The explosive growth of digital images and the widespread availability of image editing tools have made image manipulation detection an increasingly critical challenge. Current deep learning-based manipulation detection methods excel in achieving high image-level classification accuracy, they often fall short in terms of interpretability and localization of manipulated regions. Additionally, the absence of pixel-wise annotations in real-world scenarios limits the existing fully-supervised manipulation localization techniques. To address these challenges, we propose a novel weakly-supervised approach that integrates activation maps generated by image-level manipulation detection networks with segmentation maps from pre-trained models. Specifically, we build on our previous image-level work named WCBnet to produce multi-view feature maps which are subsequently fused for coarse localization. These coarse maps are then refined using detailed segmented regional information provided by pre-trained segmentation models (such as DeepLab, SegmentAnything and PSPnet), with Bayesian inference employed to enhance the manipulation localization. Experimental results demonstrate the effectiveness of our approach, highlighting the feasibility to localize image manipulations without relying on pixel-level labels.
Discrete choice models (DCMs) are used to analyze individual decision-making in contexts such as transportation choices, political elections, and consumer preferences. DCMs play a central role in applied econometrics by enabling inference on key economic variables, such as marginal rates of substitution, rather than focusing solely on predicting choices on new unlabeled data. However, while traditional DCMs offer high interpretability and support for point and interval estimation of economic quantities, these models often underperform in predictive tasks compared to deep learning (DL) models. Despite their predictive advantages, DL models remain largely underutilized in discrete choice due to concerns about their lack of interpretability, unstable parameter estimates, and the absence of established methods for uncertainty quantification. Here, we introduce a deep learning model architecture specifically designed to integrate with approximate Bayesian inference methods, such as Stochastic Gradient Langevin Dynamics (SGLD). Our proposed model collapses to behaviorally informed hypotheses when data is limited, mitigating overfitting and instability in underspecified settings while retaining the flexibility to capture complex nonlinear relationships when sufficient data is available. We demonstrate our approach using SGLD through a Monte Carlo simulation study, evaluating both predictive metrics--such as out-of-sample balanced accuracy--and inferential metrics--such as empirical coverage for marginal rates of substitution interval estimates. Additionally, we present results from two empirical case studies: one using revealed mode choice data in NYC, and the other based on the widely used Swiss train choice stated preference data.
Hollmann et al. (Nature 637 (2025) 319-326) recently introduced TabPFN, a transformer-based deep learning model for regression and classification on tabular data, which they claim "outperforms all previous methods on datasets with up to 10,000 samples by a wide margin, using substantially less training time." Furthermore, they have called TabPFN a "foundation model" for tabular data, as it can support "data generation, density estimation, learning reusable embeddings and fine-tuning". If these statements are well-supported, TabPFN may have the potential to supersede existing modeling approaches on a wide range of statistical tasks, mirroring a similar revolution in other areas of artificial intelligence that began with the advent of large language models. In this paper, we provide a tailored explanation of how TabPFN works for a statistics audience, by emphasizing its interpretation as approximate Bayesian inference. We also provide more evidence of TabPFN's "foundation model" capabilities: We show that an out-of-the-box application of TabPFN vastly outperforms specialized state-of-the-art methods for semi-supervised parameter estimation, prediction under covariate shift, and heterogeneous treatment effect estimation. We further show that TabPFN can outperform LASSO at sparse regression and can break a robustness-efficiency trade-off in classification. All experiments can be reproduced using the code provided at https://github.com/qinglong-tian/tabpfn_study (https://github.com/qinglong-tian/tabpfn_study).
