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.

Health monitoring of remote critical infrastructure is a complex and expensive activity due to the limited infrastructure accessibility. Inspection drones are ubiquitous assets that enhance the reliability of critical infrastructures through improved accessibility. However, due to the harsh operation environment, it is crucial to monitor their health to ensure successful inspection operations. The battery is a key component that determines the overall reliability of the inspection drones and, with an appropriate health management approach, contributes to reliable and robust inspections. In this context, this paper presents a novel hybrid probabilistic approach for battery end-of-discharge (EOD) voltage prediction of Li-Po batteries. The hybridization is achieved in an error-correction configuration, which combines physics-based discharge and probabilistic error-correction models to quantify the aleatoric and epistemic uncertainty. The performance of the hybrid probabilistic methodology was empirically evaluated on a dataset comprising EOD voltage under varying load conditions. The dataset was obtained from real inspection drones operated on different flights, focused on offshore wind turbine inspections. The proposed approach has been tested with different probabilistic methods and demonstrates 14.8% improved performance in probabilistic accuracy compared to the best probabilistic method. In addition, aleatoric and epistemic uncertainties provide robust estimations to enhance the diagnosis of battery health-states.

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.

Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on Euclidean spaces, when considering diffusion processes on Riemannian manifolds the geometry brings in further complications. In even higher generality, advancing from Riemannian to sub-Riemannian geometries introduces hypoellipticity, and the possibility of finding appropriate explicit approximations for the score of the diffusion process is removed. We handle these challenges and construct a method for bridge simulation on sub-Riemannian manifolds by demonstrating how recent progress in machine learning can be modified to allow for training of score approximators on sub-Riemannian manifolds. Since gradients dependent on the horizontal distribution, we generalise the usual notion of denoising loss to work with non-holonomic frames using a stochastic Taylor expansion, and we demonstrate the resulting scheme both explicitly on the Heisenberg group and more generally using adapted coordinates. We perform numerical experiments exemplifying samples from the bridge process on the Heisenberg group and the concentration of this process for small time.

We present a novel character control framework that effectively utilizes motion diffusion probabilistic models to generate high-quality and diverse character animations, responding in real-time to a variety of dynamic user-supplied control signals. At the heart of our method lies a transformer-based Conditional Autoregressive Motion Diffusion Model (CAMDM), which takes as input the character's historical motion and can generate a range of diverse potential future motions conditioned on high-level, coarse user control. To meet the demands for diversity, controllability, and computational efficiency required by a real-time controller, we incorporate several key algorithmic designs. These include separate condition tokenization, classifier-free guidance on past motion, and heuristic future trajectory extension, all designed to address the challenges associated with taming motion diffusion probabilistic models for character control. As a result, our work represents the first model that enables real-time generation of high-quality, diverse character animations based on user interactive control, supporting animating the character in multiple styles with a single unified model. We evaluate our method on a diverse set of locomotion skills, demonstrating the merits of our method over existing character controllers. Project page and source codes: https://aiganimation.github.io/CAMDM/

Mycotoxins are a group of naturally occurring, toxic chemical compounds produced by certain species of moulds (fungi), during growth on various crops and foodstuffs, including cereals, nuts, spices and dairy products (The World Health Organization (WHO), 2023). The ingestion of certain mycotoxins has been linked to a range of harmful health impacts on both humans and animals, from short-term poisoning to long-term consequences such as liver cancer, and in some cases, death (Mavrommatis et al., 2021; Marroquín-Cardona et al., 2014; Liu and Wu, 2010). Mycotoxins are secondary metabolites (that is, compounds produced by an organism that are not essential for its primary life processes) and are often produced during the pre-harvest, harvest, and storage phases under favourable conditions of humidity and temperature (Marroquín-Cardona et al., 2014; Van der Fels-Klerx et al., 2022). The most prevalent mycotoxins include aflatoxins, tricothecenes, fumonisins, zearalenones, ochratoxins and patulin, and are produced by certain plant-pathogenic species of Aspergillus, Fusarium, and Penicillium (Tola and Kebede, 2016). Mycotoxin contamination in crop products has been found to vary significantly across different geographical locations and is influenced by annual weather conditions (Logrieco et al., 2021; Leggieri et al., 2020).