Gradient information for representation and modeling

Motivated by Fisher divergence, in this paper we present a new set of information quantities which we refer to as gradient information. These measures serve as surrogates for classical information measures such as those based on logarithmic loss, Kullback-Leibler divergence, directed Shannon information, etc. in many data-processing scenarios of interest, and often provide significant computational advantage, improved stability, and robustness. As an example, we apply these measures to the Chow-Liu tree algorithm, and demonstrate remarkable performance and significant computational reduction using both synthetic and real data.