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Luigi Acerbi

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16 papers

2 author rows

TMLR Journal 2026 Journal Article

Amortized Bayesian Workflow

Chengkun Li
Aki Vehtari
Paul-Christian Bürkner
Stefan T. Radev
Luigi Acerbi
Marvin Schmitt

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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NeurIPS Conference 2025 Conference Paper

ALINE: Joint Amortization for Bayesian Inference and Active Data Acquisition

Daolang Huang
Xinyi Wen
Ayush Bharti
Samuel Kaski
Luigi Acerbi

Many critical applications, from autonomous scientific discovery to personalized medicine, demand systems that can both strategically acquire the most informative data and instantaneously perform inference based upon it. While amortized methods for Bayesian inference and experimental design offer part of the solution, neither approach is optimal in the most general and challenging task, where new data needs to be collected for instant inference. To tackle this issue, we introduce the Amortized Active Learning and Inference Engine (ALINE), a unified framework for amortized Bayesian inference and active data acquisition. ALINE leverages a transformer architecture trained via reinforcement learning with a reward based on self-estimated information gain provided by its own integrated inference component. This allows it to strategically query informative data points while simultaneously refining its predictions. Moreover, ALINE can selectively direct its querying strategy towards specific subsets of model parameters or designated predictive tasks, optimizing for posterior estimation, data prediction, or a mixture thereof. Empirical results on regression-based active learning, classical Bayesian experimental design benchmarks, and a psychometric model with selectively targeted parameters demonstrate that ALINE delivers both instant and accurate inference along with efficient selection of informative points.

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TMLR Journal 2025 Journal Article

Stacking Variational Bayesian Monte Carlo

Francesco Silvestrin
Chengkun Li
Luigi Acerbi

Approximate Bayesian inference for models with computationally expensive, black-box likelihoods poses a significant challenge, especially when the posterior distribution is complex. Many inference methods struggle to explore the parameter space efficiently under a limited budget of likelihood evaluations. Variational Bayesian Monte Carlo (VBMC) is a sample-efficient method that addresses this by building a local surrogate model of the log-posterior. However, its conservative exploration strategy, while promoting stability, can cause it to miss important regions of the posterior, such as distinct modes or long tails. In this work, we introduce Stacking Variational Bayesian Monte Carlo (S-VBMC), a method that overcomes this limitation by constructing a robust, global posterior approximation from multiple independent VBMC runs. Our approach merges these local approximations through a principled and inexpensive post-processing step that leverages VBMC's mixture posterior representation and per-component evidence estimates. Crucially, S-VBMC requires no additional likelihood evaluations and is naturally parallelisable, fitting seamlessly into existing inference workflows. We demonstrate its effectiveness on two synthetic problems designed to challenge VBMC's exploration and two real-world applications from computational neuroscience, showing substantial improvements in posterior approximation quality across all cases. Our code is available as a Python package at https://github.com/acerbilab/svbmc.

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NeurIPS Conference 2024 Conference Paper

Amortized Bayesian Experimental Design for Decision-Making

Daolang Huang
Yujia Guo
Luigi Acerbi
Samuel Kaski

Many critical decisions, such as personalized medical diagnoses and product pricing, are made based on insights gained from designing, observing, and analyzing a series of experiments. This highlights the crucial role of experimental design, which goes beyond merely collecting information on system parameters as in traditional Bayesian experimental design (BED), but also plays a key part in facilitating downstream decision-making. Most recent BED methods use an amortized policy network to rapidly design experiments. However, the information gathered through these methods is suboptimal for down-the-line decision-making, as the experiments are not inherently designed with downstream objectives in mind. In this paper, we present an amortized decision-aware BED framework that prioritizes maximizing downstream decision utility. We introduce a novel architecture, the Transformer Neural Decision Process (TNDP), capable of instantly proposing the next experimental design, whilst inferring the downstream decision, thus effectively amortizing both tasks within a unified workflow. We demonstrate the performance of our method across several tasks, showing that it can deliver informative designs and facilitate accurate decision-making.

