This paper studies the challenging black-box adversarial attack that aims to generate adversarial examples against a black-box model by only using output feedback of the model to input queries. Some previous methods improve the query efficiency by incorporating the gradient of a surrogate white-box model into query-based attacks due to the adversarial transferability. However, the localized gradient is not informative enough, making these methods still query-intensive. In this paper, we propose a Prior-guided Bayesian Optimization (P-BO) algorithm that leverages the surrogate model as a global function prior in black-box adversarial attacks. As the surrogate model contains rich prior information of the black-box one, P-BO models the attack objective with a Gaussian process whose mean function is initialized as the surrogate model's loss. Our theoretical analysis on the regret bound indicates that the performance of P-BO may be affected by a bad prior. Therefore, we further propose an adaptive integration strategy to automatically adjust a coefficient on the function prior by minimizing the regret bound. Extensive experiments on image classifiers and large vision-language models demonstrate the superiority of the proposed algorithm in reducing queries and improving attack success rates compared with the state-of-the-art black-box attacks. Code is available at https://github.com/yibo-miao/PBO-Attack.
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Optimization · Optimization and Learning under Uncertainty
Hypervolume improvement (HVI) is commonly employed in multi-objective Bayesian optimization algorithms to define acquisition functions due to its Pareto-compliant property. Rather than focusing on specific statistical moments of HVI, this work aims to provide the exact expression of HVI's probability distribution for bi-objective problems. Considering a bi-variate Gaussian random variable resulting from Gaussian process (GP) modeling, we derive the probability distribution of its hypervolume improvement via a cell partition-based method. Our exact expression is superior in numerical accuracy and computation efficiency compared to the Monte Carlo approximation of HVI's distribution. Utilizing this distribution, we propose a novel acquisition function - $\varepsilon$-probability of hypervolume improvement ($\varepsilon$-PoHVI). Experimentally, we show that on many widely-applied bi-objective test problems, $\varepsilon$-PoHVI significantly outperforms other related acquisition functions, e.g., $\varepsilon$-PoI, and expected hypervolume improvement, when the GP model exhibits a large the prediction uncertainty.
Probabilistic Methods · Variational Inference
Mixture variational distributions in black box variational inference (BBVI) have demonstrated impressive results in challenging density estimation tasks. However, currently scaling the number of mixture components can lead to a linear increase in the number of learnable parameters and a quadratic increase in inference time due to the evaluation of the evidence lower bound (ELBO). Our two key contributions address these limitations. First, we introduce the novel Multiple Importance Sampling Variational Autoencoder (MISVAE), which amortizes the mapping from input to mixture-parameter space using one-hot encodings. Fortunately, with MISVAE, each additional mixture component incurs a negligible increase in network parameters. Second, we construct two new estimators of the ELBO for mixtures in BBVI, enabling a tremendous reduction in inference time with marginal or even improved impact on performance. Collectively, our contributions enable scalability to hundreds of mixture components and provide superior estimation performance in shorter time, with fewer network parameters compared to previous Mixture VAEs. Experimenting with MISVAE, we achieve astonishing, SOTA results on MNIST. Furthermore, we empirically validate our estimators in other BBVI settings, including Bayesian phylogenetic inference, where we improve inference times for the SOTA mixture model on eight data sets.
Probabilistic Methods
Amortized Bayesian inference trains neural networks to solve stochastic inference problems using model simulations, thereby making it possible to rapidly perform Bayesian inference for any newly observed data. However, current simulation-based amortized inference methods are simulation-hungry and inflexible: They require the specification of a fixed parametric prior, simulator, and inference tasks ahead of time. Here, we present a new amortized inference method---the Simformer---which overcomes these limitations. By training a probabilistic diffusion model with transformer architectures, the Simformer outperforms current state-of-the-art amortized inference approaches on benchmark tasks and is substantially more flexible: It can be applied to models with function-valued parameters, it can handle inference scenarios with missing or unstructured data, and it can sample arbitrary conditionals of the joint distribution of parameters and data, including both posterior and likelihood. We showcase the performance and flexibility of the Simformer on simulators from ecology, epidemiology, and neuroscience, and demonstrate that it opens up new possibilities and application domains for amortized Bayesian inference on simulation-based models.
