Estimating the Partition Function of Graphical Models Using Langevin Importance Sampling
نویسندگان
چکیده
Graphical models are powerful in modeling a variety of real-world applications. Computing the partition function of a graphical model is known as an NP-hard problem for a general graph. A few sampling algorithms like Markov chain Monte Carlo (MCMC), Simulated Annealing Sampling (SAS), Annealed Importance Sampling (AIS) are developed to approximate the partition function. This paper presents a new Langevin Importance Sampling (LIS) algorithm to address this challenge. LIS performs a random walk in the configuration-temperature space guided by the Langevin equation and estimates the partition function using all the samples generated during the random walk at all the temperatures, as opposed to the other configuration-temperature sampling methods, which use only the samples at a specific temperature. Experimental results on several benchmark graphical models show that LIS can obtain much more accurate partition function than the others. LIS performs especially well on relatively large graphical models or those with a large number of local optima.
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