Estimating reciprocal partition functions to enable design space sampling

Estimating the Partition Function by Discriminance Sampling

Importance sampling (IS) and its variant, annealed IS (AIS) have been widely used for estimating the partition function in graphical models, such as Markov random fields and deep generative models. However, IS tends to underestimate the partition function and is subject to high variance when the proposal distribution is more peaked than the target distribution. On the other hand, “reverse” vers...

Partition Functions from Rao-Blackwellized Tempered Sampling

Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probabili...

Generalised partition functions: inferences on phase space distributions

It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed...

Sampling Design Optimization for Space-Time Kriging

Evolutionary Programming Based Stratified Design Space Sampling

Recently there have been advances in strati ed sampling techniques that attempt to enforce equal distributions not only across the design variables, but also onto the design space itself. This requires a numerically intensive optimization routine. Until now, no optimization strategy was able to distribute sample points evenly in the design space, but Evolutionary Algorithms (EA) act as an enabl...