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Marvin Schmitt

Publications and source records attributed to Marvin Schmitt.

17 recordsLinked to original sources
arXiv2026

BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Python

Modern Bayesian inference involves a mixture of computational methods for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows. An overarching motif of many Bayesian methods is that they are relatively slow, which often becomes prohibitive when fitting complex models to large data sets. Amortized Bayesian inference (ABI) offers a path to solving the computational challenges of Bayes. ABI trains neural networks on model simulations, rewarding users with rapid inference of any model-implied quantity, such as point estimates, likelihoods, or full posterior distributions. In this work, we present the Python library BayesFlow, Version 2.0, for general-purpose ABI. Along with direct posterior, likelihood, and ratio estimation, the software includes support for multiple popular deep learning backends, a rich collection of generative networks for sampling and density estimation, complete customization and high-level interfaces, as well as new capabilities for hyperparameter optimization, design optimization, and hierarchical modeling. Using a case study on dynamical system parameter estimation, combined with comparisons to similar software, we show that our streamlined, user-friendly workflow has strong potential to support broad adoption.

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arXiv2026

Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data

Amortized Bayesian inference (ABI) with neural networks can solve probabilistic inverse problems orders of magnitude faster than classical methods. However, ABI is not yet sufficiently robust for widespread and safe application. When performing inference on observations outside the scope of the simulated training data, posterior approximations are likely to become highly biased, which cannot be corrected by additional simulations due to the bad pre-asymptotic behavior of current neural posterior estimators. In this paper, we propose a semi-supervised approach that enables training not only on labeled simulated data generated from the model, but also on \textit{unlabeled} data originating from any source, including real data. To achieve this, we leverage Bayesian self-consistency properties that can be transformed into strictly proper losses that do not require knowledge of ground-truth parameters. We test our approach on several real-world case studies, including applications to high-dimensional time-series and image data. Our results show that semi-supervised learning with unlabeled data drastically improves the robustness of ABI in the out-of-simulation regime. Notably, inference remains accurate even when evaluated on observations far away from the labeled and unlabeled data seen during training.

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arXiv2026

Amortized Bayesian Workflow

Bayesian inference often faces a trade-off between computational speed and sampling accuracy. We propose an adaptive workflow that integrates rapid amortized inference with gold-standard MCMC techniques to achieve a favorable combination of both speed and accuracy when performing inference on many observed datasets. Our approach uses principled diagnostics to guide the choice of inference method for each dataset, moving along the Pareto front from fast amortized sampling via generative neural networks to slower but guaranteed-accurate MCMC when needed. By reusing computations across steps, our workflow synergizes amortized and MCMC-based inference. We demonstrate the effectiveness of this integrated approach on several synthetic and real-world problems with tens of thousands of datasets, showing efficiency gains while maintaining high posterior quality.

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arXiv2026

Enhancing Sentiment Classification and Irony Detection in Large Language Models through Advanced Prompt Engineering Techniques

This study investigates the use of prompt engineering to enhance large language models (LLMs), specifically GPT-4o-mini and gemini-1.5-flash, in sentiment analysis tasks. It evaluates advanced prompting techniques like few-shot learning, chain-of-thought prompting, and self-consistency against a baseline. Key tasks include sentiment classification, aspect-based sentiment analysis, and detecting subtle nuances such as irony. The research details the theoretical background, datasets, and methods used, assessing performance of LLMs as measured by accuracy, recall, precision, and F1 score. Findings reveal that advanced prompting significantly improves sentiment analysis, with the few-shot approach excelling in GPT-4o-mini and chain-of-thought prompting boosting irony detection in gemini-1.5-flash by up to 46%. Thus, while advanced prompting techniques overall improve performance, the fact that few-shot prompting works best for GPT-4o-mini and chain-of-thought excels in gemini-1.5-flash for irony detection suggests that prompting strategies must be tailored to both the model and the task. This highlights the importance of aligning prompt design with both the LLM's architecture and the semantic complexity of the task.

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arXiv2025

Simulations in Statistical Workflows

Simulations play important and diverse roles in statistical workflows, for example, in model specification, checking, validation, and even directly in model inference. Over the past decades, the application areas and overall potential of simulations in statistical workflows have expanded significantly, driven by the development of new simulation-based algorithms and exponentially increasing computational resources. In this paper, we examine past and current trends in the field and offer perspectives on how simulations may shape the future of statistical practice.