The power prior is a class of informative priors designed to incorporate historical data alongside current data in a Bayesian framework. It includes a power parameter that controls the influence of historical data, providing flexibility and adaptability. A key property of the power prior is that the resulting posterior minimizes a linear combination of KL divergences between two pseudo-posterior distributions: one ignoring historical data and the other fully incorporating it. We extend this framework by identifying the posterior distribution as the minimizer of a linear combination of Amari's $\alpha$-divergence, a generalization of KL divergence. We show that this generalization can lead to improved performance by allowing for the data to adapt to appropriate choices of the $\alpha$ parameter. Theoretical properties of this generalized power posterior are established, including behavior as a generalized geodesic on the Riemannian manifold of probability distributions, offering novel insights into its geometric interpretation.
In electromyogram (EMG)-based motion recognition, a subject-specific classifier is typically trained with sufficient labeled data. However, this process demands extensive data collection over extended periods, burdening the subject. To address this, utilizing information from pre-training on multiple subjects for the training of the target subject could be beneficial. This paper proposes an inter-subject variance transfer learning method based on a Bayesian approach. This method is founded on the simple hypothesis that while the means of EMG features vary greatly across subjects, their variances may exhibit similar patterns. Our approach transfers variance information, acquired through pre-training on multiple source subjects, to a target subject within a Bayesian updating framework, thereby allowing accurate classification using limited target calibration data. A coefficient was also introduced to adjust the amount of information transferred for efficient transfer learning. Experimental evaluations using two EMG datasets demonstrated the effectiveness of our variance transfer strategy and its superiority compared to existing methods.
Personalized Bayesian federated learning (PBFL) handles non-i.i.d. client data and quantifies uncertainty by combining personalization with Bayesian inference. However, existing PBFL methods face two limitations: restrictive parametric assumptions in client posterior inference and naive parameter averaging for server aggregation. To overcome these issues, we propose FedWBA, a novel PBFL method that enhances both local inference and global aggregation. At the client level, we use particle-based variational inference for nonparametric posterior representation. At the server level, we introduce particle-based Wasserstein barycenter aggregation, offering a more geometrically meaningful approach. Theoretically, we provide local and global convergence guarantees for FedWBA. Locally, we prove a KL divergence decrease lower bound per iteration for variational inference convergence. Globally, we show that the Wasserstein barycenter converges to the true parameter as the client data size increases. Empirically, experiments show that FedWBA outperforms baselines in prediction accuracy, uncertainty calibration, and convergence rate, with ablation studies confirming its robustness.
Neural networks are powerful tools for cognitive modeling due to their flexibility and emergent properties. However, interpreting their learned representations remains challenging due to their sub-symbolic semantics. In this work, we introduce a novel probabilistic framework for interpreting latent task representations in neural networks. Inspired by Bayesian inference, our approach defines a distribution over representational units to infer their causal contributions to task performance. Using ideas from information theory, we propose a suite of tools and metrics to illuminate key model properties, including representational distributedness, manifold complexity, and polysemanticity.
Amortized Bayesian inference (ABI) has emerged as a powerful simulation-based approach for estimating complex mechanistic models, offering fast posterior sampling via generative neural networks. However, extending ABI to hierarchical models, a cornerstone of modern Bayesian analysis, remains a major challenge due to the difficulty of scaling to large numbers of parameters. In this work, we build on compositional score matching (CSM), a divide-and-conquer strategy for Bayesian updating using diffusion models. To address existing stability issues of CSM, we propose adaptive solvers coupled with a novel, error-damping compositional estimator. Our proposed method remains stable even with hundreds of thousands of data points and parameters. We validate our approach on a controlled toy example, a high-dimensional spatial autoregressive model, and a real-world advanced microscopy biological application task involving over 750,000 parameters.
