54 research outputs found
Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models
Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We assume that only a finite number of parameters are of interest and allow the generative process to be very general; it may be a noisy nonlinear dynamical system with an unrestricted number of hidden variables. This weak assumption is useful for devising realistic models but it renders statistical inference very difficult. The main challenge is the intractability of the likelihood function. Several likelihood-free inference methods have been proposed which share the basic idea of identifying the parameters by finding values for which the discrepancy between simulated and observed data is small. A major obstacle to using these methods is their computational cost. The cost is largely due to the need to repeatedly simulate data sets and the lack of knowledge about how the parameters affect the discrepancy. We propose a strategy which combines probabilistic modeling of the discrepancy with optimization to facilitate likelihood-free inference. The strategy is implemented using Bayesian optimization and is shown to accelerate the inference through a reduction in the number of required simulations by several orders of magnitude.Peer reviewe
Optimization Monte Carlo: Efficient and Embarrassingly Parallel Likelihood-Free Inference
We describe an embarrassingly parallel, anytime Monte Carlo method for
likelihood-free models. The algorithm starts with the view that the
stochasticity of the pseudo-samples generated by the simulator can be
controlled externally by a vector of random numbers u, in such a way that the
outcome, knowing u, is deterministic. For each instantiation of u we run an
optimization procedure to minimize the distance between summary statistics of
the simulator and the data. After reweighing these samples using the prior and
the Jacobian (accounting for the change of volume in transforming from the
space of summary statistics to the space of parameters) we show that this
weighted ensemble represents a Monte Carlo estimate of the posterior
distribution. The procedure can be run embarrassingly parallel (each node
handling one sample) and anytime (by allocating resources to the worst
performing sample). The procedure is validated on six experiments.Comment: NIPS 2015 camera read
Divide and conquer in ABC: Expectation-Progagation algorithms for likelihood-free inference
ABC algorithms are notoriously expensive in computing time, as they require
simulating many complete artificial datasets from the model. We advocate in
this paper a "divide and conquer" approach to ABC, where we split the
likelihood into n factors, and combine in some way n "local" ABC approximations
of each factor. This has two advantages: (a) such an approach is typically much
faster than standard ABC and (b) it makes it possible to use local summary
statistics (i.e. summary statistics that depend only on the data-points that
correspond to a single factor), rather than global summary statistics (that
depend on the complete dataset). This greatly alleviates the bias introduced by
summary statistics, and even removes it entirely in situations where local
summary statistics are simply the identity function.
We focus on EP (Expectation-Propagation), a convenient and powerful way to
combine n local approximations into a global approximation. Compared to the EP-
ABC approach of Barthelm\'e and Chopin (2014), we present two variations, one
based on the parallel EP algorithm of Cseke and Heskes (2011), which has the
advantage of being implementable on a parallel architecture, and one version
which bridges the gap between standard EP and parallel EP. We illustrate our
approach with an expensive application of ABC, namely inference on spatial
extremes.Comment: To appear in the forthcoming Handbook of Approximate Bayesian
Computation (ABC), edited by S. Sisson, L. Fan, and M. Beaumon
Adversarial Variational Optimization of Non-Differentiable Simulators
Complex computer simulators are increasingly used across fields of science as
generative models tying parameters of an underlying theory to experimental
observations. Inference in this setup is often difficult, as simulators rarely
admit a tractable density or likelihood function. We introduce Adversarial
Variational Optimization (AVO), a likelihood-free inference algorithm for
fitting a non-differentiable generative model incorporating ideas from
generative adversarial networks, variational optimization and empirical Bayes.
We adapt the training procedure of generative adversarial networks by replacing
the differentiable generative network with a domain-specific simulator. We
solve the resulting non-differentiable minimax problem by minimizing
variational upper bounds of the two adversarial objectives. Effectively, the
procedure results in learning a proposal distribution over simulator
parameters, such that the JS divergence between the marginal distribution of
the synthetic data and the empirical distribution of observed data is
minimized. We evaluate and compare the method with simulators producing both
discrete and continuous data.Comment: v4: Final version published at AISTATS 2019; v5: Fixed typo in Eqn 1
Posterior-Aided Regularization for Likelihood-Free Inference
The recent development of likelihood-free inference aims training a flexible
density estimator for the target posterior with a set of input-output pairs
from simulation. Given the diversity of simulation structures, it is difficult
to find a single unified inference method for each simulation model. This paper
proposes a universally applicable regularization technique, called
Posterior-Aided Regularization (PAR), which is applicable to learning the
density estimator, regardless of the model structure. Particularly, PAR solves
the mode collapse problem that arises as the output dimension of the simulation
increases. PAR resolves this posterior mode degeneracy through a mixture of 1)
the reverse KL divergence with the mode seeking property; and 2) the mutual
information for the high quality representation on likelihood. Because of the
estimation intractability of PAR, we provide a unified estimation method of PAR
to estimate both reverse KL term and mutual information term with a single
neural network. Afterwards, we theoretically prove the asymptotic convergence
of the regularized optimal solution to the unregularized optimal solution as
the regularization magnitude converges to zero. Additionally, we empirically
show that past sequential neural likelihood inferences in conjunction with PAR
present the statistically significant gains on diverse simulation tasks
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