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Michael U. Gutmann

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17 papers

2 author rows

TMLR Journal 2024 Journal Article

Improving Variational Autoencoder Estimation from Incomplete Data with Mixture Variational Families

Vaidotas Simkus
Michael U. Gutmann

We consider the task of estimating variational autoencoders (VAEs) when the training data is incomplete. We show that missing data increases the complexity of the model’s posterior distribution over the latent variables compared to the fully-observed case. The increased complexity may adversely affect the fit of the model due to a mismatch between the variational and model posterior distributions. We introduce two strategies based on (i) finite variational-mixture and (ii) imputation-based variational-mixture distributions to address the increased posterior complexity. Through a comprehensive evaluation of the proposed approaches, we show that variational mixtures are effective at improving the accuracy of VAE estimation from incomplete data.

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TMLR Journal 2023 Journal Article

Bayesian Optimization with Informative Covariance

Afonso Eduardo
Michael U. Gutmann

Bayesian optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression models are given by Gaussian processes with stationary covariance functions. However, these functions are unable to express prior input-dependent information, including possible locations of the optimum. The ubiquity of stationary models has led to the common practice of exploiting prior information via informative mean functions. In this paper, we highlight that these models can perform poorly, especially in high dimensions. We propose novel informative covariance functions for optimization, leveraging nonstationarity to encode preferences for certain regions of the search space and adaptively promote local exploration during optimization. We demonstrate that the proposed functions can increase the sample efficiency of Bayesian optimization in high dimensions, even under weak prior information.

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TMLR Journal 2023 Journal Article

Conditional Sampling of Variational Autoencoders via Iterated Approximate Ancestral Sampling

Vaidotas Simkus
Michael U. Gutmann

Conditional sampling of variational autoencoders (VAEs) is needed in various applications, such as missing data imputation, but is computationally intractable. A principled choice for asymptotically exact conditional sampling is Metropolis-within-Gibbs (MWG). However, we observe that the tendency of VAEs to learn a structured latent space, a commonly desired property, can cause the MWG sampler to get “stuck” far from the target distribution. This paper mitigates the limitations of MWG: we systematically outline the pitfalls in the context of VAEs, propose two original methods that address these pitfalls, and demonstrate an improved performance of the proposed methods on a set of sampling tasks.

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TMLR Journal 2023 Journal Article

Estimating the Density Ratio between Distributions with High Discrepancy using Multinomial Logistic Regression

Akash Srivastava
Seungwook Han
Kai Xu
Benjamin Rhodes
Michael U. Gutmann

Functions of the ratio of the densities $p/q$ are widely used in machine learning to quantify the discrepancy between the two distributions $p$ and $q$. For high-dimensional distributions, binary classification-based density ratio estimators have shown great promise. However, when densities are well-separated, estimating the density ratio with a binary classifier is challenging. In this work, we show that the state-of-the-art density ratio estimators do perform poorly on well-separated cases and demonstrate that this is due to distribution shifts between training and evaluation time. We present an alternative method that leverages multi-class classification for density ratio estimation and does not suffer from distribution shift issues. The method uses a set of auxiliary densities $\{m_k\}_{k=1}^K$ and trains a multi-class logistic regression to classify the samples from $p, q$ and $\{m_k\}_{k=1}^K$ into $K+2$ classes. We show that if these auxiliary densities are constructed such that they overlap with $p$ and $q$, then a multi-class logistic regression allows for estimating $\log p/q$ on the domain of any of the $K+2$ distributions and resolves the distribution shift problems of the current state-of-the-art methods. We compare our method to state-of-the-art density ratio estimators on both synthetic and real datasets and demonstrate its superior performance on the tasks of density ratio estimation, mutual information estimation, and representation learning.

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ICML Conference 2023 Conference Paper

Is Learning Summary Statistics Necessary for Likelihood-free Inference?

Yanzhi Chen
Michael U. Gutmann
Adrian Weller

Likelihood-free inference (LFI) is a set of techniques for inference in implicit statistical models. A longstanding question in LFI has been how to design or learn good summary statistics of data, but this might now seem unnecessary due to the advent of recent end-to-end (i. e. neural network-based) LFI methods. In this work, we rethink this question with a new method for learning summary statistics. We show that learning sufficient statistics may be easier than direct posterior inference, as the former problem can be reduced to a set of low-dimensional, easy-to-solve learning problems. This suggests us to explicitly decouple summary statistics learning from posterior inference in LFI. Experiments on diverse inference tasks with different data types validate our hypothesis.

