Perpustakaan Digital ITB

In exploring engineering design based on physical experiments/stochastic simulators, noise might have significant effects on the observed sample that the use of deterministic surrogate model is not inadequate since its inability to distinguish the true function and the noise. Gaussian process (GP) is one type of surrogate models that have been extensively used in practice to handle noisy problems. In its standard procedure, the standard homoscedastic GP learn the noisy samples by assuming the noise level is uniform across the input spaces. This variant of GP however is not appropriate when the variance of the noise is varying in the input spaces, i.e., heteroscedastic. Various heteroscedastic GP (HGP) models have been developed to extend the GP model in learning heteroscedastic problems. This study focuses on this HGP model that does not require any additional replication, which has advantages in terms of experimental cost. One of the latest approaches to this variant of HGP model is called Improved Most Likely Heteroscedastic GP (IMLHGP) that have already showed good performances in modeling heteroscedastic problems. IMLHGP, as the state-of-the-art, also has a very attractive computational efficiency in training the model. However, the IMLHGP model is found to require high number of training samples as the model is observed to perform poorly when the number of training samples is rather low. This requirement is definitely unfavorable when the experimental cost is already expensive, such as in aerospace problems. In reducing the training sample size requirement, this thesis proposes a modified HGP model based on the IMLHGP by augmenting an extra distance-based nonparametric regression to tackle the wrongly interpolating noise level predictions that frequently appears in IMLHGP when the number of training samples is small. This proposed model called Nearest Neighbor Point Estimates HGP (NNPEHGP) is tested on several heteroscedastic problems, consisting of two mathematical functions, two real-world experimental datasets, two real-world analytical problems, and a stochastic simulator. The results show the superiority of NNPEHGP to the IMLHGP in terms of predictive accuracy and robustness, especially when the number of training samples is low. It is also found that NNPEHGP is much more stable in learning high dimensional heteroscedastic problems.