Bayesian principal component analysis
First Claim
1. A computer-implemented method for performing Bayesian Principal Component Analysis comprising:
- inputting a data model;
receiving a prior distribution of the data model;
determining a posterior distribution based at least in part upon the prior distribution;
generating output data of optimal dimensionality based on the posterior distribution and Principal Component Analysis; and
, outputting the output data.
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Accused Products
Abstract
Bayesian principal component analysis. In one embodiment, a computer-implemented method for performing Bayesian PCA including inputting a data model; receiving a prior distribution of the data model; determining a posterior distribution; generating output data based on the posterior distribution (such as, a data model, a plurality of principal components, and/or a distribution); and, outputting the output data. In another embodiment, a computer-implemented method including inputting a mixture of a plurality of data spaces; determining a maximum number of principal components for each of the data spaces within the mixture; and, outputting the maximum number of principal components for each of the data spaces within the mixture.
42 Citations
25 Claims
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1. A computer-implemented method for performing Bayesian Principal Component Analysis comprising:
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inputting a data model;
receiving a prior distribution of the data model;
determining a posterior distribution based at least in part upon the prior distribution;
generating output data of optimal dimensionality based on the posterior distribution and Principal Component Analysis; and
,outputting the output data. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
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10. A computer-implemented method comprising:
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inputting a first data model of continuous variables;
receiving a prior distribution of the first data model;
determining a posterior distribution based at least in part upon the prior distribution;
generating a second data model of optimal dimensionality based on the posterior distribution and Principal Component Analysis; and
,outputting the second data model.
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11. A computer-implemented method comprising:
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inputting a mixture of a data space having a number of components;
determining a maximum number of principal components for each component of the mixture utilizing Bayesian Principal Component Analysis; and
,outputting the maximum number of principal components for each component of the mixture. - View Dependent Claims (12, 13, 14, 15)
receiving a prior distribution of the component;
determining a posterior distribution; and
,determining a predictive density, including an optimal density of the component, by marginalizing the posterior distribution over parameters of the component.
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13. The method of claim 12, wherein determining the predictive density comprises performing a Laplace approximation in conjunction with type II maximum likelihood.
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14. The method of claim 12, wherein determining the predictive density comprises performing a Markov chain Monte Carlo simulation based on Gibbs sampling.
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15. The method of claim 12, wherein determining the predictive density comprises performing a variational inference based on an approximation to the posterior distribution using a factorized distribution.
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16. A machine-readable medium having instructions stored thereon for execution by a processor to perform a method comprising:
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inputting a data model;
receiving a prior distribution of the data model;
determining a posterior distribution based at least in part upon the prior distribution;
generating output data of an optimal dimensionality based on the posterior distribution; and
outputting the data model. - View Dependent Claims (17, 18, 19, 20, 21)
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22. A computerized system comprising:
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a data model having a prior distribution;
output data of an optimal dimensionality selected from the group essentially consisting of;
a second data model, a distribution, and a plurality of principal components; and
,a generator to generate the output data based on the data model and the prior distribution thereof, by determining a posterior distribution based on the data model and the prior distribution. - View Dependent Claims (23, 24)
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25. A data modeling system, comprising:
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a data model having a prior distribution; and
,a generator operative utilizing Bayesian Principal Component Analysis to generate output data based upon the data model and at least one of a second data model, a distribution and a plurality of principal components.
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Specification