Probabilistic Methods · Bayesian Models and Methods
In recent years, denoising problems have become intertwined with the development of deep generative models. In particular, diffusion models are trained like denoisers, and the distribution they model coincide with denoising priors in the Bayesian picture. However, denoising through diffusion-based posterior sampling requires the noise level and covariance to be known, preventing *blind denoising*. We overcome this limitation by introducing Gibbs Diffusion (GDiff), a general methodology addressing posterior sampling of both the signal and the noise parameters. Assuming arbitrary parametric Gaussian noise, we develop a Gibbs algorithm that alternates sampling steps from a conditional diffusion model trained to map the signal prior to the class of noise distributions, and a Monte Carlo sampler to infer the noise parameters. Our theoretical analysis highlights potential pitfalls, guides diagnostic usage, and quantifies errors in the Gibbs stationary distribution caused by the diffusion model. We showcase our method for 1) blind denoising of natural images involving colored noises with unknown amplitude and exponent, and 2) a cosmology problem, namely the analysis of cosmic microwave background data, where Bayesian inference of "noise" parameters means constraining models of the evolution of the Universe.
Optimization · Learning for Optimization
Bayesian optimization (BO) is a popular method to optimize costly black-box functions, and meta-learning has emerged as a way to leverage knowledge from related tasks to optimize new tasks faster. However, existing meta-learning methods for BO rely on surrogate models that are not scalable or are sensitive to varying input scales and noise types across tasks. Moreover, they often overlook the uncertainty associated with task similarity, leading to unreliable task adaptation when a new task differs significantly or has not been sufficiently explored yet. We propose a novel meta-learning BO approach that bypasses the surrogate model and directly learns the utility of queries across tasks. It explicitly models task uncertainty and includes an auxiliary model to enable robust adaptation to new tasks. Extensive experiments show that our method achieves strong performance and outperforms multiple meta-learning BO methods across various benchmarks.
Probabilistic Conceptual Explainers: Trustworthy Conceptual Explanations for Vision Foundation Models
PDF ↗Social Aspects · Accountability, Transparency and Interpretability
Vision transformers (ViTs) have emerged as a significant area of focus, particularly for their capacity to be jointly trained with large language models and to serve as robust vision foundation models. Yet, the development of trustworthy explanation methods for ViTs has lagged, particularly in the context of post-hoc interpretations of ViT predictions. Existing sub-image selection approaches, such as feature-attribution and conceptual models, fall short in this regard. This paper proposes five desiderata for explaining ViTs -- faithfulness, stability, sparsity, multi-level structure, and parsimony -- and demonstrates the inadequacy of current methods in meeting these criteria comprehensively. We introduce a variational Bayesian explanation framework, dubbed ProbAbilistic Concept Explainers (PACE), which models the distributions of patch embeddings to provide trustworthy post-hoc conceptual explanations. Our qualitative analysis reveals the distributions of patch-level concepts, elucidating the effectiveness of ViTs by modeling the joint distribution of patch embeddings and ViT's predictions. Moreover, these patch-level explanations bridge the gap between image-level and dataset-level explanations, thus completing the multi-level structure of PACE. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that PACE surpasses state-of-the-art methods in terms of the defined desiderata.
Probabilistic Methods · Bayesian Models and Methods
In this paper, we discuss feature engineering for single-pass uncertainty estimation. For accurate uncertainty estimates, neural networks must extract differences in the feature space that quantify uncertainty. This could be achieved by current single-pass approaches that maintain feature distances between data points as they traverse the network. While initial results are promising, maintaining feature distances within the network representations frequently inhibits information compression and opposes the learning objective. We study this effect theoretically and empirically to arrive at a simple conclusion: preserving feature distances in the output is beneficial when the preserved features contribute to learning the label distribution and act in opposition otherwise. We then propose Transitional Uncertainty with Layered Intermediate Predictions (TULIP) as a simple approach to address the shortcomings of current single-pass estimators. Specifically, we implement feature preservation by extracting features from intermediate representations before information is collapsed by subsequent layers. We refer to the underlying preservation mechanism as transitional feature preservation. We show that TULIP matches or outperforms current single-pass methods on standard benchmarks and in practical settings where these methods are less reliable (imbalances, complex architectures, medical modalities).