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arXiv2025

Amortized Bayesian Multilevel Models

Multilevel models (MLMs) are a central building block of the Bayesian workflow. They enable joint, interpretable modeling of data across hierarchical levels and provide a fully probabilistic quantification of uncertainty. Despite their well-recognized advantages, MLMs pose significant computational challenges, often rendering their estimation and evaluation intractable within reasonable time constraints. Recent advances in simulation-based inference offer promising solutions for addressing complex probabilistic models using deep generative networks. However, the utility and reliability of deep learning methods for estimating Bayesian MLMs remains largely unexplored, especially when compared with gold-standard samplers. To this end, we explore a family of neural network architectures that leverage the probabilistic factorization of multilevel models to facilitate efficient neural network training and subsequent near-instant posterior inference on unseen datasets. We test our method on several real-world case studies and provide comprehensive comparisons to Stan's gold standard sampler, where possible. Finally, we provide an open-source implementation of our methods to stimulate further research in the nascent field of amortized Bayesian inference.

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arXiv2025

Posterior SBC: Simulation-Based Calibration Checking Conditional on Data

Simulation-based calibration checking (SBC) refers to the validation of an inference algorithm and model implementation through repeated inference on data simulated from a generative model. In the original and commonly used approach, the generative model uses parameters drawn from the prior, and thus the approach is testing whether the inference works for simulated data generated with parameter values plausible under that prior. This approach is natural and desirable when we want to test whether the inference works for a wide range of datasets we might observe. However, after observing data, we are interested in answering whether the inference works conditional on that particular data. In this paper, we propose posterior SBC and demonstrate how it can be used to validate the inference conditionally on observed data. We illustrate the utility of posterior SBC in three case studies: (1) A simple multilevel model; (2) a model that is governed by differential equations; and (3) a joint integrative neuroscience model which is approximated via amortized Bayesian inference with neural networks.

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arXiv2024

Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inference

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 deep fusion, it allows researchers to analyze data from different domains and infer the parameters of complex mathematical models with increased accuracy. We consider three fusion approaches for MultiNPE (early, late, hybrid) and evaluate their performance in three challenging experiments. MultiNPE not only outperforms single-source baselines on a reference task, but also achieves superior inference on scientific models from cognitive neuroscience and cardiology. We systematically investigate the impact of partially missing data on the different fusion strategies. Across our experiments, late and hybrid fusion techniques emerge as the methods of choice for practical applications of multimodal simulation-based inference.

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arXiv2024

Consistency Models for Scalable and Fast Simulation-Based Inference

Simulation-based inference (SBI) is constantly in search of more expressive and efficient algorithms to accurately infer the parameters of complex simulation models. In line with this goal, we present consistency models for posterior estimation (CMPE), a new conditional sampler for SBI that inherits the advantages of recent unconstrained architectures and overcomes their sampling inefficiency at inference time. CMPE essentially distills a continuous probability flow and enables rapid few-shot inference with an unconstrained architecture that can be flexibly tailored to the structure of the estimation problem. We provide hyperparameters and default architectures that support consistency training over a wide range of different dimensions, including low-dimensional ones which are important in SBI workflows but were previously difficult to tackle even with unconditional consistency models. Our empirical evaluation demonstrates that CMPE not only outperforms current state-of-the-art algorithms on hard low-dimensional benchmarks, but also achieves competitive performance with much faster sampling speed on two realistic estimation problems with high data and/or parameter dimensions.

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arXiv2024

Sensitivity-Aware Amortized Bayesian Inference

Sensitivity analyses reveal the influence of various modeling choices on the outcomes of statistical analyses. While theoretically appealing, they are overwhelmingly inefficient for complex Bayesian models. In this work, we propose sensitivity-aware amortized Bayesian inference (SA-ABI), a multifaceted approach to efficiently integrate sensitivity analyses into 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 data perturbations and preprocessing steps. In contrast to most other Bayesian approaches, both steps circumvent the costly bottleneck of refitting the model for each choice of likelihood, prior, or data set. Finally, we propose to use deep ensembles to detect sensitivity arising from unreliable approximation (e.g., due to model misspecification). We demonstrate the effectiveness of our method in applied modeling problems, ranging from disease outbreak dynamics and global warming thresholds to human decision-making. Our results support sensitivity-aware inference as a default choice for amortized Bayesian workflows, automatically providing modelers with insights into otherwise hidden dimensions.

