arXiv subjects

Michael U. Gutmann

Publications and source records attributed to Michael U. Gutmann.

At least 37 records · Page 2Linked to original sources

arXiv2020

Likelihood-free inference by ratio estimation

We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference in the absence of a likelihood function. The popular synthetic likelihood approach infers the parameters by modelling summary statistics of the data by a Gaussian probability distribution. In another popular approach called approximate Bayesian computation, the inference is performed by identifying parameter values for which the summary statistics of the simulated data are close to those of the observed data. Synthetic likelihood is easier to use as no measure of `closeness' is required but the Gaussianity assumption is often limiting. Moreover, both approaches require judiciously chosen summary statistics. We here present an alternative inference approach that is as easy to use as synthetic likelihood but not as restricted in its assumptions, and that, in a natural way, enables automatic selection of relevant summary statistic from a large set of candidates. The basic idea is to frame the problem of estimating the posterior as a problem of estimating the ratio between the data generating distribution and the marginal distribution. This problem can be solved by logistic regression, and including regularising penalty terms enables automatic selection of the summary statistics relevant to the inference task. We illustrate the general theory on canonical examples and employ it to perform inference for challenging stochastic nonlinear dynamical systems and high-dimensional summary statistics.

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arXiv2020

Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation

Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in scientific experiments. A fundamental question is how to design the experiments so that the collected data are most useful. The field of Bayesian experimental design advocates that, ideally, we should choose designs that maximise the mutual information (MI) between the data and the parameters. For implicit models, however, this approach is severely hampered by the high computational cost of computing posteriors and maximising MI, in particular when we have more than a handful of design variables to optimise. In this paper, we propose a new approach to Bayesian experimental design for implicit models that leverages recent advances in neural MI estimation to deal with these issues. We show that training a neural network to maximise a lower bound on MI allows us to jointly determine the optimal design and the posterior. Simulation studies illustrate that this gracefully extends Bayesian experimental design for implicit models to higher design dimensions.

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arXiv2020

Adaptive Approximate Bayesian Computation Tolerance Selection

Approximate Bayesian Computation (ABC) methods are increasingly used for inference in situations in which the likelihood function is either computationally costly or intractable to evaluate. Extensions of the basic ABC rejection algorithm have improved the computational efficiency of the procedure and broadened its applicability. The ABC-Population Monte Carlo (ABC-PMC) approach of Beaumont et al. (2009) has become a popular choice for approximate sampling from the posterior. ABC-PMC is a sequential sampler with an iteratively decreasing value of the tolerance, which specifies how close the simulated data need to be to the real data for acceptance. We propose a method for adaptively selecting a sequence of tolerances that improves the computational efficiency of the algorithm over other common techniques. In addition we define a stopping rule as a by-product of the adaptation procedure, which assists in automating termination of sampling. The proposed automatic ABC-PMC algorithm can be easily implemented and we present several examples demonstrating its benefits in terms of computational efficiency.

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arXiv2020

Sequential Bayesian Experimental Design for Implicit Models via Mutual Information

Bayesian experimental design (BED) is a framework that uses statistical models and decision making under uncertainty to optimise the cost and performance of a scientific experiment. Sequential BED, as opposed to static BED, considers the scenario where we can sequentially update our beliefs about the model parameters through data gathered in the experiment. A class of models of particular interest for the natural and medical sciences are implicit models, where the data generating distribution is intractable, but sampling from it is possible. Even though there has been a lot of work on static BED for implicit models in the past few years, the notoriously difficult problem of sequential BED for implicit models has barely been touched upon. We address this gap in the literature by devising a novel sequential design framework for parameter estimation that uses the Mutual Information (MI) between model parameters and simulated data as a utility function to find optimal experimental designs, which has not been done before for implicit models. Our approach uses likelihood-free inference by ratio estimation to simultaneously estimate posterior distributions and the MI. During the sequential BED procedure we utilise Bayesian optimisation to help us optimise the MI utility. We find that our framework is efficient for the various implicit models tested, yielding accurate parameter estimates after only a few iterations.

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arXiv2020

Robust Optimisation Monte Carlo

This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically prohibitively expensive. Approximate Bayesian Computation (ABC) is a framework to perform approximate inference in such situations. While basic ABC algorithms are widely applicable, they are notoriously slow and much research has focused on increasing their efficiency. Optimisation Monte Carlo (OMC) has recently been proposed as an efficient and embarrassingly parallel method that leverages optimisation to accelerate the inference. In this paper, we demonstrate an important previously unrecognised failure mode of OMC: It generates strongly overconfident approximations by collapsing regions of similar or near-constant likelihood into a single point. We propose an efficient, robust generalisation of OMC that corrects this. It makes fewer assumptions, retains the main benefits of OMC, and can be performed either as post-processing to OMC or as a stand-alone computation. We demonstrate the effectiveness of the proposed Robust OMC on toy examples and tasks in inverse-graphics where we perform Bayesian inference with a complex image renderer.

