We propose a method to improve the efficiency and accuracy of amortized Bayesian inference (ABI) by leveraging universal symmetries in the probabilistic joint model $p(\theta, y)$ of parameters $\theta$ and data $y$. In a nutshell, we invert Bayes' theorem and estimate the marginal likelihood based on approximate representations of the joint model. Upon perfect approximation, the marginal likelihood is constant across all parameter values by definition. However, approximation error leads to undesirable variance in the marginal likelihood estimates across different parameter values. We formulate violations of this symmetry as a loss function to accelerate the learning dynamics of conditional neural density estimators. We apply our method to a bimodal toy problem with an explicit likelihood (likelihood-based) and a realistic model with an implicit likelihood (simulation-based).

Although existing machine learning-based methods for traffic accident analysis can provide good quality results to downstream tasks, they lack interpretability which is crucial for this critical problem. This paper proposes an interpretable framework based on Bayesian Networks for traffic accident prediction. To enable the ease of interpretability, we design a dataset construction pipeline to feed the traffic data into the framework while retaining the essential traffic data information. With a concrete case study, our framework can derive a Bayesian Network from a dataset based on the causal relationships between weather and traffic events across the United States. Consequently, our framework enables the prediction of traffic accidents with competitive accuracy while examining how the probability of these events changes under different conditions, thus illustrating transparent relationships between traffic and weather events. Additionally, the visualization of the network simplifies the analysis of relationships between different variables, revealing the primary causes of traffic accidents and ultimately providing a valuable reference for reducing traffic accidents.

We propose FedGT, a novel framework for identifying malicious clients in federated learning with secure aggregation. Inspired by group testing, the framework leverages overlapping groups of clients to identify the presence of malicious clients in the groups via a decoding operation. The clients identified as malicious are then removed from the training of the model, which is performed over the remaining clients. By choosing the size, number, and overlap between groups, FedGT strikes a balance between privacy and security. Specifically, the server learns the aggregated model of the clients in each group - vanilla federated learning and secure aggregation correspond to the extreme cases of FedGT with group size equal to one and the total number of clients, respectively. The effectiveness of FedGT is demonstrated through extensive experiments on the MNIST, CIFAR-10, and ISIC2019 datasets in a cross-silo setting under different data-poisoning attacks. These experiments showcase FedGT's ability to identify malicious clients, resulting in high model utility. We further show that FedGT significantly outperforms the private robust aggregation approach based on the geometric median recently proposed by Pillutla et al. on heterogeneous client data (ISIC2019) and in the presence of targeted attacks (CIFAR-10 and ISIC2019).

A hierarchical Bayesian framework is introduced for developing rich mixture models for real-valued time series, partly motivated by important applications in financial time series analysis. At the top level, meaningful discrete states are identified as appropriately quantised values of some of the most recent samples. These observable states are described as a discrete context-tree model. At the bottom level, a different, arbitrary model for real-valued time series -- a base model -- is associated with each state. This defines a very general framework that can be used in conjunction with any existing model class to build flexible and interpretable mixture models. We call this the Bayesian Context Trees State Space Model, or the BCT-X framework. Efficient algorithms are introduced that allow for effective, exact Bayesian inference and learning in this setting; in particular, the maximum a posteriori probability (MAP) context-tree model can be identified. These algorithms can be updated sequentially, facilitating efficient online forecasting. The utility of the general framework is illustrated in two particular instances: When autoregressive (AR) models are used as base models, resulting in a nonlinear AR mixture model, and when conditional heteroscedastic (ARCH) models are used, resulting in a mixture model that offers a powerful and systematic way of modelling the well-known volatility asymmetries in financial data. In forecasting, the BCT-X methods are found to outperform state-of-the-art techniques on simulated and real-world data, both in terms of accuracy and computational requirements. In modelling, the BCT-X structure finds natural structure present in the data. In particular, the BCT-ARCH model reveals a novel, important feature of stock market index data, in the form of an enhanced leverage effect.

In this paper, we propose a general framework for solving high-dimensional partial differential equations with tensor networks. Our approach uses Monte-Carlo simulations to update the solution and re-estimates the new solution from samples as a tensor-network using a recently proposed tensor train sketching technique. We showcase the versatility and flexibility of our approach by applying it to two specific scenarios: simulating the Fokker-Planck equation through Langevin dynamics and quantum imaginary time evolution via auxiliary-field quantum Monte Carlo. We also provide convergence guarantees and numerical experiments to demonstrate the efficacy of the proposed method.