Density-Softmax: Efficient Test-time Model for Uncertainty Estimation and Robustness under Distribution Shifts
PDF ↗Social Aspects · Trustworthy Machine Learning
Sampling-based methods, e.g., Deep Ensembles and Bayesian Neural Nets have become promising approaches to improve the quality of uncertainty estimation and robust generalization. However, they suffer from a large model size and high latency at test time, which limits the scalability needed for low-resource devices and real-time applications. To resolve these computational issues, we propose Density-Softmax, a sampling-free deterministic framework via combining a density function built on a Lipschitz-constrained feature extractor with the softmax layer. Theoretically, we show that our model is the solution of minimax uncertainty risk and is distance-aware on feature space, thus reducing the over-confidence of the standard softmax under distribution shifts. Empirically, our method enjoys competitive results with state-of-the-art techniques in terms of uncertainty and robustness, while having a lower number of model parameters and a lower latency at test time.
Probabilistic Methods · Bayesian Models and Methods
Generative Flow Networks (GFlowNets) have been shown effective to generate combinatorial objects with desired properties. We here propose a new GFlowNet training framework, with policy-dependent rewards, that bridges keeping flow balance of GFlowNets to optimizing the expected accumulated reward in traditional Reinforcement-Learning (RL). This enables the derivation of new policy-based GFlowNet training methods, in contrast to existing ones resembling value-based RL. It is known that the design of backward policies in GFlowNet training affects efficiency. We further develop a coupled training strategy that jointly solves GFlowNet forward policy training and backward policy design. Performance analysis is provided with a theoretical guarantee of our policy-based GFlowNet training. Experiments on both simulated and real-world datasets verify that our policy-based strategies provide advanced RL perspectives for robust gradient estimation to improve GFlowNet performance. Our code is available at: [github.com/niupuhua1234/GFN-PG](https://github.com/niupuhua1234/GFN-PG).
Probabilistic Methods · Bayesian Models and Methods
Particle-based Bayesian inference methods by sampling from a partition-free target (posterior) distribution, e.g., Stein variational gradient descent (SVGD), have attracted significant attention. We propose a path-guided particle-based sampling (PGPS) method based on a novel Log-weighted Shrinkage (LwS) density path linking an initial distribution to the target distribution. We propose to utilize a Neural network to learn a vector field motivated by the Fokker-Planck equation of the designed density path. Particles, initiated from the initial distribution, evolve according to the ordinary differential equation defined by the vector field. The distribution of these particles is guided along a density path from the initial distribution to the target distribution. The proposed LwS density path allows for an efficient search of modes of the target distribution while canonical methods fail. We theoretically analyze the Wasserstein distance of the distribution of the PGPS-generated samples and the target distribution due to approximation and discretization errors. Practically, the proposed PGPS-LwS method demonstrates higher Bayesian inference accuracy and better calibration ability in experiments conducted on both synthetic and real-world Bayesian learning tasks, compared to baselines, such as SVGD and Langevin dynamics, etc.
A Unified View of FANOVA: A Comprehensive Bayesian Framework for Component Selection and Estimation
PDF ↗Probabilistic Methods · Bayesian Models and Methods
This paper presents a comprehensive Bayesian framework for FANOVA models. We provide guidelines for tuning and practical implementation to improve scalability of learning and prediction. Our model is very flexible and can handle different levels of sparsity across and within decomposition orders, as well as among covariates. This flexibility enables the modeling of complex real-world data while enhancing interpretability. Additionally, it allows our model to unify diverse deterministic and Bayesian non-parametric approaches into a single equation, making comparisons and understanding easier. Notably, our model serves as the Bayesian counterpart of several deterministic methods allowing uncertainty quantification. This general framework unlocks potential for novel model developments that have been previously overlooked, such as the proposed Dirichlet mixing model that addresses limitations of existing models.