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arXiv2020

Generative Ratio Matching Networks

Deep generative models can learn to generate realistic-looking images, but many of the most effective methods are adversarial and involve a saddlepoint optimization, which requires a careful balancing of training between a generator network and a critic network. Maximum mean discrepancy networks (MMD-nets) avoid this issue by using kernel as a fixed adversary, but unfortunately, they have not on their own been able to match the generative quality of adversarial training. In this work, we take their insight of using kernels as fixed adversaries further and present a novel method for training deep generative models that does not involve saddlepoint optimization. We call our method generative ratio matching or GRAM for short. In GRAM, the generator and the critic networks do not play a zero-sum game against each other, instead, they do so against a fixed kernel. Thus GRAM networks are not only stable to train like MMD-nets but they also match and beat the generative quality of adversarially trained generative networks.

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arXiv2019

To Stir or Not to Stir: Online Estimation of Liquid Properties for Pouring Actions

Our brains are able to exploit coarse physical models of fluids to solve everyday manipulation tasks. There has been considerable interest in developing such a capability in robots so that they can autonomously manipulate fluids adapting to different conditions. In this paper, we investigate the problem of adaptation to liquids with different characteristics. We develop a simple calibration task (stirring with a stick) that enables rapid inference of the parameters of the liquid from RBG data. We perform the inference in the space of simulation parameters rather than on physically accurate parameters. This facilitates prediction and optimization tasks since the inferred parameters may be fed directly to the simulator. We demonstrate that our "stirring" learner performs better than when the robot is calibrated with pouring actions. We show that our method is able to infer properties of three different liquids -- water, glycerin and gel -- and present experimental results by executing stirring and pouring actions on a UR10. We believe that decoupling of the training actions from the goal task is an important step towards simple, autonomous learning of the behavior of different fluids in unstructured environments.

cs.RO↗

arXiv2019

Efficient Bayesian Inference of Atomistic Structure in Complex Functional Materials

Tailoring the functional properties of advanced organic/inorganic heterogeonous devices to their intended technological applications requires knowledge and control of the microscopic structure inside the device. Atomistic quantum mechanical simulation methods deliver accurate energies and properties for individual configurations, however, finding the most favourable configurations remains computationally prohibitive. We propose a 'building block'-based Bayesian Optimisation Structure Search (BOSS) approach for addressing extended organic/inorganic interface problems and demonstrate its feasibility in a molecular surface adsorption study. In BOSS, a likelihood-free Bayesian scheme accelerates the identification of material energy landscapes with the number of sampled configurations during active learning, enabling structural inference with high chemical accuracy and featuring large simulation cells. This allowed us to identify several most favourable molecular adsorption configurations for $\mathrm{C}_{60}$ on the (101) surface of $\mathrm{TiO}_2$ anatase and clarify the key molecule-surface interactions governing structural assembly. Inferred structures were in good agreement with detailed experimental images of this surface adsorbate, demonstrating good predictive power of BOSS and opening the route towards large-scale surface adsorption studies of molecular aggregates and films.

cond-mat.mtrl-sci↗

arXiv2019

Adaptive Gaussian Copula ABC

Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the combination of two classical ABC approaches --- regression ABC and sequential ABC. The key idea is that rather than learning the posterior directly, we first target another auxiliary distribution that can be learned accurately by existing methods, through which we then subsequently learn the desired posterior with the help of a Gaussian copula. During this process, the complexity of the model changes adaptively according to the data at hand. Experiments on a synthetic dataset as well as three real-world inference tasks demonstrates that the proposed method is fast, accurate, and easy to use.

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arXiv2018

Dynamic Likelihood-free Inference via Ratio Estimation (DIRE)

Parametric statistical models that are implicitly defined in terms of a stochastic data generating process are used in a wide range of scientific disciplines because they enable accurate modeling. However, learning the parameters from observed data is generally very difficult because their likelihood function is typically intractable. Likelihood-free Bayesian inference methods have been proposed which include the frameworks of approximate Bayesian computation (ABC), synthetic likelihood, and its recent generalization that performs likelihood-free inference by ratio estimation (LFIRE). A major difficulty in all these methods is choosing summary statistics that reduce the dimensionality of the data to facilitate inference. While several methods for choosing summary statistics have been proposed for ABC, the literature for synthetic likelihood and LFIRE is very thin to date. We here address this gap in the literature, focusing on the important special case of time-series models. We show that convolutional neural networks trained to predict the input parameters from the data provide suitable summary statistics for LFIRE. On a wide range of time-series models, a single neural network architecture produced equally or more accurate posteriors than alternative methods.

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arXiv2018

Efficient acquisition rules for model-based approximate Bayesian computation

Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate models such as Gaussian processes have been proposed. Bayesian optimisation enables one to intelligently decide where to evaluate the model next but common BO strategies are not designed for the goal of estimating the posterior distribution. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to a lack of simulations to estimate this quantity accurately, and define a loss function that measures this uncertainty. We then propose to select the next evaluation location to minimise the expected loss. Experiments show that the proposed method often produces the most accurate approximations as compared to common BO strategies.

