Convolutional Neural Networks as Summary Statistics for Approximate Bayesian Computation

Åkesson, Maria; Singh, Prashant; Wrede, Fredrik; Hellander, Andreas

doi:10.48550/arxiv.2001.11760

Cited by 4 publications

(10 citation statements)

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“…However, we note that our approach is not restricted to these types of architectures. Our motivation behind choosing a convolutional architecture is that they have demonstrated excellent performance in identifying intricate patterns in complex, high-dimensional time-series data (Dinev & Gutmann, 2018;Sadouk, 2019;Åkesson et al, 2020) as well as images (Greenberg et al, 2019a). For further information on the implementation we refer the reader to supplementary materials.…”

Section: Methodsmentioning

confidence: 99%

“…In particular, NN based regression models have delivered highly promising results towards learning the estimated posterior mean as summary statistics from high-dimensional detailed time series (Jiang et al, 2017;Wiqvist et al, 2019;Åkesson et al, 2020). Such models learn the mapping F w (y) → E[θ] which can be seen as an amortized point estimate for a given y, where w are the weights of the regression model.…”

Section: Related Workmentioning

confidence: 99%

“…The Lotka-Volterra predator-prey dynamics model is a popular parameter estimation benchmark problem ( Åkesson et al, 2020;Greenberg et al, 2019b). The model is implemented as a stochastic Markov jump process (Prangle et al, 2017) simulated using the stochastic simulation algorithm (SSA) (Gillespie, 1977).…”

Section: Lotka-volterra Predator-prey Modelmentioning

confidence: 99%

“…An alternative approach to handpicking summary statistics is to utilize embedded neural networks (NN) to learn summary statistics from simulated data (Jiang et al, 2017;Dinev & Gutmann, 2018;Wiqvist et al, 2019;Åkesson et al, 2020;Chen et al, 2020). Some of these methods require a postprocessing ABC scheme to yield the posterior, others work in conjunction with neural density estimators (Lueckmann et al, 2021) to either estimate the posterior directly, or use synthesized likelihoods which requires Markov chain Monte Carlo (MCMC) sampling.…”

Section: Introductionmentioning

confidence: 99%

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Robust and integrative Bayesian neural networks for likelihood-free parameter inference

Wrede¹,

Eriksson²,

Jiang³

et al. 2021

Preprint

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State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihoodfree parameter inference. Existing approaches require density estimation as a post-processing step building upon deterministic neural networks, and do not take network prediction uncertainty into account. This work proposes a robust integrated approach that learns summary statistics using Bayesian neural networks, and directly estimates the posterior density using categorical distributions. An adaptive sampling scheme selects simulation locations to efficiently and iteratively refine the predictive posterior of the network conditioned on observations. This allows for more efficient and robust convergence on comparatively large prior spaces. We demonstrate our approach on benchmark examples and compare against related methods.

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Section: Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Lotka-volterra Predator-prey Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust and integrative Bayesian neural networks for likelihood-free parameter inference

Wrede¹,

Eriksson²,

Jiang³

et al. 2021

Preprint

Self Cite

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show abstract

“…In order to reduce the dimensionality of the data, ABC usually relies on a set of summary statistics, whose choice is not straightforward. Recently, the expressive capabilities of Neural Networks (NNs) have been leveraged to learn statistics to be used in ABC [Jiang et al, 2017, Wiqvist et al, 2019, Åkesson et al, 2020. These techniques entail generating a training set of parameter-simulation pairs from the simulator, on which NNs parametrizing the statistics are trained by minimizing a suitable loss.…”

Section: Introductionmentioning

confidence: 99%

Score Matched Neural Exponential Families for Likelihood-Free Inference

Pacchiardi¹,

Dutta²

2020

Preprint

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To perform Bayesian inference for stochastic simulator models for which the likelihood is not accessible, Likelihood-Free Inference (LFI) relies on simulations from the model. Standard LFI methods can be split according to how these simulations are used: to build an explicit Surrogate Likelihood, or to accept/reject parameter values according to a measure of distance from the observations (Approximate Bayesian Computation (ABC)). In both cases, simulations are adaptively tailored to the value of the observation. Here, we generate parameter-simulation pairs from the model independently on the observation, and use them to learn a conditional exponential family likelihood approximation; to parametrize it, we use Neural Networks whose weights are tuned with Score Matching. With our likelihood approximation, we can employ MCMC for doubly intractable distributions to draw samples from the posterior for any number of observations without additional model simulations, with performance competitive to comparable approaches. Further, the sufficient statistics of the exponential family can be used as summaries in ABC, outperforming the state-ofthe-art method in five different models with known likelihood. Finally, we apply our method to a challenging model from meteorology.

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Electoral David vs Goliath: How does the Spatial Concentration of Electors affect District-based Elections?

Mitra

2020

Preprint

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Many democratic countries use district-based elections where there is a "seat" for each district in the governing body such as parliament or assembly. In each district, the party whose candidate gets the maximum number of votes is declared the winner of the corresponding seat. The result of the election is decided based on the number of seats won this way by the different parties. The electors (or voters) are assigned to different districts based on their residence, and each elector can vote only in the district in which they are assigned. Thus, locations of the electors and boundaries of the districts may severely affect the election result even if the proportion of popular support (number of electors) of different parties remains unchanged. In this setting, it is also possible that a party with less number of supporters overall, may end up winning more seats if their supporters are suitably distributed. This has led to significant amount of research on the topic of "gerrymandering", i.e. how districts may be redrawn or electors may be moved to ensure maximum seats for a particular party. In this paper, we frame the spatial distribution of electors in a probabilistic setting, and analyze different models to capture the intra-district polarization of electors in favour of a party, or the spatial concentration of supporters of different parties. Our models are inspired by elections in India, where supporters of different parties tend to be concentrated, turning various districts into strongholds of certain parties. We show with extensive simulations that our model can capture different statistical properties of real elections held in India. For this purpose, we frame parameter estimation problems to fit our models to the observed election results. Since analytical calculation of the likelihood functions are infeasible for our complex models, we make use of Likelihood-free Inference methods under the framework of Approximate Bayesian Computation (ABC). Since this approach is highly timeconsuming, we explore how supervised regression using Logistic Regression or Deep Neural Networks can be used to speed it up. We also explore how the election results can change drastically by varying the spatial distributions of the voters, even when the proportions of popular support of the parties remain constant.

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Convolutional Neural Networks as Summary Statistics for Approximate Bayesian Computation

Cited by 4 publications

References 0 publications

Robust and integrative Bayesian neural networks for likelihood-free parameter inference

Robust and integrative Bayesian neural networks for likelihood-free parameter inference

Score Matched Neural Exponential Families for Likelihood-Free Inference

Electoral David vs Goliath: How does the Spatial Concentration of Electors affect District-based Elections?

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