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NeurIPS Conference 2024 Conference Paper

Improving robustness to corruptions with multiplicative weight perturbations

Trung Trinh
Markus Heinonen
Luigi Acerbi
Samuel Kaski

Deep neural networks (DNNs) excel on clean images but struggle with corrupted ones. Incorporating specific corruptions into the data augmentation pipeline can improve robustness to those corruptions but may harm performance on clean images and other types of distortion. In this paper, we introduce an alternative approach that improves the robustness of DNNs to a wide range of corruptions without compromising accuracy on clean images. We first demonstrate that input perturbations can be mimicked by multiplicative perturbations in the weight space. Leveraging this, we propose Data Augmentation via Multiplicative Perturbation (DAMP), a training method that optimizes DNNs under random multiplicative weight perturbations. We also examine the recently proposed Adaptive Sharpness-Aware Minimization (ASAM) and show that it optimizes DNNs under adversarial multiplicative weight perturbations. Experiments on image classification datasets (CIFAR-10/100, TinyImageNet and ImageNet) and neural network architectures (ResNet50, ViT-S/16, ViT-B/16) show that DAMP enhances model generalization performance in the presence of corruptions across different settings. Notably, DAMP is able to train a ViT-S/16 on ImageNet from scratch, reaching the top-1 error of 23. 7% which is comparable to ResNet50 without extensive data augmentations.

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ICLR Conference 2024 Conference Paper

Input-gradient space particle inference for neural network ensembles

Trung Q. Trinh
Markus Heinonen
Luigi Acerbi
Samuel Kaski

Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets and transfer learning tasks show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.

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NeurIPS Conference 2024 Conference Paper

Preferential Normalizing Flows

Petrus Mikkola
Luigi Acerbi
Arto Klami

Eliciting a high-dimensional probability distribution from an expert via noisy judgments is notoriously challenging, yet useful for many applications, such as prior elicitation and reward modeling. We introduce a method for eliciting the expert's belief density as a normalizing flow based solely on preferential questions such as comparing or ranking alternatives. This allows eliciting in principle arbitrarily flexible densities, but flow estimation is susceptible to the challenge of collapsing or diverging probability mass that makes it difficult in practice. We tackle this problem by introducing a novel functional prior for the flow, motivated by a decision-theoretic argument, and show empirically that the belief density can be inferred as the function-space maximum a posteriori estimate. We demonstrate our method by eliciting multivariate belief densities of simulated experts, including the prior belief of a general-purpose large language model over a real-world dataset.

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NeurIPS Conference 2023 Conference Paper

Learning Robust Statistics for Simulation-based Inference under Model Misspecification

Daolang Huang
Ayush Bharti
Amauri Souza
Luigi Acerbi
Samuel Kaski

Simulation-based inference (SBI) methods such as approximate Bayesian computation (ABC), synthetic likelihood, and neural posterior estimation (NPE) rely on simulating statistics to infer parameters of intractable likelihood models. However, such methods are known to yield untrustworthy and misleading inference outcomes under model misspecification, thus hindering their widespread applicability. In this work, we propose the first general approach to handle model misspecification that works across different classes of SBI methods. Leveraging the fact that the choice of statistics determines the degree of misspecification in SBI, we introduce a regularized loss function that penalizes those statistics that increase the mismatch between the data and the model. Taking NPE and ABC as use cases, we demonstrate the superior performance of our method on high-dimensional time-series models that are artificially misspecified. We also apply our method to real data from the field of radio propagation where the model is known to be misspecified. We show empirically that the method yields robust inference in misspecified scenarios, whilst still being accurate when the model is well-specified.

