiving, at the computing device, the indication of the at least one chain as included in the subset from the requesting device.

27. The computer-implemented method of claim 26, comprising:

coordinating with another computing device to derive the posterior probability distribution in parallel with the other computing device deriving the posterior probability distribution;

generating, at the computing device, the portion of the set of simulated samples in parallel with the other computing device generating another portion of the set of simulated samples; and

generating, at the computing device, the portion of the set of UPDFs in parallel with the other computing device generating another portion of the set of UPDFs.

28. The computer-implemented method of claim 27, comprising coordinating with the other computing device to perform of a Bayesian analysis to derive the posterior probability distribution from at least a prior probability distribution in parallel with the other computing device performing the Bayesian analysis to derive the posterior probability distribution from at least the prior probability distribution.

29. The computer-implemented method of claim 28, comprising distributing, from the computing device, at least the prior probability distribution to at least the other computing device.

30. The computer-implemented method of claim 25, comprising:

receiving, at the computing device, at least one other draw of the chain from the other computing device, wherein the at least one other draw is selected to include in the subset based on another indication of the at least one other chain as included in the subset, wherein the other indication specifies the at least one other draw by at least one other UPDF of the set of UPDFs, and wherein the at least one other UPDF is associated with the at least one other draw; and

combining, at the computing device, parameters values of the at least one draw with parameter values of the at least one other draw, wherein transmitting the parameter values of the at least one draw to the requesting device comprises transmitting the parameters of the at least one other draw to the requesting device.