More Like this

1. Demonstrating the Power and Flexibility of Variational Assumptions for Amortized Neural Posterior Estimation in Environmental Applications

   https://doi.org/10.1002/env.70074  

   Maceda, Elliot; Hector, Emily C; Lenzi, Amanda; Reich, Brian J (January 2026, Environmetrics)

   ABSTRACT Classic Bayesian methods with complex environmental models are frequently infeasible due to an intractable likelihood. Simulation‐based inference methods, such as neural posterior estimation, calculate posteriors without accessing a likelihood function by leveraging the fact that data can be quickly simulated from the model, but converge slowly and/or poorly in high‐dimensional settings. In this paper, we suggest that imposing strict variational assumptions on the form of the posterior can often combat these computational issues. Posterior distributions of model parameters are efficiently obtained by assuming a parametric form for the posterior, parametrized by the machine learning model, which is trained with the simulated data as inputs and the associated parameters as outputs. We show theoretically that if the parametric family of the variational posterior is correct, our posteriors converge to the true posteriors in Kullback–Leibler divergence. We also provide tools to help us identify if our parametric assumption is close to the true posterior, and modeling options if that is not the case. Comprehensive simulation studies using environmental models highlight our method's robustness and versatility. An analysis of the Zika virus in Brazil provides a thorough case study. 

   more » « less
2. Learning and Inference in Sparse Coding Models With Langevin Dynamics

   https://doi.org/10.1162/neco_a_01505  

   Fang, Michael Y.-S.; Mudigonda, Mayur; Zarcone, Ryan; Khosrowshahi, Amir; Olshausen, Bruno A. (July 2022, Neural Computation)

   Abstract We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models—sampling the posterior distribution over latent variables—is proposed to be solved by harnessing natural sources of stochasticity inherent in electronic and neural systems. We demonstrate this idea for a sparse coding model by deriving a continuous-time equation for inferring its latent variables via Langevin dynamics. The model parameters are learned by simultaneously evolving according to another continuous-time equation, thus bypassing the need for digital accumulators or a global clock. Moreover, we show that Langevin dynamics lead to an efficient procedure for sampling from the posterior distribution in the L0 sparse regime, where latent variables are encouraged to be set to zero as opposed to having a small L1 norm. This allows the model to properly incorporate the notion of sparsity rather than having to resort to a relaxed version of sparsity to make optimization tractable. Simulations of the proposed dynamical system on both synthetic and natural image data sets demonstrate that the model is capable of probabilistically correct inference, enabling learning of the dictionary as well as parameters of the prior. 

   more » « less
3. Deep Learning and Likelihood Approaches for Viral Phylogeography Converge on the Same Answers Whether the Inference Model Is Right or Wrong

   https://doi.org/10.1093/sysbio/syad074  

   Thompson, Ammon; Liebeskind, Benjamin J; Scully, Erik J; Landis, Michael J (January 2024, Systematic Biology)

   Perez, Manolo (Ed.)

   Abstract Analysis of phylogenetic trees has become an essential tool in epidemiology. Likelihood-based methods fit models to phylogenies to draw inferences about the phylodynamics and history of viral transmission. However, these methods are often computationally expensive, which limits the complexity and realism of phylodynamic models and makes them ill-suited for informing policy decisions in real-time during rapidly developing outbreaks. Likelihood-free methods using deep learning are pushing the boundaries of inference beyond these constraints. In this paper, we extend, compare, and contrast a recently developed deep learning method for likelihood-free inference from trees. We trained multiple deep neural networks using phylogenies from simulated outbreaks that spread among 5 locations and found they achieve close to the same levels of accuracy as Bayesian inference under the true simulation model. We compared robustness to model misspecification of a trained neural network to that of a Bayesian method. We found that both models had comparable performance, converging on similar biases. We also implemented a method of uncertainty quantification called conformalized quantile regression that we demonstrate has similar patterns of sensitivity to model misspecification as Bayesian highest posterior density (HPD) and greatly overlap with HPDs, but have lower precision (more conservative). Finally, we trained and tested a neural network against phylogeographic data from a recent study of the SARS-Cov-2 pandemic in Europe and obtained similar estimates of region-specific epidemiological parameters and the location of the common ancestor in Europe. Along with being as accurate and robust as likelihood-based methods, our trained neural networks are on average over 3 orders of magnitude faster after training. Our results support the notion that neural networks can be trained with simulated data to accurately mimic the good and bad statistical properties of the likelihood functions of generative phylogenetic models. 

   more » « less
4. A comparative study of simulation-based inference methods for epidemic models with identifiability considerations

   https://doi.org/10.1371/journal.pcbi.1014364  

   Jang, Geunsoo; Candan, K Selçuk; Chowell, Gerardo (June 2026, PLOS Computational Biology)

   Miles, Christopher E (Ed.)

   Epidemic models play a critical role in understanding transmission dynamics, generating forecasts, and informing public health interventions when they are properly calibrated to epidemiological data. Traditional Bayesian inference methods rely on the likelihood function to update prior knowledge using observed data. However, for realistic epidemic models, likelihood functions are often analytically intractable or computationally prohibitive, which can limit the applicability of these methods. Simulation-based inference provides a promising alternative by approximating posterior distributions through forward simulations rather than an explicit likelihood evaluation. In this study, we present a systematic comparison of four approaches: Approximate Bayesian Computation (ABC), Neural Posterior Estimation (NPE), a neural method with temporal embedding, and Preconditioned Neural Posterior Estimation (PNPE), which integrates elements of both classical and neural techniques. These methods are evaluated across epidemic models of increasing complexity under fixed simulation budgets and varying levels of observational noise, with explicit attention to both structural and practical identifiability. Our results show that neural methods generally improve posterior fidelity and predictive accuracy compared with ABC under constrained simulation budgets. PNPE achieved strong performance in several simulation settings, whereas temporal embeddings improved inference in models with complex epidemic dynamics by capturing sequential dependencies. These gains come with important trade-offs: PNPE required substantially greater computational resources and, unlike fully amortized NPE-based methods, may require reconditioning for each new observation. In contrast, ABC remained computationally efficient and provided reasonable, though often more conservative, posterior estimates. Overall, our findings highlight trade-offs among computational efficiency, posterior accuracy, uncertainty calibration, and inference reusability, suggesting that method selection should depend on model complexity, data quality, identifiability, and available computational resources. 

   more » « less
5. Streaming Variational Monte Carlo

   https://doi.org/10.1109/TPAMI.2022.3153225  

   Zhao, Yuan; Nassar, Josue; Jordan, Ian; Bugallo, Monica; Park, Il Memming (February 2022, IEEE Transactions on Pattern Analysis and Machine Intelligence)

   Nonlinear state-space models are powerful tools to describe dynamical structures in complex time series. In a streaming setting where data are processed one sample at a time, simultaneous inference of the state and its nonlinear dynamics has posed significant challenges in practice. We develop a novel online learning framework, leveraging variational inference and sequential Monte Carlo, which enables flexible and accurate Bayesian joint filtering. Our method provides an approximation of the filtering posterior which can be made arbitrarily close to the true filtering distribution for a wide class of dynamics models and observation models. Specifically, the proposed framework can efficiently approximate a posterior over the dynamics using sparse Gaussian processes, allowing for an interpretable model of the latent dynamics. Constant time complexity per sample makes our approach amenable to online learning scenarios and suitable for real-time applications. 

   more » « less