# Amortized Monte Carlo Integration

@article{Goliski2019AmortizedMC, title={Amortized Monte Carlo Integration}, author={Adam Goliński and Frank Wood and Tom Rainforth}, journal={ArXiv}, year={2019}, volume={abs/1907.08082} }

Current approaches to amortizing Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions - a computational pipeline which is inefficient when the target function(s) are known upfront. In this paper, we address this inefficiency by introducing AMCI, a method for amortizing Monte Carlo integration directly. AMCI operates similarly to amortized inference but produces…

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- 2020

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## 34 References

### Faithful Inversion of Generative Models for Effective Amortized Inference

- Computer ScienceNeurIPS
- 2018

This work introduces an algorithm for faithfully, and minimally, inverting the graphical model structure of any generative model and proves the correctness of the approach and empirically shows that the resulting minimally faithful inverses lead to better inference amortization than existing heuristic approaches.

### Learning Stochastic Inverses

- Computer Science, MathematicsNIPS
- 2013

The Inverse MCMC algorithm is described, which uses stochastic inverses to make block proposals for a Metropolis-Hastings sampler, and the efficiency of this sampler for a variety of parameter regimes and Bayes nets is explored.

### Deep Amortized Inference for Probabilistic Programs

- Computer ScienceArXiv
- 2016

A system for amortized inference in PPLs is proposed in the form of a parameterized guide program, which explores in detail the common machine learning pattern in which a 'local' model is specified by 'global' random values and used to generate independent observed data points; this gives rise to amortization local inference supporting global model learning.

### On Nesting Monte Carlo Estimators

- MathematicsICML
- 2018

The statistical implications of nesting MC estimators, including cases of multiple levels of nesting, are investigated, and corresponding rates of convergence are derived and empirical evidence that these rates are observed in practice is provided.

### Inference Networks for Sequential Monte Carlo in Graphical Models

- Computer ScienceICML
- 2016

A procedure for constructing and learning a structured neural network which represents an inverse factorization of the graphical model, resulting in a conditional density estimator that takes as input particular values of the observed random variables, and returns an approximation to the distribution of the latent variables.

### Inference Trees: Adaptive Inference with Exploration

- Computer Science
- 2018

We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with…

### Variational Inference with Normalizing Flows

- Computer Science, MathematicsICML
- 2015

It is demonstrated that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.

### Advances in Importance Sampling

- Computer ScienceWiley StatsRef: Statistics Reference Online
- 2021

The basic IS algorithm is described and the recent advances in this methodology are revisited, focusing on multiple IS (MIS), the case where more than one proposal is available.

### Approximate inference for the loss-calibrated Bayesian

- Computer ScienceAISTATS
- 2011

This work proposes an EM-like algorithm on the Bayesian posterior risk and shows how it can improve a standard approach to Gaussian process classication when losses are asymmetric.

### Methods for Approximating Integrals in Statistics with Special Emphasis on Bayesian Integration Problems

- Mathematics
- 1995

This paper is a survey of the major techniques and approaches available for the numerical approximation of integrals in statistics. We classify these into five broad categories; namely, asymptotic…