Neural Density Estimation and Likelihood-free Inference

Papamakarios, George

doi:10.48550/arxiv.1910.13233

Cited by 20 publications

(22 citation statements)

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“…We use different sufficient statistics which may have varying magnitudes. As recommended in [11] we run 1000 simulations and save the mean and standard deviations to normalize the simulator outputs for the SBI inference modules.…”

Section: Parameter Identification By Sbi Methodsmentioning

confidence: 99%

“…The likelihood P(x|θ ) is approximated from the simulated data by computing the probability of the simulated outputs Pr( x − x 0 < ε) around the vicinity of the observed data x 0 . Since the chance of hitting in the probability ball defined in the high dimensional probability function is low, the likelihood-free methods usually give less accurate results when compared to the MCMC methods where the likelihood can be evaluated ( [11], [23]).…”

Section: A General Overviewmentioning

confidence: 99%

“…In parallel to those listed, in this paper, we introduce the use of a new technique for identifying vehicle parameters: Simulation-Based Inference (SBI) for parameter identification, bringing a current machine learning method for the approximate Bayesian inference into the vehicle parameter identification literature. The SBI method yields posteriors of the parameters in the form of neural density estimators ( [11]). The most notable contribution of the SBI method is its potential to handle many parameters simultaneously without compromising the nonlinear nature of the formulation and the form of probability density.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Identification of Vehicle Dynamics Parameters Using Simulation-based Inference

Boyali¹,

Thompson²,

Wong³

2021

Preprint

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Identifying tire and vehicle parameters is an essential step in designing control and planning algorithms for autonomous vehicles. This paper proposes a new method: Simulation-Based Inference (SBI), a modern interpretation of Approximate Bayesian Computation methods (ABC) for parameter identification. The simulation-based inference is an emerging method in the machine learning literature and has proven to yield accurate results for many parameter sets in complex problems. We demonstrate in this paper that it can handle the identification of highly nonlinear vehicle dynamics parameters and gives accurate estimates of the parameters for the governing equations.

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Section: Parameter Identification By Sbi Methodsmentioning

confidence: 99%

Section: A General Overviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Identification of Vehicle Dynamics Parameters Using Simulation-based Inference

Boyali¹,

Thompson²,

Wong³

2021

Preprint

View full text Add to dashboard Cite

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“…The amount of simulations required to perform density estimation grows exponentially as data dimensionality increases, and this is generally referred to as the curse of dimensionality in machine learning. Papamakarios (2019) illustrate this problem faced by density estimation using a simple example. Due to the overall advantages of SNL over SNRE, we use the former along with FPCA dimensionality reduction.…”

Section: Likelihood-free Inference Of Abundancesmentioning

confidence: 99%

Functional Data Analysis for Extracting the Intrinsic Dimensionality of Spectra: Application to Chemical Homogeneity in the Open Cluster M67

Patil,

Bovy,

Eadie

et al. 2021

Preprint

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High-resolution spectroscopic surveys of the Milky Way have entered the Big Data regime and have opened avenues for solving outstanding questions in Galactic Archaeology. However, exploiting their full potential is limited by complex systematics, whose characterization has not received much attention in modern spectroscopic analyses. In this work, we present a novel method to disentangle the component of spectral data space intrinsic to the stars from that due to systematics. Using functional principal component analysis on a sample of 18, 933 giant spectra from APOGEE, we find that the intrinsic structure above the level of observational uncertainties requires ≈10 Functional Principal Components (FPCs). Our FPCs can reduce the dimensionality of spectra, remove systematics, and impute masked wavelengths, thereby enabling accurate studies of stellar populations. To demonstrate the applicability of our FPCs, we use them to infer stellar parameters and abundances of 28 giants in the open cluster M67. We employ Sequential Neural Likelihood, a simulation-based Bayesian inference method that learns likelihood functions using neural density estimators, to incorporate non-Gaussian effects in spectral likelihoods. By hierarchically combining the inferred abundances, we limit the spread of the following elements in M67: Fe 0.02 dex; C 0.03 dex; O, Mg, Si, Ni 0.04 dex; Ca 0.05 dex; N, Al 0.07 dex (at 68% confidence). Our constraints suggest a lack of self-pollution by core-collapse supernovae in M67, which has promising implications for the future of chemical tagging to understand the star formation history and dynamical evolution of the Milky Way.

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“…The main idea behind any ABC method is to model the posterior distribution by approximating the likelihood as a fraction of accepted simulated data points from the simulator model, by the use of a distance measure δ and a tolerance value . The first approach, known as the ABC-rejection scheme, was successfully applied in biology [Pritchard et al, 1999, Tavaré et al, 1997 and since then many alternative versions of the algorithm have been introduced, with the three main groups represented by Markov Chain Monte Carlo ABC [Marjoram et al, 2003], Sequential Monte Carlo (SMC) ABC [Beaumont et al, 2009], and neural-network-based ABC [Papamakarios, 2019. Here, we focus on the MCMC-ABC version [Andrieu et al, 2009] as it can be more readily implemented and the computational costs are lower [Jasra et al, 2007].…”

Section: Introductionmentioning

confidence: 99%

ABC-Di: Approximate Bayesian Computation for Discrete Data

Auzina,

Tomczak

2020

Preprint

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Many real-life problems are represented as a black-box, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables likelihood-free inference problems can be solved by a group of methods under the name of Approximate Bayesian Computation (ABC). However, a similar approach for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose to use a populationbased MCMC ABC framework. Further, we present a valid Markov kernel, and propose a new kernel that is inspired by Differential Evolution. We assess the proposed approach on a problem with the known likelihood function, namely, discovering the underlying diseases based on a QMR-DT Network, and three likelihood-free inference problems: (i) the QMR-DT Network with the unknown likelihood function, (ii) learning binary neural network, and (iii) Neural Architecture Search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel.

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Neural Density Estimation and Likelihood-free Inference

Cited by 20 publications

References 0 publications

Identification of Vehicle Dynamics Parameters Using Simulation-based Inference

Identification of Vehicle Dynamics Parameters Using Simulation-based Inference

Functional Data Analysis for Extracting the Intrinsic Dimensionality of Spectra: Application to Chemical Homogeneity in the Open Cluster M67

ABC-Di: Approximate Bayesian Computation for Discrete Data

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