Adversarial examples have been shown to cause neural networks to fail on a wide range of vision and language tasks, but recent work has claimed that Bayesian neural networks (bnns) are inherently robust to adversarial perturbations. In this work, we examine this claim. To study the adversarial robustness of bnns, we investigate whether it is possible to successfully break state-of-the-art bnn inference methods and prediction pipelines using even relatively unsophisticated attacks for three tasks: (1) label prediction under the posterior predictive mean, (2) adversarial example detection with Bayesian predictive uncertainty, and (3) semantic shift detection. We find that bnns trained with state-of-the-art approximate inference methods, and even bnns trained with Hamiltonian Monte Carlo, are highly susceptible to adversarial attacks. We also identify various conceptual and experimental errors in previous works that claimed inherent adversarial robustness of bnns and conclusively demonstrate that bnns and uncertainty-aware Bayesian prediction pipelines are not inherently robust against adversarial attacks.

Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among these, the exponential family graphical models are especially popular, given their fairly well-understood statistical properties and computational scalability to high-dimensional data based on pseudo-likelihood methods. These models have been successfully applied in many fields, such as the Ising model in statistical physics and count graphical models in genomics. Another strand of models allows some nodes to be latent, so as to allow the marginal distribution of the observable nodes to depart from exponential family to capture more complex dependence. These approaches form the basis of generative models in artificial intelligence, such as the Boltzmann machines and their restricted versions. A fundamental barrier to likelihood-based (i.e., both maximum likelihood and fully Bayesian) inference in both fully and partially observed cases is the intractability of the likelihood. The usual workaround is via adopting pseudo-likelihood based approaches, following the pioneering work of Besag (1974). The goal of this paper is to demonstrate that full likelihood based analysis of these models is feasible in a computationally efficient manner. The chief innovation lies in using a technique of Geyer (1991) to estimate the intractable normalizing constant, as well as its gradient, for intractable graphical models. Extensive numerical results, supporting theory and comparisons with pseudo-likelihood based approaches demonstrate the applicability of the proposed method.

We propose data-dependent uniform generalization bounds by approaching the problem from a PAC-Bayesian perspective. We first apply the PAC-Bayesian framework on `random sets' in a rigorous way, where the training algorithm is assumed to output a data-dependent hypothesis set after observing the training data. This approach allows us to prove data-dependent bounds, which can be applicable in numerous contexts. To highlight the power of our approach, we consider two main applications. First, we propose a PAC-Bayesian formulation of the recently developed fractal-dimension-based generalization bounds. The derived results are shown to be tighter and they unify the existing results around one simple proof technique. Second, we prove uniform bounds over the trajectories of continuous Langevin dynamics and stochastic gradient Langevin dynamics. These results provide novel information about the generalization properties of noisy algorithms.

In this paper, we show how mixed-integer conic optimization can be used to combine feature subset selection with holistic generalized linear models to fully automate the model selection process. Concretely, we directly optimize for the Akaike and Bayesian information criteria while imposing constraints designed to deal with multicollinearity in the feature selection task. Specifically, we propose a novel pairwise correlation constraint that combines the sign coherence constraint with ideas from classical statistical models like Ridge regression and the OSCAR model.

This work introduces a new method for selecting the number of components in finite mixture models (FMMs) using variational Bayes, inspired by the large-sample properties of the Evidence Lower Bound (ELBO) derived from mean-field (MF) variational approximation. Specifically, we establish matching upper and lower bounds for the ELBO without assuming conjugate priors, suggesting the consistency of model selection for FMMs based on maximizing the ELBO. As a by-product of our proof, we demonstrate that the MF approximation inherits the stable behavior (benefited from model singularity) of the posterior distribution, which tends to eliminate the extra components under model misspecification where the number of mixture components is over-specified. This stable behavior also leads to the $n^{-1/2}$ convergence rate for parameter estimation, up to a logarithmic factor, under this model overspecification. Empirical experiments are conducted to validate our theoretical findings and compare with other state-of-the-art methods for selecting the number of components in FMMs.

