Uncertainty Quantification for the Gaussian Information Bottleneck

Abstract

This thesis applies techniques of uncertainty quantification to a low-dimensional case of the Gaussian Information Bottleneck (GIB) model. The GIB model has an input parameter of the joint probability distribution governing the relationship between the past X and the future Y , characterized by a 3x3 matrix, and has an output parameter of a 2x2 projection matrix mapping of X to a compressed version T. The output matrix is characterized by the values of its individual elements and by its rank, since at least one of its rows consists of a zero vector. Both theoretical and empirical analysis is conducted to determine how uncertainty in the input parameters affects the distribution of output parameters. The theoretical analysis finds analytic expressions of sensitivity in the output matrix to the input matrix and discusses theoretical underpinnings for these expressions. The empirical work finds that the significant errors in estimates of the output parameters should warrant the use of uncertainty quantification in experimental work.