# A Note on Simulation-Based Inference by Matching Random Features

@inproceedings{Shalizi2021ANO, title={A Note on Simulation-Based Inference by Matching Random Features}, author={Cosma Rohilla Shalizi}, year={2021} }

We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of randomly chosen functions of the simulation output match the values of those some functions calculated on the data. Results from the “state-space reconstruction” or “geometry from a time series” literature in nonlinear dynamics indicate that just 2d + 1 such functions will typically suffice to identify a model with a d-dimensional parameter space. Results from…

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Matching random features

- Computer Science
- 2022

Some of the key results are sketched, numerical evidence about the new method’s properties are presented, and an agenda for research is laid out.

## References

SHOWING 1-10 OF 64 REFERENCES

Statistical Inference for Generative Models with Maximum Mean Discrepancy

- Computer Science, MathematicsArXiv
- 2019

Theoretical properties of a class of minimum distance estimators for intractable generative models, that is, statistical models for which the likelihood is intracted, but simulation is cheap, are studied, showing that they are consistent, asymptotically normal and robust to model misspecification.

Constructing summary statistics for approximate Bayesian computation: semi‐automatic approximate Bayesian computation

- Computer Science
- 2012

This work shows how to construct appropriate summary statistics for ABC in a semi‐automatic manner, and shows that optimal summary statistics are the posterior means of the parameters.

The potential of likelihood-free inference of cosmological parameters with weak lensing data

- MathematicsProceedings of the International Astronomical Union
- 2014

Abstract In the statistical framework of likelihood-free inference, the posterior distribution of model parameters is explored via simulation rather than direct evaluation of the likelihood function,…

Simulation-based econometric methods

- Economics
- 1996

This book introduces a new generation of statistical econometrics, where the previous difficulties presented by the presence of integrals of large dimensions in the probability density functions or in the moments can be circumvented by a simulation-based approach.

A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration

- Mathematics
- 1989

This paper proposes a simple modification of a conventional generalized method of moments estimator for a discrete response model, replacing response probabilities that require numerical integration…

Consistent estimation of joint distributions for sufficiently mixing random fields

- Mathematics
- 1997

The joint distribution of a d-dimensional random field restricted to a box of size k can be estimated by looking at a realization in a box of size n >> k and computing the empirical distribution.…

The Error Probability of Random Fourier Features is Dimensionality Independent

- Computer Science, MathematicsArXiv
- 2017

Compared to prior work, this work is the first to show that the error probability for random Fourier features is independent of the dimensionality of data points as well as the size of their domain.

Considerate approaches to achieving sufficiency for ABC model selection

- Computer Science, Mathematics
- 2011

This work employs an information-theoretical framework that can be used to construct (approximately) sufficient statistics by combining different statistics until the loss of information is minimized, and applies this approach to a range of illustrative and real-world model selection problems.

Random Feature Stein Discrepancies

- Computer ScienceNeurIPS
- 2018

Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to goodness-of-fit testing.…

Indirect inference through prediction

- Computer Science
- 2018

By recasting indirect inference estimation as a prediction rather than a minimization and by using regularized regressions, we can bypass the three major problems of estimation: selecting the summary…