While deep neural networks (DNNs) based personalized federated learning (PFL) is demanding for addressing data heterogeneity and shows promising performance, existing methods for federated learning (FL) suffer from efficient systematic uncertainty quantification. The Bayesian DNNs-based PFL is usually questioned of either over-simplified model structures or high computational and memory costs. In this paper, we introduce FedSI, a novel Bayesian DNNs-based subnetwork inference PFL framework. FedSI is simple and scalable by leveraging Bayesian methods to incorporate systematic uncertainties effectively. It implements a client-specific subnetwork inference mechanism, selects network parameters with large variance to be inferred through posterior distributions, and fixes the rest as deterministic ones. FedSI achieves fast and scalable inference while preserving the systematic uncertainties to the fullest extent. Extensive experiments on three different benchmark datasets demonstrate that FedSI outperforms existing Bayesian and non-Bayesian FL baselines in heterogeneous FL scenarios.

Multi-label Recognition (MLR) involves the identification of multiple objects within an image. To address the additional complexity of this problem, recent works have leveraged information from vision-language models (VLMs) trained on large text-images datasets for the task. These methods learn an independent classifier for each object (class), overlooking correlations in their occurrences. Such co-occurrences can be captured from the training data as conditional probabilities between a pair of classes. We propose a framework to extend the independent classifiers by incorporating the co-occurrence information for object pairs to improve the performance of independent classifiers. We use a Graph Convolutional Network (GCN) to enforce the conditional probabilities between classes, by refining the initial estimates derived from image and text sources obtained using VLMs. We validate our method on four MLR datasets, where our approach outperforms all state-of-the-art methods.

Learning and understanding car-following (CF) behaviors are crucial for microscopic traffic simulation. Traditional CF models, though simple, often lack generalization capabilities, while many data-driven methods, despite their robustness, operate as "black boxes" with limited interpretability. To bridge this gap, this work introduces a Bayesian Matrix Normal Mixture Regression (MNMR) model that simultaneously captures feature correlations and temporal dynamics inherent in CF behaviors. This approach is distinguished by its separate learning of row and column covariance matrices within the model framework, offering an insightful perspective into the human driver decision-making processes. Through extensive experiments, we assess the model's performance across various historical steps of inputs, predictive steps of outputs, and model complexities. The results consistently demonstrate our model's adeptness in effectively capturing the intricate correlations and temporal dynamics present during CF. A focused case study further illustrates the model's outperforming interpretability of identifying distinct operational conditions through the learned mean and covariance matrices. This not only underlines our model's effectiveness in understanding complex human driving behaviors in CF scenarios but also highlights its potential as a tool for enhancing the interpretability of CF behaviors in traffic simulations and autonomous driving systems.

In many applications, ranging from logistics to engineering, a designer is faced with a sequence of optimization tasks for which the objectives are in the form of black-box functions that are costly to evaluate. For example, the designer may need to tune the hyperparameters of neural network models for different learning tasks over time. Rather than evaluating the objective function for each candidate solution, the designer may have access to approximations of the objective functions, for which higher-fidelity evaluations entail a larger cost. Existing multi-fidelity black-box optimization strategies select candidate solutions and fidelity levels with the goal of maximizing the information accrued about the optimal value or solution for the current task. Assuming that successive optimization tasks are related, this paper introduces a novel information-theoretic acquisition function that balances the need to acquire information about the current task with the goal of collecting information transferable to future tasks. The proposed method includes shared inter-task latent variables, which are transferred across tasks by implementing particle-based variational Bayesian updates. Experimental results across synthetic and real-world examples reveal that the proposed provident acquisition strategy that caters to future tasks can significantly improve the optimization efficiency as soon as a sufficient number of tasks is processed.

In the dynamic hospital setting, decision support can be a valuable tool for improving patient outcomes. Data-driven inference of future outcomes is challenging in this dynamic setting, where long sequences such as laboratory tests and medications are updated frequently. This is due in part to heterogeneity of data types and mixed-sequence types contained in variable length sequences. In this work we design a probabilistic unsupervised model for multiple arbitrary-length sequences contained in hospitalization Electronic Health Record (EHR) data. The model uses a latent variable structure and captures complex relationships between medications, diagnoses, laboratory tests, neurological assessments, and medications. It can be trained on original data, without requiring any lossy transformations or time binning. Inference algorithms are derived that use partial data to infer properties of the complete sequences, including their length and presence of specific values. We train this model on data from subjects receiving medical care in the Kaiser Permanente Northern California integrated healthcare delivery system. The results are evaluated against held-out data for predicting the length of sequences and presence of Intensive Care Unit (ICU) in hospitalization bed sequences. Our method outperforms a baseline approach, showing that in these experiments the trained model captures information in the sequences that is informative of their future values.