Gaussian processes are the model of choice in Bayesian optimization and active learning. Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding good hyperparameters in the literature. We demonstrate the impact of selecting good hyperparameters for GPs and present two acquisition functions that explicitly prioritize hyperparameter learning. Statistical distance-based Active Learning (SAL) considers the average disagreement between samples from the posterior, as measured by a statistical distance. SAL outperforms the state-of-the-art in Bayesian active learning on several test functions. We then introduce Self-Correcting Bayesian Optimization (SCoreBO), which extends SAL to perform Bayesian optimization and active learning simultaneously. SCoreBO learns the model hyperparameters at improved rates compared to vanilla BO, while outperforming the latest Bayesian optimization methods on traditional benchmarks. Moreover, we demonstrate the importance of self-correction on atypical Bayesian optimization tasks.

StepMix is an open-source Python package for the pseudo-likelihood estimation (one-, two- and three-step approaches) of generalized finite mixture models (latent profile and latent class analysis) with external variables (covariates and distal outcomes). In many applications in social sciences, the main objective is not only to cluster individuals into latent classes, but also to use these classes to develop more complex statistical models. These models generally divide into a measurement model that relates the latent classes to observed indicators, and a structural model that relates covariates and outcome variables to the latent classes. The measurement and structural models can be estimated jointly using the so-called one-step approach or sequentially using stepwise methods, which present significant advantages for practitioners regarding the interpretability of the estimated latent classes. In addition to the one-step approach, StepMix implements the most important stepwise estimation methods from the literature, including the bias-adjusted three-step methods with Bolk-Croon-Hagenaars and maximum likelihood corrections and the more recent two-step approach. These pseudo-likelihood estimators are presented in this paper under a unified framework as specific expectation-maximization subroutines. To facilitate and promote their adoption among the data science community, StepMix follows the object-oriented design of the scikit-learn library and provides an additional R wrapper.

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case. Bayesian inference has been very successful because this technique provides a representation of the parameters as a posterior probability distribution, with uncertainties informed by the precision of the experimental measurements. During the last couple of decades, many specific advances have been proposed and employed in order to solve a large variety of different problems. In this work, we present a Markov Chain Monte Carlo (MCMC) algorithm that integrates many of those concepts into a single MCMC package. For this purpose, we have built {\tt Eryn}, a user-friendly and multipurpose toolbox for Bayesian inference, which can be utilized for solving parameter estimation and model selection problems, ranging from simple inference questions, to those with large-scale model variation requiring trans-dimensional MCMC methods, like the LISA global fit problem. In this paper, we describe this sampler package and illustrate its capabilities on a variety of use cases.

While hyperparameter tuning shows theoretical promise, its practical efficacy is not universally superior, as evidenced in Figure 4. The results thus offer a balanced perspective that marries theoretical rigor with empirical validation, fulfilling both academic and practical requirements. Implications for the Field of Machine Learning and Predictive Modeling Robustness and Generalization: The ensemble and stacking methods offer a mathematically substantiated pathway to improve the generalization capabilities of predictive models. Interpretability: The feature integration techniques not only improve model performance but also offer better interpretability by highlighting important features through mathematical formulations. Optimization: The proven convergence of Bayesian Optimization to the global optimum has far-reaching implications for hyperparameter tuning in models, as formalized by the EI equation. Unified Framework: This research provides a unified, mathematically rigorous framework for integrating Bayesian and non-Bayesian approaches, thereby setting a new benchmark for hybrid predictive systems. Future Research Directions Scalability: Investigating the scalability of the proposed methods, particularly in the context of the ensemble and Bayesian optimization equations, for larger datasets and more models. Real-world Applications: Extending this research to specific domains like healthcare, finance, and natural language processing to assess the practical utility of the proposed methods. Advanced Optimization Techniques: Exploring other optimization techniques that could further improve the efficiency and effectiveness of the proposed hybrid models, perhaps by introducing new mathematical formulations.

At present, most surface-quality prediction methods can only perform single-task prediction which results in under-utilised datasets, repetitive work and increased experimental costs. To counter this, the authors propose a Bayesian hierarchical model to predict surface-roughness measurements for a turning machining process. The hierarchical model is compared to multiple independent Bayesian linear regression models to showcase the benefits of partial pooling in a machining setting with respect to prediction accuracy and uncertainty quantification.