# Deep Involutive Generative Models for Neural MCMC

@article{Spanbauer2020DeepIG, title={Deep Involutive Generative Models for Neural MCMC}, author={Span Spanbauer and Cameron E. Freer and Vikash K. Mansinghka}, journal={ArXiv}, year={2020}, volume={abs/2006.15167} }

We introduce deep involutive generative models, a new architecture for deep generative modeling, and use them to define Involutive Neural MCMC, a new approach to fast neural MCMC. An involutive generative model represents a probability kernel $G(\phi \mapsto \phi')$ as an involutive (i.e., self-inverting) deterministic function $f(\phi, \pi)$ on an enlarged state space containing auxiliary variables $\pi$. We show how to make these models volume preserving, and how to use deep volume-preserving…

## 8 Citations

### Automating Involutive MCMC using Probabilistic and Differentiable Programming.

- Computer Science
- 2020

The paper shows example Gen code for a split-merge reversible jump move in an infinite Gaussian mixture model and a state-dependent mixture of proposals on a combinatorial space of covariance functions for a Gaussian process.

### Neural Group Actions

- Computer ScienceArXiv
- 2020

It is conjecture, by analogy to a universality result for involutive neural networks, that generative models built from Neural Group Actions are universal approximators for collections of probabilistic transitions adhering to the group laws.

### Semi-Empirical Objective Functions for MCMC Proposal Optimization

- Computer Science2022 26th International Conference on Pattern Recognition (ICPR)
- 2022

This work introduces and demonstrates a semi-empirical procedure for determining approximate objective functions suitable for optimizing arbitrarily parameterized proposal distributions in MCMC methods and finds that Ab Initio objective functions are sufficiently robust to enable the confident optimization of neural proposal distributions parameterized by deep generative networks extending beyond the regimes of traditional MCMC schemes.

### A Neural Network MCMC Sampler That Maximizes Proposal Entropy

- Computer ScienceEntropy
- 2021

A neural network MCMC sampler that has a flexible and tractable proposal distribution that utilizes the gradient of the target distribution for generating proposals and achieved significantly higher efficiency in a variety of sampling tasks.

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

- Computer Science
- 2020

This paper develops general tools to ensure that a class of nonreversible Markov kernels, possibly relying on complex transforms, has the desired invariance property and lead to convergent algorithms.

### Ergodic variational flows

- MathematicsArXiv
- 2022

This work presents a new class of variational family— ergodic variational ﬂows — that not only enables tractable i.i.d. sampling and density evaluation, but also comes with MCMC-like convergence…

### Path Integral Sampler: A Stochastic Control Approach For Sampling

- Computer ScienceICLR
- 2022

The PIS is built on the Schrödinger bridge problem which aims to recover the most likely evolution of a diffusion process given its initial distribution and terminal distribution and is formulated as a stochastic optimal control problem whose running cost is the control energy and terminal cost is chosen according to the target distribution.

### Orbital MCMC

- Computer ScienceAISTATS
- 2022

It is demonstrated that the proposed framework (Involutive MCMC) is a special case of a larger family of algorithms operating on orbits of continuous deterministic bijections, which is called orbital MCMC (oMCMC).

## References

SHOWING 1-10 OF 22 REFERENCES

### A-NICE-MC: Adversarial Training for MCMC

- Computer ScienceNIPS
- 2017

A-NICE-MC provides the first framework to automatically design efficient domain-specific Markov Chain Monte Carlo proposals, and is able to significantly outperform competing methods such as Hamiltonian Monte Carlo.

### NICE: Non-linear Independent Components Estimation

- Computer Science, MathematicsICLR
- 2015

We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is…

### i-RevNet: Deep Invertible Networks

- Computer ScienceICLR
- 2018

The i-RevNet is built, a network that can be fully inverted up to the final projection onto the classes, i.e. no information is discarded, and linear interpolations between natural image representations are reconstructed.

### Auto-Encoding Variational Bayes

- Computer ScienceICLR
- 2014

A stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case is introduced.

### Analyzing Inverse Problems with Invertible Neural Networks

- Computer ScienceICLR
- 2019

It is argued that a particular class of neural networks is well suited for this task -- so-called Invertible Neural Networks (INNs), and it is verified experimentally that INNs are a powerful analysis tool to find multi-modalities in parameter space, to uncover parameter correlations, and to identify unrecoverable parameters.

### Generalizing Hamiltonian Monte Carlo with Neural Networks

- Computer ScienceICLR
- 2018

This work presents a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution, and releases an open source TensorFlow implementation.

### Meta-Learning MCMC Proposals

- Computer ScienceNeurIPS
- 2018

A meta-learning approach to building effective and generalizable MCMC proposals that generalize to occurrences of common structural motifs across different models, allowing for the construction of a library of learned inference primitives that can accelerate inference on unseen models with no model-specific training required.

### Stochastic Backpropagation and Approximate Inference in Deep Generative Models

- Computer ScienceICML
- 2014

We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and…

### Neural Variational Inference and Learning in Belief Networks

- Computer ScienceICML
- 2014

This work proposes a fast non-iterative approximate inference method that uses a feedforward network to implement efficient exact sampling from the variational posterior and shows that it outperforms the wake-sleep algorithm on MNIST and achieves state-of-the-art results on the Reuters RCV1 document dataset.

### Picture: A probabilistic programming language for scene perception

- Computer Science2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
- 2015

Picture is presented, a probabilistic programming language for scene understanding that allows researchers to express complex generative vision models, while automatically solving them using fast general-purpose inference machinery.