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JMLR Journal 2023 Journal Article

Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data

Vaidotas Simkus
Benjamin Rhodes
Michael U. Gutmann

Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are controlled by free parameters that are typically estimated from data by maximum-likelihood estimation or approximations thereof. However, when faced with real-world data sets many of the models run into a critical issue: they are formulated in terms of fully-observed data, whereas in practice the data sets are plagued with missing data. The theory of statistical model estimation from incomplete data is conceptually similar to the estimation of latent-variable models, where powerful tools such as variational inference (VI) exist. However, in contrast to standard latent-variable models, parameter estimation with incomplete data often requires estimating exponentially-many conditional distributions of the missing variables, hence making standard VI methods intractable. We address this gap by introducing variational Gibbs inference (VGI), a new general-purpose method to estimate the parameters of statistical models from incomplete data. We validate VGI on a set of synthetic and real-world estimation tasks, estimating important machine learning models such as variational autoencoders and normalising flows from incomplete data. The proposed method, whilst general-purpose, achieves competitive or better performance than existing model-specific estimation methods. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

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TMLR Journal 2022 Journal Article

Enhanced gradient-based MCMC in discrete spaces

Benjamin Rhodes
Michael U. Gutmann

The recent introduction of gradient-based Markov chain Monte Carlo (MCMC) for discrete spaces holds great promise, and comes with the tantalising possibility of new discrete counterparts to celebrated continuous methods such as the Metropolis-adjusted Langevin algorithm (MALA). Towards this goal, we introduce several discrete Metropolis-Hastings samplers that are conceptually inspired by MALA, and demonstrate their strong empirical performance across a range of challenging sampling problems in Bayesian inference and energy-based modelling. Methodologically, we identify why discrete analogues to \emph{preconditioned} MALA are generally intractable, motivating us to introduce a new kind of preconditioning based on auxiliary variables and the `Gaussian integral trick'.

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NeurIPS Conference 2021 Conference Paper

Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods

Desi R Ivanova
Adam Foster
Steven Kleinegesse
Michael U. Gutmann
Thomas Rainforth

We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy network upfront, which can then be deployed quickly at the time of the experiment. The iDAD network can be trained on any model which simulates differentiable samples, unlike previous design policy work that requires a closed form likelihood and conditionally independent experiments. At deployment, iDAD allows design decisions to be made in milliseconds, in contrast to traditional BOED approaches that require heavy computation during the experiment itself. We illustrate the applicability of iDAD on a number of experiments, and show that it provides a fast and effective mechanism for performing adaptive design with implicit models.

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ICLR Conference 2021 Conference Paper

Neural Approximate Sufficient Statistics for Implicit Models

Yanzhi Chen
Dinghuai Zhang
Michael U. Gutmann
Aaron C. Courville
Zhanxing Zhu

We consider the fundamental problem of how to automatically construct summary statistics for implicit generative models where the evaluation of the likelihood function is intractable but sampling data from the model is possible. The idea is to frame the task of constructing sufficient statistics as learning mutual information maximizing representations of the data with the help of deep neural networks. The infomax learning procedure does not need to estimate any density or density ratio. We apply our approach to both traditional approximate Bayesian computation and recent neural likelihood methods, boosting their performance on a range of tasks.

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ICML Conference 2020 Conference Paper

Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation

Steven Kleinegesse
Michael U. Gutmann

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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ICLR Conference 2020 Conference Paper

Generative Ratio Matching Networks

Akash Srivastava
Kai Xu 0016
Michael U. Gutmann
Charles Sutton

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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IROS Conference 2020 Conference Paper

Stir to Pour: Efficient Calibration of Liquid Properties for Pouring Actions

Tatiana Lopez-Guevara
Rita Pucci
Nicholas K. Taylor
Michael U. Gutmann
Subramanian Ramamoorthy
Kartic Subr

