Numerical Evaluation of Gaussian Mixture Entropy

We develop an approximation method for the differential entropy h(X) of a q-component Gaussian mixture in Rn. We provide two examples of approximations using our method denoted by h¯C,mTaylor(X) and h¯CPolyfit(X). We show that h¯C,mTaylor(X) provides an easy-to-compute lower bound to h(X), while h¯CPolyfit(X) provides an accurate and efficient approximation to h(X). h¯CPolyfit(X) is more accurate than known bounds and is conjectured to be much more resilient than other approximations in high dimensions.