Bayesian Tensor Regression with Rank Selection

Abstract

With the rapid development of technology the information we can collect is becoming more and more various Not only a vector or a matrix but also a multi-dimensional array Electroencephalography (EEG) and Magnetic Resonance Imaging (MRI) are examples Tensor regression treat the high-dimensional array data as explanatory variables Instead of variable selection rank selection is a major problem when we deal with tensor regression problem Choosing a suitable rank reduces the parameters we need whereas choosing too small a rank loses relevant information We can also observe the structure of the tensor through the rank at the same time Therefore rank selection plays an important role in tensor regression analogous to variable selection in regression problem rank selection can be done in a similar way George and McCulloch (1993) proposed Stochastic Search Variable Selection (SSVS) approach for variable selection They added indicator variables to linear regression model and solve the variable selection problem by the Bayesian method In this thesis different from the previous Bayesian tensor regression we follow the idea of SSVS and add the new indicator variables to the tensor regression model We find the suitable rank in the regression model based on these indicator variables by our Gibbs sampling algorithm At the end of the thesis we use MNIST database considering handwritten digits classification Our method and Lasso are compatible in terms of prediction accuracy Additionally we learned the structure of images through the tensor with different ranks

Date of Award	2021
Original language	English
Supervisor	Sheng-Mao Chang (Supervisor)