Numerical Evaluation of Gaussian Mixture Entropy

Key Points

• The research aims to develop efficient approximation methods for calculating the differential entropy of Gaussian mixtures.
• Developed two approximation methods: h¯C,mTaylor(X) and h¯CPolyfit(X).
• Evaluated the accuracy and efficiency of both approximations.
• Compared the new methods against existing bounds and approximations.
• h¯C,mTaylor(X) serves as a lower bound for the differential entropy h(X).
• h¯CPolyfit(X) provides accurate approximations, outperforming known bounds.
• h¯CPolyfit(X) is conjectured to be resilient in high-dimensional settings.