Minimum Relative Entropy Inference for Normal and Monte Carlo Distributions
This work addresses inference challenges in statistics and machine learning, but it appears incremental as it builds on existing entropy-based methods.
The paper tackled the problem of inferring distributions from partial information by representing affine sub-manifolds as minimum relative entropy sub-manifolds, resulting in analytical formulas for normal distributions and improved Monte Carlo simulations for generalized expectations.
We represent affine sub-manifolds of exponential family distributions as minimum relative entropy sub-manifolds. With such representation we derive analytical formulas for the inference from partial information on expectations and covariances of multivariate normal distributions; and we improve the numerical implementation via Monte Carlo simulations for the inference from partial information of generalized expectation type.