Nonreversible MCMC from conditional invertible transforms: a complete recipe with convergence guarantees

• URL: http://arxiv.org/abs/2012.15550v2
• Date: Mon, 29 Mar 2021 12:30:47 GMT
• Title: Nonreversible MCMC from conditional invertible transforms: a complete recipe with convergence guarantees
• Authors: Achille Thin, Nikita Kotelevskii, Christophe Andrieu, Alain Durmus, Eric Moulines, Maxim Panov
• Abstract summary: MCMC is a class of algorithms to sample complex and high-dimensional probability distributions. Reversibility is a tractable property that implies a less tractable but essential property here, invariance. This paper fills the gap by developing general tools to ensure that a class of nonreversible Markov kernels has the desired invariance property.
• Score: 16.889031401821754
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Markov Chain Monte Carlo (MCMC) is a class of algorithms to sample complex and high-dimensional probability distributions. The Metropolis-Hastings (MH) algorithm, the workhorse of MCMC, provides a simple recipe to construct reversible Markov kernels. Reversibility is a tractable property that implies a less tractable but essential property here, invariance. Reversibility is however not necessarily desirable when considering performance. This has prompted recent interest in designing kernels breaking this property. At the same time, an active stream of research has focused on the design of novel versions of the MH kernel, some nonreversible, relying on the use of complex invertible deterministic transforms. While standard implementations of the MH kernel are well understood, the aforementioned developments have not received the same systematic treatment to ensure their validity. This paper fills the gap by developing general tools to ensure that a class of nonreversible Markov kernels, possibly relying on complex transforms, has the desired invariance property and leads to convergent algorithms. This leads to a set of simple and practically verifiable conditions.

Related papers

• Non-Unitary Quantum Machine Learning [0.0]
  We introduce several novel probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning. Among our contributions are quantum native implementations of Residual Networks (ResNet); demonstrating a path to avoiding barren plateaus. We also show how this framework can be used to parameterise and control the amount of symmetry in an encoding.
  arXiv  Detail & Related papers  (2024-05-27T17:42:02Z)
• Deciphering RNA Secondary Structure Prediction: A Probabilistic K-Rook Matching Perspective [63.3632827588974]
  We introduce RFold, a method that learns to predict the most matching K-Rook solution from the given sequence. RFold achieves competitive performance and about eight times faster inference efficiency than state-of-the-art approaches.
  arXiv  Detail & Related papers  (2022-12-02T16:34:56Z)
• Scalable Stochastic Parametric Verification with Stochastic Variational Smoothed Model Checking [1.5293427903448025]
  Smoothed model checking (smMC) aims at inferring the satisfaction function over the entire parameter space from a limited set of observations. In this paper, we exploit recent advances in probabilistic machine learning to push this limitation forward. We compare the performances of smMC against those of SV-smMC by looking at the scalability, the computational efficiency and the accuracy of the reconstructed satisfaction function.
  arXiv  Detail & Related papers  (2022-05-11T10:43:23Z)
• Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration [77.99182201815763]
  Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. We propose a novel monomial selection algorithm based on pruning methods to allow an application to more complex problems. We demonstrate the improved sample complexity on the Rotated-MNIST, SVHN and CIFAR-10 datasets.
  arXiv  Detail & Related papers  (2022-02-08T16:16:11Z)
• Structured Stochastic Gradient MCMC [20.68905354115655]
  We propose a new non-parametric variational approximation that makes no assumptions about the approximate posterior's functional form. We obtain better predictive likelihoods and larger effective sample sizes than full SGMCMC.
  arXiv  Detail & Related papers  (2021-07-19T17:18:10Z)
• What Are Bayesian Neural Network Posteriors Really Like? [63.950151520585024]
  We show that Hamiltonian Monte Carlo can achieve significant performance gains over standard and deep ensembles. We also show that deep distributions are similarly close to HMC as standard SGLD, and closer than standard variational inference.
  arXiv  Detail & Related papers  (2021-04-29T15:38:46Z)
• Continual Learning with Fully Probabilistic Models [70.3497683558609]
  We present an approach for continual learning based on fully probabilistic (or generative) models of machine learning. We propose a pseudo-rehearsal approach using a Gaussian Mixture Model (GMM) instance for both generator and classifier functionalities. We show that GMR achieves state-of-the-art performance on common class-incremental learning problems at very competitive time and memory complexity.
  arXiv  Detail & Related papers  (2021-04-19T12:26:26Z)
• Towards interpretability of Mixtures of Hidden Markov Models [0.0]
  Mixtures of Hidden Markov Models (MHMMs) are frequently used for clustering of sequential data. An information-theoretic measure (entropy) is proposed for interpretability of MHMMs. An entropy-regularized Expectation Maximization (EM) algorithm is proposed to improve interpretability.
  arXiv  Detail & Related papers  (2021-03-23T14:25:03Z)
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
  Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
  arXiv  Detail & Related papers  (2021-02-04T02:21:08Z)
• Orbital MCMC [82.54438698903775]
  We propose two practical algorithms for constructing periodic orbits from any diffeomorphism. We also perform an empirical study demonstrating the practical advantages of both kernels.
  arXiv  Detail & Related papers  (2020-10-15T22:25:52Z)
• Non-convex Learning via Replica Exchange Stochastic Gradient MCMC [25.47669573608621]
  We propose an adaptive replica exchange SGMCMC (reSGMCMC) to automatically correct the bias and study the corresponding properties. Empirically, we test the algorithm through extensive experiments on various setups and obtain the results.
  arXiv  Detail & Related papers  (2020-08-12T15:02:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.