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NeurIPS Conference 2023 Conference Paper

Practical Equivariances via Relational Conditional Neural Processes

Daolang Huang
Manuel Haussmann
Ulpu Remes
ST John
Grégoire Clarté
Kevin Luck
Samuel Kaski
Luigi Acerbi

Conditional Neural Processes (CNPs) are a class of metalearning models popular for combining the runtime efficiency of amortized inference with reliable uncertainty quantification. Many relevant machine learning tasks, such as in spatio-temporal modeling, Bayesian Optimization and continuous control, inherently contain equivariances – for example to translation – which the model can exploit for maximal performance. However, prior attempts to include equivariances in CNPs do not scale effectively beyond two input dimensions. In this work, we propose Relational Conditional Neural Processes (RCNPs), an effective approach to incorporate equivariances into any neural process model. Our proposed method extends the applicability and impact of equivariant neural processes to higher dimensions. We empirically demonstrate the competitive performance of RCNPs on a large array of tasks naturally containing equivariances.

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ICML Conference 2022 Conference Paper

Tackling covariate shift with node-based Bayesian neural networks

Trung Q. Trinh
Markus Heinonen
Luigi Acerbi
Samuel Kaski

Bayesian neural networks (BNNs) promise improved generalization under covariate shift by providing principled probabilistic representations of epistemic uncertainty. However, weight-based BNNs often struggle with high computational complexity of large-scale architectures and datasets. Node-based BNNs have recently been introduced as scalable alternatives, which induce epistemic uncertainty by multiplying each hidden node with latent random variables, while learning a point-estimate of the weights. In this paper, we interpret these latent noise variables as implicit representations of simple and domain-agnostic data perturbations during training, producing BNNs that perform well under covariate shift due to input corruptions. We observe that the diversity of the implicit corruptions depends on the entropy of the latent variables, and propose a straightforward approach to increase the entropy of these variables during training. We evaluate the method on out-of-distribution image classification benchmarks, and show improved uncertainty estimation of node-based BNNs under covariate shift due to input perturbations. As a side effect, the method also provides robustness against noisy training labels.

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NeurIPS Conference 2020 Conference Paper

Dynamic allocation of limited memory resources in reinforcement learning

Nisheet Patel
Luigi Acerbi
Alexandre Pouget

Biological brains are inherently limited in their capacity to process and store information, but are nevertheless capable of solving complex tasks with apparent ease. Intelligent behavior is related to these limitations, since resource constraints drive the need to generalize and assign importance differentially to features in the environment or memories of past experiences. Recently, there have been parallel efforts in reinforcement learning and neuroscience to understand strategies adopted by artificial and biological agents to circumvent limitations in information storage. However, the two threads have been largely separate. In this article, we propose a dynamical framework to maximize expected reward under constraints of limited resources, which we implement with a cost function that penalizes precise representations of action-values in memory, each of which may vary in its precision. We derive from first principles an algorithm, Dynamic Resource Allocator (DRA), which we apply to two standard tasks in reinforcement learning and a model-based planning task, and find that it allocates more resources to items in memory that have a higher impact on cumulative rewards. Moreover, DRA learns faster when starting with a higher resource budget than what it eventually allocates for performing well on tasks, which may explain why frontal cortical areas in biological brains appear more engaged in early stages of learning before settling to lower asymptotic levels of activity. Our work provides a normative solution to the problem of learning how to allocate costly resources to a collection of uncertain memories in a manner that is capable of adapting to changes in the environment.

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NeurIPS Conference 2020 Conference Paper

Variational Bayesian Monte Carlo with Noisy Likelihoods

Luigi Acerbi

Variational Bayesian Monte Carlo (VBMC) is a recently introduced framework that uses Gaussian process surrogates to perform approximate Bayesian inference in models with black-box, non-cheap likelihoods. In this work, we extend VBMC to deal with noisy log-likelihood evaluations, such as those arising from simulation-based models. We introduce new global' acquisition functions, such as expected information gain (EIG) and variational interquantile range (VIQR), which are robust to noise and can be efficiently evaluated within the VBMC setting. In a novel, challenging, noisy-inference benchmark comprising of a variety of models with real datasets from computational and cognitive neuroscience, VBMC+VIQR achieves state-of-the-art performance in recovering the ground-truth posteriors and model evidence. In particular, our method vastly outperforms local' acquisition functions and other surrogate-based inference methods while keeping a small algorithmic cost. Our benchmark corroborates VBMC as a general-purpose technique for sample-efficient black-box Bayesian inference also with noisy models.

