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Consistency Models for Scalable and Fast Simulation-Based Inference
Dec 09, 2023
Simulation-based inference (SBI) is constantly in search of more expressive algorithms for accurately inferring the parameters of complex models from noisy data. We present consistency models for neural posterior estimation (CMPE), a new free-form conditional sampler for scalable, fast, and amortized SBI with generative neural networks. CMPE combines the advantages of normalizing flows and flow matching methods into a single generative architecture: It essentially distills a continuous probability flow and enables rapid few-shot inference with an unconstrained architecture that can be tailored to the structure of the estimation problem. Our empirical evaluation demonstrates that CMPE not only outperforms current state-of-the-art algorithms on three hard low-dimensional problems, but also achieves competitive performance in a high-dimensional Bayesian denoising experiment and in estimating a computationally demanding multi-scale model of tumor spheroid growth.
Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference
Dec 08, 2023Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to predictions, inference, and subsequent decision-relevant quantities. However, quantifying and then propagating the uncertainty of surrogates is usually limited to special analytic cases or is otherwise computationally very expensive. In this paper, we propose a framework enabling a scalable, Bayesian approach to surrogate modeling with thorough uncertainty quantification, propagation, and validation. Specifically, we present three methods for Bayesian inference with surrogate models given measurement data. This is a task where the propagation of surrogate uncertainty is especially relevant, because failing to account for it may lead to biased and/or overconfident estimates of the parameters of interest. We showcase our approach in two detailed case studies for both linear and nonlinear modeling scenarios. Uncertainty propagation in surrogate models enables more reliable and safe approximation of expensive simulators and will therefore be useful in various fields of applications.
Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inference
Nov 17, 2023
We present multimodal neural posterior estimation (MultiNPE), a method to integrate heterogeneous data from different sources in simulation-based inference with neural networks. Inspired by advances in attention-based deep fusion learning, it empowers researchers to analyze data from different domains and infer the parameters of complex mathematical models with increased accuracy. We formulate different multimodal fusion approaches for MultiNPE (early, late, and hybrid) and evaluate their performance in three challenging numerical experiments. MultiNPE not only outperforms na\"ive baselines on a benchmark model, but also achieves superior inference on representative scientific models from neuroscience and cardiology. In addition, we systematically investigate the impact of partially missing data on the different fusion strategies. Across our different experiments, late and hybrid fusion techniques emerge as the methods of choice for practical applications of multimodal simulation-based inference.
Sensitivity-Aware Amortized Bayesian Inference
Oct 23, 2023Bayesian inference is a powerful framework for making probabilistic inferences and decisions under uncertainty. Fundamental choices in modern Bayesian workflows concern the specification of the likelihood function and prior distributions, the posterior approximator, and the data. Each choice can significantly influence model-based inference and subsequent decisions, thereby necessitating sensitivity analysis. In this work, we propose a multifaceted approach to integrate sensitivity analyses into amortized Bayesian inference (ABI, i.e., simulation-based inference with neural networks). First, we utilize weight sharing to encode the structural similarities between alternative likelihood and prior specifications in the training process with minimal computational overhead. Second, we leverage the rapid inference of neural networks to assess sensitivity to various data perturbations or pre-processing procedures. In contrast to most other Bayesian approaches, both steps circumvent the costly bottleneck of refitting the model(s) for each choice of likelihood, prior, or dataset. Finally, we propose to use neural network ensembles to evaluate variation in results induced by unreliable approximation on unseen data. We demonstrate the effectiveness of our method in applied modeling problems, ranging from the estimation of disease outbreak dynamics and global warming thresholds to the comparison of human decision-making models. Our experiments showcase how our approach enables practitioners to effectively unveil hidden relationships between modeling choices and inferential conclusions.
Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference
Oct 10, 2023We propose a method to improve the efficiency and accuracy of amortized Bayesian inference (ABI) by leveraging universal symmetries in the probabilistic joint model $p(\theta, y)$ of parameters $\theta$ and data $y$. In a nutshell, we invert Bayes' theorem and estimate the marginal likelihood based on approximate representations of the joint model. Upon perfect approximation, the marginal likelihood is constant across all parameter values by definition. However, approximation error leads to undesirable variance in the marginal likelihood estimates across different parameter values. We formulate violations of this symmetry as a loss function to accelerate the learning dynamics of conditional neural density estimators. We apply our method to a bimodal toy problem with an explicit likelihood (likelihood-based) and a realistic model with an implicit likelihood (simulation-based).
Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models
Aug 22, 2023
A central characteristic of Bayesian statistics is the ability to consistently incorporate prior knowledge into various modeling processes. In this paper, we focus on translating domain expert knowledge into corresponding prior distributions over model parameters, a process known as prior elicitation. Expert knowledge can manifest itself in diverse formats, including information about raw data, summary statistics, or model parameters. A major challenge for existing elicitation methods is how to effectively utilize all of these different formats in order to formulate prior distributions that align with the expert's expectations, regardless of the model structure. To address these challenges, we develop a simulation-based elicitation method that can learn the hyperparameters of potentially any parametric prior distribution from a wide spectrum of expert knowledge using stochastic gradient descent. We validate the effectiveness and robustness of our elicitation method in four representative case studies covering linear models, generalized linear models, and hierarchical models. Our results support the claim that our method is largely independent of the underlying model structure and adaptable to various elicitation techniques, including quantile-based, moment-based, and histogram-based methods.
BayesFlow: Amortized Bayesian Workflows With Neural Networks
Jul 10, 2023
Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis. Typical problems in Bayesian workflows are the approximation of intractable posterior distributions for diverse model types and the comparison of competing models of the same process in terms of their complexity and predictive performance. This manuscript introduces the Python library BayesFlow for simulation-based training of established neural network architectures for amortized data compression and inference. Amortized Bayesian inference, as implemented in BayesFlow, enables users to train custom neural networks on model simulations and re-use these networks for any subsequent application of the models. Since the trained networks can perform inference almost instantaneously, the upfront neural network training is quickly amortized.
JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models
Feb 17, 2023
This work proposes ''jointly amortized neural approximation'' (JANA) of intractable likelihood functions and posterior densities arising in Bayesian surrogate modeling and simulation-based inference. We train three complementary networks in an end-to-end fashion: 1) a summary network to compress individual data points, sets, or time series into informative embedding vectors; 2) a posterior network to learn an amortized approximate posterior; and 3) a likelihood network to learn an amortized approximate likelihood. Their interaction opens a new route to amortized marginal likelihood and posterior predictive estimation -- two important ingredients of Bayesian workflows that are often too expensive for standard methods. We benchmark the fidelity of JANA on a variety of simulation models against state-of-the-art Bayesian methods and propose a powerful and interpretable diagnostic for joint calibration. In addition, we investigate the ability of recurrent likelihood networks to emulate complex time series models without resorting to hand-crafted summary statistics.
A Deep Learning Method for Comparing Bayesian Hierarchical Models
Jan 27, 2023
Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then use our method to compare four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. In this application, we corroborate evidence for the recently proposed L\'evy flight model of decision-making and show how transfer learning can be leveraged to enhance training efficiency. Reproducible code for all analyses is provided.
Neural Superstatistics: A Bayesian Method for Estimating Dynamic Models of Cognition
Nov 30, 2022
Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic, regardless of the reference time scale. Thus, we propose to augment mechanistic cognitive models with a temporal dimension and estimate the resulting dynamics from a superstatistics perspective. In its simplest form, such a model entails a hierarchy between a low-level observation model and a high-level transition model. The observation model describes the local behavior of a system, and the transition model specifies how the parameters of the observation model evolve over time. To overcome the estimation challenges resulting from the complexity of superstatistical models, we develop and validate a simulation-based deep learning method for Bayesian inference, which can recover both time-varying and time-invariant parameters. We first benchmark our method against two existing frameworks capable of estimating time-varying parameters. We then apply our method to fit a dynamic version of the diffusion decision model to long time series of human response times data. Our results show that the deep learning approach is very efficient in capturing the temporal dynamics of the model. Furthermore, we show that the erroneous assumption of static or homogeneous parameters will hide important temporal information.