We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes the graph. The model is designed to capture various signal structures through highly adaptive kernel that incorporates flexible polynomial function in spectral domain. Unlike most existing approaches, we learn such kernel, where setup enables learning without need eigen-decomposition Laplacian. In addi...

Recently, there has been a growing interest for mixed-categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies either by using continuous kernels (e.g., relaxation and Gower distance GP) or direct estimation of the correlation matrix. paper, we present kernel-based approach that extends exponential to handle variabl...

In this paper, an efficient Kernel based algorithm is developed with application in nonlinear system identification. Kernel adaptive filters are famous for their universal approximation property with Gaussian kernel, and online learning capabilities. The proposed adaptive step-size KLMS (ASS-KLMS) algorithm can exhibit universal approximation capability, irrespective of the choice of reproducin...

This thesis concerns the prediction of travel times between two points on a map, based on a combination of link-scale road network data and historical trip-scale data. The main idea is that the predictions using the road network data can be improved by a correction factor estimated from historical trip data. The correction factor is estimated both using a Machine Learning approach, more specifi...

We propose a new fast Gaussian summation algorithm for high-dimensional datasets with high accuracy. First, we extend the original fast multipole-type methods to use approximation schemes with both hard and probabilistic error. Second, we utilize a new data structure called subspace tree which maps each data point in the node to its lower dimensional mapping as determined by any linear dimensio...

We study how the speed of spread for an integrodifference equation depends on the dispersal pattern of individuals. When the dispersal kernel has finite variance, the central limit theorem states that convolutions of the kernel with itself will approach a suitably chosen Gaussian distribution. Despite this fact, the speed of spread cannot be obtained from the Gaussian approximation. We give sev...

Memory effects in the dynamics of open systems have been subject significant interest last decades. The methods involved quantifying this effect, however, are often difficult to compute and may lack analytical insight. With mind, we consider Gaussian collisional models, where non-Markovianity is introduced by means additional interactions between neighboring environmental units. By focusing on ...