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NeurIPS Conference 2018 Conference Paper

Variational Bayesian Monte Carlo

Luigi Acerbi

Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to the gradient or a large number of likelihood evaluations. We introduce here a novel sample-efficient inference framework, Variational Bayesian Monte Carlo (VBMC). VBMC combines variational inference with Gaussian-process based, active-sampling Bayesian quadrature, using the latter to efficiently approximate the intractable integral in the variational objective. Our method produces both a nonparametric approximation of the posterior distribution and an approximate lower bound of the model evidence, useful for model selection. We demonstrate VBMC both on several synthetic likelihoods and on a neuronal model with data from real neurons. Across all tested problems and dimensions (up to D = 10), VBMC performs consistently well in reconstructing the posterior and the model evidence with a limited budget of likelihood evaluations, unlike other methods that work only in very low dimensions. Our framework shows great promise as a novel tool for posterior and model inference with expensive, black-box likelihoods.

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NeurIPS Conference 2017 Conference Paper

Practical Bayesian Optimization for Model Fitting with Bayesian Adaptive Direct Search

Luigi Acerbi
Wei Ji Ma

Computational models in fields such as computational neuroscience are often evaluated via stochastic simulation or numerical approximation. Fitting these models implies a difficult optimization problem over complex, possibly noisy parameter landscapes. Bayesian optimization (BO) has been successfully applied to solving expensive black-box problems in engineering and machine learning. Here we explore whether BO can be applied as a general tool for model fitting. First, we present a novel hybrid BO algorithm, Bayesian adaptive direct search (BADS), that achieves competitive performance with an affordable computational overhead for the running time of typical models. We then perform an extensive benchmark of BADS vs. many common and state-of-the-art nonconvex, derivative-free optimizers, on a set of model-fitting problems with real data and models from six studies in behavioral, cognitive, and computational neuroscience. With default settings, BADS consistently finds comparable or better solutions than other methods, including `vanilla' BO, showing great promise for advanced BO techniques, and BADS in particular, as a general model-fitting tool.

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NeurIPS Conference 2014 Conference Paper

A Framework for Testing Identifiability of Bayesian Models of Perception

Luigi Acerbi
Wei Ji Ma
Sethu Vijayakumar

Bayesian observer models are very effective in describing human performance in perceptual tasks, so much so that they are trusted to faithfully recover hidden mental representations of priors, likelihoods, or loss functions from the data. However, the intrinsic degeneracy of the Bayesian framework, as multiple combinations of elements can yield empirically indistinguishable results, prompts the question of model identifiability. We propose a novel framework for a systematic testing of the identifiability of a significant class of Bayesian observer models, with practical applications for improving experimental design. We examine the theoretical identifiability of the inferred internal representations in two case studies. First, we show which experimental designs work better to remove the underlying degeneracy in a time interval estimation task. Second, we find that the reconstructed representations in a speed perception task under a slow-speed prior are fairly robust.

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TCS Journal 2009 Journal Article

Conservation of some dynamical properties for operations on cellular automata

Luigi Acerbi
Alberto Dennunzio
Enrico Formenti

We consider the family of all the Cellular Automata (CA) sharing the same local rule but having different memories. This family contains also all CA with memory m ≤ 0 (one-sided CA) which can act both on A Z and on A N. We study several set theoretical and topological properties for these classes. In particular, we investigate whether the properties of a given CA are preserved when considering the CA obtained by changing the memory of the original one (shifting operation). Furthermore, we focus our attention on the one-sided CA acting on A Z, starting from the one-sided CA acting on A N and having the same local rule (lifting operation). As a particular consequence of these investigations, we prove that the long-standing conjecture [Surjectivity ⇒ Dense Periodic Orbits (DPO)] can be restated in several different (but equivalent) ways. Furthermore, we give some results on properties conserved under the iteration of the CA global map.

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