Massive multiple-input multiple-output (MIMO) stands as a key technology for advancing performance metrics such as data rate, reliability, and spectrum efficiency in the fifth generation (5G) and beyond of wireless networks. However, its efficiency depends greatly on obtaining accurate channel state information. This task becomes particularly challenging with increasing user mobility. In this paper, we focus on an uplink scenario in which a massive MIMO base station serves multiple high-mobility users. We leverage variational Bayesian(VB) inference for joint channel estimation and data detection(JED), tailored for time-varying channels. In particular, we use the VB framework to provide approximations of the true posterior distributions. To cover more real-world scenarios, we assume the time correlation coefficients associated with the channels are unknown. Our simulations demonstrate the efficacy of our proposed VB-based approach in tracking these unknown time correlation coefficients. We present two processing strategies within the VB framework: online and block processing strategies. The online strategy offers a low-complexity solution for a given time slot, requiring only the knowledge of the parameters/statistics within that time slot. In contrast, the block processing strategy focuses on the entire communication block and processes all received signals together to reduce channel estimation errors. Additionally, we introduce an interleaved structure for the online processing strategy to further enhance its performance. Finally, we conduct a comparative analysis of our VB approach against the linear minimum mean squared error(LMMSE), the Kalman Filter(KF), and the expectation propagation(EP) methods in terms of symbol error rate(SER) and channel normalized mean squared error(NMSE). Our findings reveal that our VB framework surpasses these benchmarks across the performance metrics.
Adapting to the addressee is crucial for successful explanations, yet poses significant challenges for dialogsystems. We adopt the approach of treating explanation generation as a non-stationary decision process, where the optimal strategy varies according to changing beliefs about the explainee and the interaction context. In this paper we address the questions of (1) how to track the interaction context and the relevant listener features in a formally defined computational partner model, and (2) how to utilize this model in the dynamically adjusted, rational decision process that determines the currently best explanation strategy. We propose a Bayesian inference-based approach to continuously update the partner model based on user feedback, and a non-stationary Markov Decision Process to adjust decision-making based on the partner model values. We evaluate an implementation of this framework with five simulated interlocutors, demonstrating its effectiveness in adapting to different partners with constant and even changing feedback behavior. The results show high adaptivity with distinct explanation strategies emerging for different partners, highlighting the potential of our approach to improve explainable AI systems and dialogsystems in general.
Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational overhead. We adapt the subset samplers for this setting where gradient information is not available or is unreliable. To achieve this, we introduce data-driven proxies in place of Taylor expansions and define a novel computation-cost aware adaptive controller. We undertake an extensive evaluation for a challenging disease modelling task and a configurable task with similar irregularity in the likelihood surface. We find our improved version of Hierarchical Importance with Nested Training Samples (HINTS), with adaptive proposals and a data-driven proxy, obtains the best sampling error in a fixed computational budget. We conclude that subset evaluations can provide cheap and naturally-tempered exploration, while a data-driven proxy can pre-screen proposals successfully in explored regions of the state space. These two elements combine through hierarchical delayed acceptance to achieve efficient, exact sampling.
We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling methods, are effective for sampling from single-mode distributions in high-dimensional spaces. However, these methods struggle to produce samples with the correct proportions for each mode in multimodal distributions, especially for distributions with well separated modes. To address the challenges posed by multimodality, we adopt a divide-and-conquer strategy. We start by minimizing the energy function with initial guesses uniformly distributed within the prior domain to identify all the modes of the energy function. Then, we train a classifier to segment the domain corresponding to each mode. After the domain decomposition, we train a diffusion-model-assisted generative model for each identified mode within its support. Once each mode is characterized, we employ bridge sampling to estimate the normalizing constant, allowing us to directly adjust the ratios between the modes. Our numerical examples demonstrate that the proposed framework can effectively handle multimodal distributions with varying mode shapes in up to 100 dimensions. An application to Bayesian inverse problem for partial differential equations is also provided.
