The primary focus of my research is to develop nonparametric tools to measure (statistical) dependence between two or more random variables. I am involved in developing algorithms for information theoretic learning and adaptive signal processing. I have also partially worked on echo state networks and compressed sensing.

Fields of interest

• Dependence measure
• A measure of dependence should satisfy a set of desirable properties that were first proposed by Renyi and later extended or modified by many other authors. A measure of independence must achieve its minimum value (which is preferably 0) if and only if the random variables are (mutually) independent. However, a measure of dependence differs from a measure of independence in the fact that it should also be bounded (preferably between 0 and 1) with a clear explanation of what happens when the upper bound is reached. For example, maximal correlation, which is a valid dependence measure, reaches its maximum value when the random variables share a functional relationship. Another example of a valid dependence measure is the mutual information, properly normalized.
  
• Conditional independence and causality
• Detecting conditional independence is a similar but slightly difficult problem than detecting just independence. The problem involves three random variables and the objective is to decide whether two variables are independent or not, when value of the third variable is known. A simple example is the random variables U=XZ and V=YZ where X,Y and Z are three mutually independent random variables. U and V are not independent as they share a common random variable Z. However, they are conditionally independent given Z is known i.e. Z=z. [ref]
  
• Information Theoretic Learning [course]
  
• Signal Processing in Reproducing Kernel Hilbert Space [wikipedia]
  
• Adaptive Signal Processing [course]