In this short course I will discuss exponential families, density estimation, and conditional estimators such as Gaussian Process classification, regression, and conditional random fields. The key point is that I will be providing a unified view of these estimation methods. In the second part I will discuss how moment matching techniques in Hilbert space can be used to design two-sample tests and independence tests in statistics. I will describe the basic principles and show how they can be used to correct covariate shift, select features, or merge databases.