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arXiv2024

Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference

We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. 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, errors in approximate inference lead to undesirable variance in the marginal likelihood estimates across different parameter values. We penalize violations of this symmetry with a \textit{self-consistency loss} which significantly improves the quality of approximate inference in low data regimes and can be used to augment the training of popular neural density estimators. We apply our method to a number of synthetic problems and realistic scientific models, discovering notable advantages in the context of both neural posterior and likelihood approximation.

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arXiv2024

Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigation

Recent advances in probabilistic deep learning enable efficient amortized Bayesian inference in settings where the likelihood function is only implicitly defined by a simulation program (simulation-based inference; SBI). But how faithful is such inference if the simulation represents reality somewhat inaccurately, that is, if the true system behavior at test time deviates from the one seen during training? We conceptualize the types of such model misspecification arising in SBI and systematically investigate how the performance of neural posterior approximators gradually deteriorates as a consequence, making inference results less and less trustworthy. To notify users about this problem, we propose a new misspecification measure that can be trained in an unsupervised fashion (i.e., without training data from the true distribution) and reliably detects model misspecification at test time. Our experiments clearly demonstrate the utility of our new measure both on toy examples with an analytical ground-truth and on representative scientific tasks in cell biology, cognitive decision making, disease outbreak dynamics, and computer vision. We show how the proposed misspecification test warns users about suspicious outputs, raises an alarm when predictions are not trustworthy, and guides model designers in their search for better simulators.

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arXiv2024

The Simplex Projection: Lossless Visualization of 4D Compositional Data on a 2D Canvas

The simplex projection expands the capabilities of simplex plots (also known as ternary plots) to achieve a lossless visualization of 4D compositional data on a 2D canvas. Previously, this was only possible for 3D compositional data. We demonstrate how our approach can be applied to individual data points, point clouds, and continuous probability density functions on simplices. While we showcase our visualization technique specifically for 4D compositional data, we offer rigorous proofs that support its extension to compositional data of any (finite) dimensionality.

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arXiv2023

BayesFlow: Amortized Bayesian Workflows With Neural Networks

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.

cs.LG↗
arXiv2023

JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models

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.

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arXiv2023

Meta-Uncertainty in Bayesian Model Comparison

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed data of interest. These posterior model probabilities (PMPs) are measures of uncertainty, but -- when derived from a finite number of observations -- are also uncertain themselves. In this paper, we conceptualize distinct levels of uncertainty which arise in BMC. We explore a fully probabilistic framework for quantifying meta-uncertainty, resulting in an applied method to enhance any BMC workflow. Drawing on both Bayesian and frequentist techniques, we represent the uncertainty over the uncertain PMPs via meta-models which combine simulated and observed data into a predictive distribution for PMPs on new data. We demonstrate the utility of the proposed method in the context of conjugate Bayesian regression, likelihood-based inference with Markov chain Monte Carlo, and simulation-based inference with neural networks.

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arXiv2022

Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks

Neural density estimators have proven remarkably powerful in performing efficient simulation-based Bayesian inference in various research domains. In particular, the BayesFlow framework uses a two-step approach to enable amortized parameter estimation in settings where the likelihood function is implicitly defined by a simulation program. But how faithful is such inference when simulations are poor representations of reality? In this paper, we conceptualize the types of model misspecification arising in simulation-based inference and systematically investigate the performance of the BayesFlow framework under these misspecifications. We propose an augmented optimization objective which imposes a probabilistic structure on the latent data space and utilize maximum mean discrepancy (MMD) to detect potentially catastrophic misspecifications during inference undermining the validity of the obtained results. We verify our detection criterion on a number of artificial and realistic misspecifications, ranging from toy conjugate models to complex models of decision making and disease outbreak dynamics applied to real data. Further, we show that posterior inference errors increase as a function of the distance between the true data-generating distribution and the typical set of simulations in the latent summary space. Thus, we demonstrate the dual utility of MMD as a method for detecting model misspecification and as a proxy for verifying the faithfulness of amortized Bayesian inference.

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