On the stability and bias-variance analysis of kernel matrix learning

Stability and bias-variance analysis are two powerful tools to understand learning algorithms better. We use these tools to analyze learning the kernel matrix (LKM) algorithm. The motivation comes from: (i) LKM works in the transductive setting where both training and test data points are to be given apriori. Hence, it is worth knowing the stability of LKM under small variations in the data set and (ii) It has been argued that LKMs overfit the given data set. In particular we are interested in answering the following questions: (a) Is LKM a stable algorithm? (b) do they overfit (c) what is the bias behavior with different optimal kernels?. Our experimental results show that LKMs do not overfit the given data set. The stability analysis reveals that LKMs are unstable algorithms.