Deep Learning · Graph Neural Networks
Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for independent data its applicability to graphs remains under-explored. We propose the first extensive study of Uncertainty Sampling for node classification: **(1)** We benchmark Uncertainty Sampling beyond predictive uncertainty and highlight a significant performance gap to other Active Learning strategies. **(2)** We develop ground-truth Bayesian uncertainty estimates in terms of the data generating process and prove their effectiveness in guiding Uncertainty Sampling toward optimal queries. We confirm our results on synthetic data and design an approximate approach that consistently outperforms other uncertainty estimators on real datasets. **(3)** Based on this analysis, we relate pitfalls in modeling uncertainty to existing methods. Our analysis enables and informs the development of principled uncertainty estimation on graphs.
Reinforcement Learning
Bayesian reinforcement learning (RL) offers a principled and elegant approach for sequential decision making under uncertainty. Most notably, Bayesian agents do not face an exploration/exploitation dilemma, a major pathology of frequentist methods. However theoretical understanding of model-free approaches is lacking. In this paper, we introduce a novel Bayesian model-free formulation and the first analysis showing that model-free approaches can yield Bayes-optimal policies. We show all existing model-free approaches make approximations that yield policies that can be arbitrarily Bayes-suboptimal. As a first step towards model-free Bayes optimality, we introduce the Bayesian exploration network (BEN) which uses normalising flows to model both the aleatoric uncertainty (via density estimation) and epistemic uncertainty (via variational inference) in the Bellman operator. In the limit of complete optimisation, BEN learns true Bayes-optimal policies, but like in variational expectation-maximisation, partial optimisation renders our approach tractable. Empirical results demonstrate that BEN can learn true Bayes-optimal policies in tasks where existing model-free approaches fail.
Probabilistic Methods · Monte Carlo and Sampling Methods
Building upon score-based learning, new interest in stochastic localization techniques has recently emerged. In these models, one seeks to noise a sample from the data distribution through a stochastic process, called observation process, and progressively learns a denoiser associated to this dynamics. Apart from specific applications, the use of stochastic localization for the problem of sampling from an unnormalized target density has not been explored extensively. This work contributes to fill this gap. We consider a general stochastic localization framework and introduce an explicit class of observation processes, associated with flexible denoising schedules. We provide a complete methodology, *Stochastic Localization via Iterative Posterior Sampling* (**SLIPS**), to obtain approximate samples of these dynamics, and as a by-product, samples from the target distribution. Our scheme is based on a Markov chain Monte Carlo estimation of the denoiser and comes with detailed practical guidelines. We illustrate the benefits and applicability of **SLIPS** on several benchmarks of multi-modal distributions, including Gaussian mixtures in increasing dimensions, Bayesian logistic regression and a high-dimensional field system from statistical-mechanics.
Applications · Time Series
In real-world scenarios such as traffic and energy management, we frequently encounter large volumes of time-series data characterized by missing values, noise, and irregular sampling patterns. While numerous imputation methods have been proposed, the majority tend to operate within a local horizon, which involves dividing long sequences into batches of fixed-length segments for model training. This local horizon often leads to the overlooking of global trends and periodic patterns. More importantly, most methods assume the observations are sampled at regular timestamps, and fail to handle complex irregular sampled time series in various applications. Additionally, most existing methods are learned in an offline manner. Thus, it is not suitable for applications with rapidly arriving streaming data. To address these challenges, we propose BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition. Our method conceptualizes multivariate time series as the weighted combination of groups of low-rank temporal factors with different patterns. We employ a suite of Gaussian Processes (GPs),each with a unique kernel, as functional priors to model these factors. For computational efficiency, we further convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE), and developing a scalable algorithm for online inference. The proposed method can not only handle imputation over arbitrary timestamps, but also offer uncertainty quantification and interpretability for the downstream application. We evaluate our method on both synthetic and real-world datasets. We release the code at https://github.com/xuangu-fang/BayOTIDE.
