Estimating Local Function Complexity via Mixture of Gaussian Processes

Real world data often exhibit inhomogeneity, e.g., the noise level, the sampling distribution or the complexity of the target function may change over the input space. In this paper, we try to isolate local function complexity in a practical, robust way. This is achieved by first estimating the locally optimal kernel bandwidth as a functional relationship. Specifically, we propose Spatially Adaptive Bandwidth Estimation in Regression (SABER), which employs the mixture of experts consisting of multinomial kernel logistic regression as a gate and Gaussian process regression models as experts. Using the locally optimal kernel bandwidths, we deduce an estimate to the local function complexity by drawing parallels to the theory of locally linear smoothing. We demonstrate the usefulness of local function complexity for model interpretation and active learning in quantum chemistry experiments and fluid dynamics simulations.Comment: 19 pages, 16 figure

Application of Dirichlet Distribution for Polytopic Model Estimation

The polytopic model (PM) structure is often used in the areas of automatic control and fault detection and isolation (FDI). It is an alternative to the multiple model approach which explicitly allows for interpolation among local models. This thesis proposes a novel approach to PM estimation by modeling the set of PM weights as a random vector with Dirichlet Distribution (DD). A new approximate (adaptive) PM estimator, referred to as a Quasi-Bayesian Adaptive Kalman Filter (QBAKF) is derived and implemented. The model weights and state estimation in the QBAKF is performed adaptively by a simple QB weights\u27 estimator and a single KF on the PM with the estimated weights. Since PM estimation problem is nonlinear and non-Gaussian, a DD marginalized particle filter (DDMPF) is also developed and implemented similar to MPF. The simulation results show that the newly proposed algorithms have better estimation accuracy, design simplicity, and computational requirements for PM estimation

Application of Dirichlet Distribution for Polytopic Model Estimation

The polytopic model (PM) structure is often used in the areas of automatic control and fault detection and isolation (FDI). It is an alternative to the multiple model approach which explicitly allows for interpolation among local models. This thesis proposes a novel approach to PM estimation by modeling the set of PM weights as a random vector with Dirichlet Distribution (DD). A new approximate (adaptive) PM estimator, referred to as a Quasi-Bayesian Adaptive Kalman Filter (QBAKF) is derived and implemented. The model weights and state estimation in the QBAKF is performed adaptively by a simple QB weights\u27 estimator and a single KF on the PM with the estimated weights. Since PM estimation problem is nonlinear and non-Gaussian, a DD marginalized particle filter (DDMPF) is also developed and implemented similar to MPF. The simulation results show that the newly proposed algorithms have better estimation accuracy, design simplicity, and computational requirements for PM estimation