Abstract:
|
In this talk, we extend a recent approach, called the generalized probabilistic principal component analysis, to model large incomplete matrices of correlated data. This research features scalable computation by decomposing Gaussian random field with multi-dimensional input domain into the products of orthogonal components with lower dimensional inputs. As various Gaussian processes with one dimensional input can be written as stochastic differential equations, we are able to apply the continuous-time Kalman Filter to compute the likelihood and predictive distribution with linear computational complexity without any approximation. We also develop a flexible way to model the mean function and derive the closed-form expressions of the marginal posterior distribution of the mean parameters. Analysis of simulated and real spatial data, spatio-temporal data and functional data confirms excellent performance of our approach.
|