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arXiv2018

ELFI: Engine for Likelihood-Free Inference

Engine for Likelihood-Free Inference (ELFI) is a Python software library for performing likelihood-free inference (LFI). ELFI provides a convenient syntax for arranging components in LFI, such as priors, simulators, summaries or distances, to a network called ELFI graph. The components can be implemented in a wide variety of languages. The stand-alone ELFI graph can be used with any of the available inference methods without modifications. A central method implemented in ELFI is Bayesian Optimization for Likelihood-Free Inference (BOLFI), which has recently been shown to accelerate likelihood-free inference up to several orders of magnitude by surrogate-modelling the distance. ELFI also has an inbuilt support for output data storing for reuse and analysis, and supports parallelization of computation from multiple cores up to a cluster environment. ELFI is designed to be extensible and provides interfaces for widening its functionality. This makes the adding of new inference methods to ELFI straightforward and automatically compatible with the inbuilt features.

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arXiv2018

Conditional Noise-Contrastive Estimation of Unnormalised Models

Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random fields, and neural network models in unsupervised deep learning. In previous work, the estimation principle called noise-contrastive estimation (NCE) was introduced where unnormalised models are estimated by learning to distinguish between data and auxiliary noise. An open question is how to best choose the auxiliary noise distribution. We here propose a new method that addresses this issue. The proposed method shares with NCE the idea of formulating density estimation as a supervised learning problem but in contrast to NCE, the proposed method leverages the observed data when generating noise samples. The noise can thus be generated in a semi-automated manner. We first present the underlying theory of the new method, show that score matching emerges as a limiting case, validate the method on continuous and discrete valued synthetic data, and show that we can expect an improved performance compared to NCE when the data lie in a lower-dimensional manifold. Then we demonstrate its applicability in unsupervised deep learning by estimating a four-layer neural image model.

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arXiv2017

VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning

Deep generative models provide powerful tools for distributions over complicated manifolds, such as those of natural images. But many of these methods, including generative adversarial networks (GANs), can be difficult to train, in part because they are prone to mode collapse, which means that they characterize only a few modes of the true distribution. To address this, we introduce VEEGAN, which features a reconstructor network, reversing the action of the generator by mapping from data to noise. Our training objective retains the original asymptotic consistency guarantee of GANs, and can be interpreted as a novel autoencoder loss over the noise. In sharp contrast to a traditional autoencoder over data points, VEEGAN does not require specifying a loss function over the data, but rather only over the representations, which are standard normal by assumption. On an extensive set of synthetic and real world image datasets, VEEGAN indeed resists mode collapsing to a far greater extent than other recent GAN variants, and produces more realistic samples.

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arXiv2017

Simultaneous Estimation of Non-Gaussian Components and their Correlation Structure

The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data. While such models have been proposed, they usually concentrated on higher-order correlations such as energy (square) correlations. Yet, linear correlations are a most fundamental and informative form of dependency in many real data sets. Linear correlations are usually completely removed by ICA and related methods, so they can only be analyzed by developing new methods which explicitly allow for linearly correlated components. In this paper, we propose a probabilistic model of linear non-Gaussian components which are allowed to have both linear and energy correlations. The precision matrix of the linear components is assumed to be randomly generated by a higher-order process and explicitly parametrized by a parameter matrix. The estimation of the parameter matrix is shown to be particularly simple because using score matching, the objective function is a quadratic form. Using simulations with artificial data, we demonstrate that the proposed method improves identifiability of non-Gaussian components by simultaneously learning their correlation structure. Applications on simulated complex cells with natural image input, as well as spectrograms of natural audio data show that the method finds new kinds of dependencies between the components.

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arXiv2017

Likelihood-free inference via classification

Increasingly complex generative models are being used across disciplines as they allow for realistic characterization of data, but a common difficulty with them is the prohibitively large computational cost to evaluate the likelihood function and thus to perform likelihood-based statistical inference. A likelihood-free inference framework has emerged where the parameters are identified by finding values that yield simulated data resembling the observed data. While widely applicable, a major difficulty in this framework is how to measure the discrepancy between the simulated and observed data. Transforming the original problem into a problem of classifying the data into simulated versus observed, we find that classification accuracy can be used to assess the discrepancy. The complete arsenal of classification methods becomes thereby available for inference of intractable generative models. We validate our approach using theory and simulations for both point estimation and Bayesian inference, and demonstrate its use on real data by inferring an individual-based epidemiological model for bacterial infections in child care centers.

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arXiv2015

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.

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arXiv2015

Classification and Bayesian Optimization for Likelihood-Free Inference

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by finding the values which yield simulated data that resemble the observed data. This approach faces at least two major difficulties: The first difficulty is the choice of the discrepancy measure which is used to judge whether the simulated data resemble the observed data. The second difficulty is the computationally efficient identification of regions in the parameter space where the discrepancy is low. We give here an introduction to our recent work where we tackle the two difficulties through classification and Bayesian optimization.

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