Abstract
Sampling technique is one of the asymptotically unbiased estimation approaches for inference in Bayesian probabilistic models. Markov chain Monte Carlo (MCMC) is a kind of sampling methods, which is widely used in the inference of complex probabilistic models. However, current MCMC methods can incur high autocorrelation of samples, which means that the samples generated by MCMC samplers are far from independent. In this paper, we propose the neural networks Langevin Monte Carlo (NNLMC) which makes full use of the flexibility of neural networks and the high efficiency of the Langevin dynamics sampling to construct a new MCMC sampling method. We propose the new update function to generate samples and employ appropriate loss functions to improve the performance of NNLMC during the process of sampling. We evaluate our method on a large diversity of challenging distributions and real datasets. Our results show that NNLMC is able to sample from the target distribution with low autocorrelation and rapid convergence, and outperforms the state-of-the-art MCMC samplers.
Highlights
In Bayesian machine learning, the inference of the complex probabilistic models generally needs the evaluation of the intractable integrals, which is challenging
1) We introduce the neural networks to Langevin dynamics to construct a novel Markov chain Monte Carlo sampler
In order to sample from the target distribution independently and rapidly, we propose neural networks Langevin Monte Carlo (NNLMC), which adjust the Langevin dynamics through neural networks to obtain samples, instead of obtaining samples using (2)
Summary
In Bayesian machine learning, the inference of the complex probabilistic models generally needs the evaluation of the intractable integrals, which is challenging. Magnetic Hamiltonian Monte Carlo (MHMC) [9] further adjusts the range of the exploration through the magnetic field, which reduces the autocorrelation of the samples and enhances the convergence speed. To improve the performance of the dynamics based MCMC methods, we design a new sampler, which is called neural networks Langevin Monte Carlo (NNLMC). The pure dynamics based MCMC methods only consider about the gradient information of the target distribution, while NNLMC uses the gradient information of the target distribution and learns to improve the performance of the sampler during the process of sampling. 1) We introduce the neural networks to Langevin dynamics to construct a novel Markov chain Monte Carlo sampler.
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