Network interference occurs when treatments assigned to some units affect the outcomes of others. Traditional approaches often assume that the observed network correctly specifies the interference structure. However, in practice, researchers frequently only have access to proxy measurements of the interference network due to limitations in data collection or potential mismatches between measured networks and actual interference pathways. In this paper, we introduce a framework for estimating causal effects when only proxy networks are available. Our approach leverages a structural causal model that accommodates diverse proxy types, including noisy measurements, multiple data sources, and multilayer networks, and defines causal effects as interventions on population-level treatments. Since the true interference network is latent, estimation poses significant challenges. To overcome them, we develop a Bayesian inference framework. We propose a Block Gibbs sampler with Locally Informed Proposals to update the latent network, thereby efficiently exploring the high-dimensional posterior space composed of both discrete and continuous parameters. We illustrate the performance of our method through numerical experiments, demonstrating its accuracy in recovering causal effects even when only proxies of the interference network are available.
Bayesian inference has many advantages in decision making of agents (e.g. robotics/simulative agent) over a regular data-driven black-box neural network: Data-efficiency, generalization, interpretability, and safety where these advantages benefit directly/indirectly from the uncertainty quantification of Bayesian inference. However, there are few comprehensive reviews to summarize the progress of Bayesian inference on reinforcement learning (RL) for decision making to give researchers a systematic understanding. This paper focuses on combining Bayesian inference with RL that nowadays is an important approach in agent decision making. To be exact, this paper discusses the following five topics: 1) Bayesian methods that have potential for agent decision making. First basic Bayesian methods and models (Bayesian rule, Bayesian learning, and Bayesian conjugate models) are discussed followed by variational inference, Bayesian optimization, Bayesian deep learning, Bayesian active learning, Bayesian generative models, Bayesian meta-learning, and lifelong Bayesian learning. 2) Classical combinations of Bayesian methods with model-based RL (with approximation methods), model-free RL, and inverse RL. 3) Latest combinations of potential Bayesian methods with RL. 4) Analytical comparisons of methods that combine Bayesian methods with RL with respect to data-efficiency, generalization, interpretability, and safety. 5) In-depth discussions in six complex problem variants of RL, including unknown reward, partial-observability, multi-agent, multi-task, non-linear non-Gaussian, and hierarchical RL problems and the summary of how Bayesian methods work in the data collection, data processing and policy learning stages of RL to pave the way for better agent decision-making strategies.
Bayesian inference typically relies on a large number of model evaluations to estimate posterior distributions. Established methods like Markov Chain Monte Carlo (MCMC) and Amortized Bayesian Inference (ABI) can become computationally challenging. While ABI enables fast inference after training, generating sufficient training data still requires thousands of model simulations, which is infeasible for expensive models. Surrogate models offer a solution by providing approximate simulations at a lower computational cost, allowing the generation of large data sets for training. However, the introduced approximation errors and uncertainties can lead to overconfident posterior estimates. To address this, we propose Uncertainty-Aware Surrogate-based Amortized Bayesian Inference (UA-SABI) - a framework that combines surrogate modeling and ABI while explicitly quantifying and propagating surrogate uncertainties through the inference pipeline. Our experiments show that this approach enables reliable, fast, and repeated Bayesian inference for computationally expensive models, even under tight time constraints.
Recent studies claim that human behavior in a two-armed Bernoulli bandit (TABB) task is described by positivity and confirmation biases, implying that humans do not integrate new information objectively. However, we find that even if the agent updates its belief via objective Bayesian inference, fitting the standard Q-learning model with asymmetric learning rates still recovers both biases. Bayesian inference cast as an effective Q-learning algorithm has symmetric, though decreasing, learning rates. We explain this by analyzing the stochastic dynamics of these learning systems using master equations. We find that both confirmation bias and unbiased but decreasing learning rates yield the same behavioral signatures. Finally, we propose experimental protocols to disentangle true cognitive biases from artifacts of decreasing learning rates.