Humans use simple probing actions to develop intuition about the physical behavior of common objects. Such intuition is particularly useful for adaptive estimation of favorable manipulation strategies of those objects in novel contexts. For example, observing the effect of tilt on a transparent bottle containing an unknown liquid provides clues on how the liquid might be poured. It is desirable to equip general-purpose robotic systems with this capability because it is inevitable that they will encounter novel objects and scenarios. In this paper, we teach a robot to use a simple, specified probing strategy - stirring with a stick- to reduce spillage when pouring unknown liquids. In the probing step, we continuously observe the effects of a real robot stirring a liquid, while simultaneously tuning the parameters to a model (simulator) until the two outputs are in agreement. We obtain optimal simulation parameters, characterizing the unknown liquid, via a Bayesian Optimizer that minimizes the discrepancy between real and simulated outcomes. Then, we optimize the pouring policy conditioning on the optimal simulation parameters determined via stirring. We show that using stirring as a probing strategy result in reduced spillage for three qualitatively different liquids when executed on a UR10 Robot, compared to probing via pouring. Finally, we provide quantitative insights into the reason for stirring being a suitable calibration task for pouring -a step towards automatic discovery of probing strategies.

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NeurIPS Conference 2020 Conference Paper

Telescoping Density-Ratio Estimation

Benjamin Rhodes
Kai Xu
Michael U. Gutmann

Density-ratio estimation via classification is a cornerstone of unsupervised learning. It has provided the foundation for state-of-the-art methods in representation learning and generative modelling, with the number of use-cases continuing to proliferate. However, it suffers from a critical limitation: it fails to accurately estimate ratios p/q for which the two densities differ significantly. Empirically, we find this occurs whenever the KL divergence between p and q exceeds tens of nats. To resolve this limitation, we introduce a new framework, telescoping density-ratio estimation (TRE), that enables the estimation of ratios between highly dissimilar densities in high-dimensional spaces. Our experiments demonstrate that TRE can yield substantial improvements over existing single-ratio methods for mutual information estimation, representation learning and energy-based modelling.

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ICML Conference 2018 Conference Paper

Conditional Noise-Contrastive Estimation of Unnormalised Models

Ciwan Ceylan
Michael U. Gutmann

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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JMLR Journal 2018 Journal Article

ELFI: Engine for Likelihood-Free Inference

Jarno Lintusaari
Henri Vuollekoski
Antti Kangasrääsiö
Kusti Skytén
Marko Järvenpää
Pekka Marttinen
Michael U. Gutmann
Aki Vehtari

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. [abs] [ pdf ][ bib ] [ webpage ] [ code ] &copy JMLR 2018. ( edit, beta )

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JMLR Journal 2016 Journal Article

Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models

Michael U. Gutmann
Jukka Corander

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. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

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JMLR Journal 2012 Journal Article

Noise-Contrastive Estimation of Unnormalized Statistical Models, with Applications to Natural Image Statistics

Michael U. Gutmann
Aapo Hyvärinen

We consider the task of estimating, from observed data, a probabilistic model that is parameterized by a finite number of parameters. In particular, we are considering the situation where the model probability density function is unnormalized. That is, the model is only specified up to the partition function. The partition function normalizes a model so that it integrates to one for any choice of the parameters. However, it is often impossible to obtain it in closed form. Gibbs distributions, Markov and multi-layer networks are examples of models where analytical normalization is often impossible. Maximum likelihood estimation can then not be used without resorting to numerical approximations which are often computationally expensive. We propose here a new objective function for the estimation of both normalized and unnormalized models. The basic idea is to perform nonlinear logistic regression to discriminate between the observed data and some artificially generated noise. With this approach, the normalizing partition function can be estimated like any other parameter. We prove that the new estimation method leads to a consistent (convergent) estimator of the parameters. For large noise sample sizes, the new estimator is furthermore shown to behave like the maximum likelihood estimator. In the estimation of unnormalized models, there is a trade-off between statistical and computational performance. We show that the new method strikes a competitive trade-off in comparison to other estimation methods for unnormalized models. As an application to real data, we estimate novel two-layer models of natural image statistics with spline nonlinearities. [abs] [ pdf ][ bib ] &copy JMLR 2012. ( edit, beta )

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