Deep Learning
With the increasing computational costs associated with deep learning, automated hyperparameter optimization methods, strongly relying on black-box Bayesian optimization (BO), face limitations. Freeze-thaw BO offers a promising grey-box alternative, strategically allocating scarce resources incrementally to different configurations. However, the frequent surrogate model updates inherent to this approach pose challenges for existing methods, requiring retraining or fine-tuning their neural network surrogates online, introducing overhead, instability, and hyper-hyperparameters. In this work, we propose FT-PFN, a novel surrogate for Freeze-thaw style BO. FT-PFN is a prior-data fitted network (PFN) that leverages the transformers' in-context learning ability to efficiently and reliably do Bayesian learning curve extrapolation in a single forward pass. Our empirical analysis across three benchmark suites shows that the predictions made by FT-PFN are more accurate and 10-100 times faster than those of the deep Gaussian process and deep ensemble surrogates used in previous work. Furthermore, we show that, when combined with our novel acquisition mechanism (MFPI-random), the resulting in-context freeze-thaw BO method (ifBO), yields new state-of-the-art performance in the same three families of deep learning HPO benchmarks considered in prior work.
Optimization · Zero-order and Black-box Optimization
Bayesian Optimization (BO) is a technique for sample-efficient black-box optimization that employs probabilistic models to identify promising input for evaluation. When dealing with composite-structured functions, such as $f=g \circ h$, evaluating a specific location $x$ yields observations of both the final outcome $f(x) = g(h(x))$ as well as the intermediate output(s) $h(x)$. Previous research has shown that integrating information from these intermediate outputs can enhance BO performance substantially. However, existing methods struggle if the outputs $h(x)$ are high-dimensional. Many relevant problems fall into this setting, including in the context of generative AI, molecular design, or robotics. To effectively tackle these challenges, we introduce Joint Composite Latent Space Bayesian Optimization (JoCo), a novel framework that jointly trains neural network encoders and probabilistic models to adaptively compress high-dimensional input and output spaces into manageable latent representations. This enables effective BO on these compressed representations, allowing JoCo to outperform other state-of-the-art methods in high-dimensional BO on a wide variety of simulated and real-world problems.
BRAIn: Bayesian Reward-conditioned Amortized Inference for natural language generation from feedback
PDF ↗Reinforcement Learning · Batch/Offline
Distribution matching methods for language model alignment such as Generation with Distributional Control (GDC) and Distributional Policy Gradient (DPG) have not received the same level of attention in reinforcement learning from human feedback (RLHF) as contrastive methods such as Sequence Likelihood Calibration (SLiC), Direct Preference Optimization (DPO) and its variants. We identify high variance of the gradient estimate as the primary reason for the lack of success of these methods and propose a self-normalized baseline to reduce the variance. We further generalize the target distribution in DPG, GDC and DPO by using Bayes' rule to define the reward-conditioned posterior. The resulting approach, referred to as BRAIn - Bayesian Reward-conditioned Amortized Inference acts as a bridge between distribution matching methods and DPO and significantly outperforms prior art in summarization and Antropic HH tasks.
Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in real-world datasets, ultimately limiting the usability of these methods. Building on previous attempts, we show how to incorporate causal assumptions within the Bayesian framework. Identifying causal direction then becomes a Bayesian model selection problem. This enables us to construct models with realistic assumptions, and consequently allows for the differentiation between Markov equivalent causal structures. We analyse why Bayesian model selection works in situations where methods based on maximum likelihood fail. To demonstrate our approach, we construct a Bayesian non-parametric model that can flexibly model the joint distribution. We then outperform previous methods on a wide range of benchmark datasets with varying data generating assumptions.