When the likelihood is analytically unavailable and computationally intractable, approximate Bayesian computation (ABC) has emerged as a widely used methodology for approximate posterior inference; however, it suffers from severe computational inefficiency in high-dimensional settings or under diffuse priors. To overcome these limitations, we propose Adaptive Bayesian Inference (ABI), a framework that bypasses traditional data-space discrepancies and instead compares distributions directly in posterior space through nonparametric distribution matching. By leveraging a novel Marginally-augmented Sliced Wasserstein (MSW) distance on posterior measures and exploiting its quantile representation, ABI transforms the challenging problem of measuring divergence between posterior distributions into a tractable sequence of one-dimensional conditional quantile regression tasks. Moreover, we introduce a new adaptive rejection sampling scheme that iteratively refines the posterior approximation by updating the proposal distribution via generative density estimation. Theoretically, we establish parametric convergence rates for the trimmed MSW distance and prove that the ABI posterior converges to the true posterior as the tolerance threshold vanishes. Through extensive empirical evaluation, we demonstrate that ABI significantly outperforms data-based Wasserstein ABC, summary-based ABC, and state-of-the-art likelihood-free simulators, especially in high-dimensional or dependent observation regimes.
Future mobile networks are projected to support integrated sensing and communications in high-speed communication scenarios. Nevertheless, large Doppler shifts induced by time-varying channels may cause severe inter-carrier interference (ICI). Frequency domain shows the potential of reducing ISAC complexity as compared with other domains. However, parameter mismatching issue still exists for such sensing. In this paper, we develop a novel sensing scheme based on sparse Bayesian framework, where the delay and Doppler estimation problem in time-varying channels is formulated as a 3D multiple measurement-sparse signal recovery (MM-SSR) problem. We then propose a novel two-layer variational Bayesian inference (VBI) method to decompose the 3D MM-SSR problem into two layers and estimate the Doppler in the first layer and the delay in the second layer alternatively. Subsequently, as is benefited from newly unveiled signal construction, a simplified two-stage multiple signal classification (MUSIC)-based VBI method is proposed, where the delay and the Doppler are estimated by MUSIC and VBI, respectively. Additionally, the Cram\'er-Rao bound (CRB) of the considered sensing parameters is derived to characterize the lower bound for the proposed estimators. Corroborated by extensive simulation results, our proposed method can achieve improved mean square error (MSE) than its conventional counterparts and is robust against the target number and target speed, thereby validating its wide applicability and advantages over prior arts.
This paper studies a passive source localization system, where a single base station (BS) is employed to estimate the positions and attitudes of multiple mobile stations (MSs). The BS and the MSs are equipped with uniform rectangular arrays, and the MSs are located in the near-field region of the BS array. To avoid the difficulty of tackling the problem directly based on the near-field signal model, we establish a subarray-wise far-field received signal model. In this model, the entire BS array is divided into multiple subarrays to ensure that each MS is in the far-field region of each BS subarray. By exploiting the angles of arrival (AoAs) of an MS antenna at different BS subarrays, we formulate the attitude and location estimation problem under the Bayesian inference framework. Based on the factor graph representation of the probabilistic problem model, a message passing algorithm named array partitioning based pose and location estimation (APPLE) is developed to solve this problem. An estimation-error lower bound is obtained as a performance benchmark of the proposed algorithm. Numerical results demonstrate that the proposed APPLE algorithm outperforms other baseline methods in the accuracy of position and attitude estimation.
Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean variance estimation (MVE) networks can learn this type of uncertainty but require ad-hoc regularization strategies to avoid overfitting and are unable to predict epistemic uncertainty (model uncertainty). Conversely, Bayesian neural networks predict epistemic uncertainty but are notoriously difficult to train due to the approximate nature of Bayesian inference. We propose to cooperatively train a variance network with a Bayesian neural network and demonstrate that the resulting model disentangles aleatoric and epistemic uncertainties while improving the mean estimation. We demonstrate the effectiveness and scalability of this method across a diverse range of datasets, including a time-dependent heteroscedastic regression dataset we created where the aleatoric uncertainty is known. The proposed method is straightforward to implement, robust, and adaptable to various model architectures.