The Theory and Algorithm of Ergodic Inference
Approximate inference algorithm is one of the fundamental research fields in machine learning. The two dominant theoretical inference frameworks in machine learning are variational inference (VI) and Markov chain Monte Carlo (MCMC). However, because of the fundamental limitation in the theory, it is very challenging to improve existing VI and MCMC methods on both the computational scalability and statistical efficiency. To overcome this obstacle, we propose a new theoretical inference framework called ergodic Inference based on the fundamental property of ergodic transformations. The key contribution of this work is to establish the theoretical foundation of ergodic inference for the development of practical algorithms in future work.
Code (0)
등록된 구현이 없습니다.
Tasks
BIG-bench Machine LearningVariational InferenceSimilar Papers 제목 키워드 기반
Geometric Ergodicity in Modified Variations of Riemannian Manifold and Lagrangian Monte Carlo
Riemannian manifold Hamiltonian (RMHMC) and Lagrangian Monte Carlo (LMC) have emerged as powerful methods of Bayesian inference. Unlike Euclidean Hamiltonian Monte Carlo (EHMC) and the Metropolis-adjusted Langevin algori…
Bayesian InferenceErgodic Measure Preserving Flows
Training probabilistic models with neural network components is intractable in most cases and requires to use approximations such as Markov chain Monte Carlo (MCMC), which is not scalable and requires significant hyper-p…
Variational InferenceCentral Limit Theorem for ergodic averages of Markov chains \& the comparison of sampling algorithms for heavy-tailed distributions
Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478}, a vast literature has emerged on the …
Adam-like Algorithm with Smooth Clipping Attains Global Minima: Analysis Based on Ergodicity of Functional SDEs
In this paper, we prove that an Adam-type algorithm with smooth clipping approaches the global minimizer of the regularized non-convex loss function. Adding smooth clipping and taking the state space as the set of all tr…
Policy Optimization Algorithms in a Unified Framework
Policy optimization algorithms are crucial in many fields but challenging to grasp and implement, often due to complex calculations related to Markov decision processes and varying use of discount and average reward setu…