Multinomial Dirichlet Gaussian Process Model for Classification of Multidimensional Data
We present probabilistic multinomial Dirichlet
classification model for multidimensional data and Gaussian process
priors. Here, we have considered efficient computational method that
can be used to obtain the approximate posteriors for latent variables
and parameters needed to define the multiclass Gaussian process
classification model. We first investigated the process of inducing a
posterior distribution for various parameters and latent function by
using the variational Bayesian approximations and important sampling
method, and next we derived a predictive distribution of latent
function needed to classify new samples. The proposed model is
applied to classify the synthetic multivariate dataset in order to verify
the performance of our model. Experiment result shows that our model
is more accurate than the other approximation methods.
[1] C. E. Rasmussen, and C. K. I. Williams, Gaussian Processes for Machine
Learning, MIT Press, 2006.
[2] H. Nicklisch, and C. E. Rasmussen, “Approximation for Binary Gaussian
process Classification”, Journal of Machine Learning Research, vol 9, pp
2035-75, 2008.
[3] C. K. I. Williams, and D. Barber, “Bayesian Classification with Gaussian
Processes”, IEEE Tran. On PAMI, vol 12, pp 1342-1351, 1998.
[4] T. P. Minka, “Expectation Propagation for Approximate Bayesian
Inference”, In UAI, Morgan Kaufmann, pp 362-369, 2001.
[5] M. Opper, and O. Winther, “Gaussian Processes for Classification: Mean
Field Algorithms”, Neural Computation, vol 12 pp 2655-2204, 2000.
[6] L. Csato, E. Fokoue, M. Opper, and B. Schottky, “Efficient Approaches
to Gaussian Process Classification”, In Neural Information Processing
Systems, vol 12, pp 251-257, 2000.
[7] M. Girolami and S. Rogers, “Variational Bayesian Multinomial Probit
Regression with Gaussian Process Priors”, Neural Computation, vol 18
pp 1790-1817, 2006.
[1] C. E. Rasmussen, and C. K. I. Williams, Gaussian Processes for Machine
Learning, MIT Press, 2006.
[2] H. Nicklisch, and C. E. Rasmussen, “Approximation for Binary Gaussian
process Classification”, Journal of Machine Learning Research, vol 9, pp
2035-75, 2008.
[3] C. K. I. Williams, and D. Barber, “Bayesian Classification with Gaussian
Processes”, IEEE Tran. On PAMI, vol 12, pp 1342-1351, 1998.
[4] T. P. Minka, “Expectation Propagation for Approximate Bayesian
Inference”, In UAI, Morgan Kaufmann, pp 362-369, 2001.
[5] M. Opper, and O. Winther, “Gaussian Processes for Classification: Mean
Field Algorithms”, Neural Computation, vol 12 pp 2655-2204, 2000.
[6] L. Csato, E. Fokoue, M. Opper, and B. Schottky, “Efficient Approaches
to Gaussian Process Classification”, In Neural Information Processing
Systems, vol 12, pp 251-257, 2000.
[7] M. Girolami and S. Rogers, “Variational Bayesian Multinomial Probit
Regression with Gaussian Process Priors”, Neural Computation, vol 18
pp 1790-1817, 2006.
@article{"International Journal of Information, Control and Computer Sciences:71568", author = "Wanhyun Cho and Soonja Kang and Sangkyoon Kim and Soonyoung Park", title = "Multinomial Dirichlet Gaussian Process Model for Classification of Multidimensional Data", abstract = "We present probabilistic multinomial Dirichlet
classification model for multidimensional data and Gaussian process
priors. Here, we have considered efficient computational method that
can be used to obtain the approximate posteriors for latent variables
and parameters needed to define the multiclass Gaussian process
classification model. We first investigated the process of inducing a
posterior distribution for various parameters and latent function by
using the variational Bayesian approximations and important sampling
method, and next we derived a predictive distribution of latent
function needed to classify new samples. The proposed model is
applied to classify the synthetic multivariate dataset in order to verify
the performance of our model. Experiment result shows that our model
is more accurate than the other approximation methods.", keywords = "Multinomial dirichlet classification model, Gaussian
process priors, variational Bayesian approximation, Importance
sampling, approximate posterior distribution, Marginal likelihood
evidence.", volume = "9", number = "12", pages = "2453-5", }