The assumptions of stationarity and isotropy often stated over spatial processes have not aged well during the last two decades, partly explained by the combination of computational developments and the increasing availability of high-resolution spatial data. While a plethora of approaches have been developed to relax these assumptions, it is often a costly tradeoff between flexibility and a diversity of computational challenges. In this paper, we present a class of covariance functions that relies on fixed, observable spatial information that provides a convenient tradeoff while offering an extra layer of numerical and visual representation of the flexible spatial dependencies. This model allows for separate parametric structures for different sources of nonstationarity, such as marginal standard deviation, geometric anisotropy, and smoothness. It simplifies to a Mat\'ern covariance function in its basic form and is adaptable for large datasets, enhancing flexibility and computational efficiency. We analyze the capabilities of the presented model through simulation studies and an application to Swiss precipitation data.

Variational Autoencoders (VAE) are popular generative models used to sample from complex data distributions. Despite their empirical success in various machine learning tasks, significant gaps remain in understanding their theoretical properties, particularly regarding convergence guarantees. This paper aims to bridge that gap by providing non-asymptotic convergence guarantees for VAE trained using both Stochastic Gradient Descent and Adam algorithms.We derive a convergence rate of $\mathcal{O}(\log n / \sqrt{n})$, where $n$ is the number of iterations of the optimization algorithm, with explicit dependencies on the batch size, the number of variational samples, and other key hyperparameters. Our theoretical analysis applies to both Linear VAE and Deep Gaussian VAE, as well as several VAE variants, including $\beta$-VAE and IWAE. Additionally, we empirically illustrate the impact of hyperparameters on convergence, offering new insights into the theoretical understanding of VAE training.

One of the main challenges of federated learning (FL) is handling non-independent and identically distributed (non-IID) client data, which may occur in practice due to unbalanced datasets and use of different data sources across clients. Knowledge sharing and model personalization are key strategies for addressing this issue. Clustered federated learning is a class of FL methods that groups clients that observe similarly distributed data into clusters, such that every client is typically associated with one data distribution and participates in training a model for that distribution along their cluster peers. In this paper, we present a unified Bayesian framework for clustered FL which associates clients to clusters. Then we propose several practical algorithms to handle the, otherwise growing, data associations in a way that trades off performance and computational complexity. This work provides insights on client-cluster associations and enables client knowledge sharing in new ways. The proposed framework circumvents the need for unique client-cluster associations, which is seen to increase the performance of the resulting models in a variety of experiments.

Conventional medical artificial intelligence (AI) models face barriers in clinical application and ethical issues owing to their inability to handle the privacy-sensitive characteristics of medical data. We present a novel personalized federated learning (pFL) method for medical visual question answering (VQA) models, addressing privacy reliability challenges in the medical domain. Our method introduces learnable prompts into a Transformer architecture to efficiently train it on diverse medical datasets without massive computational costs. Then we introduce a reliable client VQA model that incorporates Dempster-Shafer evidence theory to quantify uncertainty in predictions, enhancing the model's reliability. Furthermore, we propose a novel inter-client communication mechanism that uses maximum likelihood estimation to balance accuracy and uncertainty, fostering efficient integration of insights across clients.

This paper presents a novel Integer Programming (IP) approach for discovering the Markov Equivalent Class (MEC) of Bayesian Networks (BNs) through observational data. The MEC-IP algorithm utilizes a unique clique-focusing strategy and Extended Maximal Spanning Graphs (EMSG) to streamline the search for MEC, thus overcoming the computational limitations inherent in other existing algorithms. Our numerical results show that not only a remarkable reduction in computational time is achieved by our algorithm but also an improvement in causal discovery accuracy is seen across diverse datasets. These findings underscore this new algorithm's potential as a powerful tool for researchers and practitioners in causal discovery and BNSL, offering a significant leap forward toward the efficient and accurate analysis of complex data structures.

In business process simulation, resource availability is typically modeled by assigning a calendar to each resource, e.g., Monday-Friday, 9:00-18:00. Resources are assumed to be always available during each time slot in their availability calendar. This assumption often becomes invalid due to interruptions, breaks, or time-sharing across processes. In other words, existing approaches fail to capture intermittent availability. Another limitation of existing approaches is that they either do not consider multitasking behavior, or if they do, they assume that resources always multitask (up to a maximum capacity) whenever available. However, studies have shown that the multitasking patterns vary across days. This paper introduces a probabilistic approach to model resource availability and multitasking behavior for business process simulation. In this approach, each time slot in a resource calendar has an associated availability probability and a multitasking probability per multitasking level. For example, a resource may be available on Fridays between 14:00-15:00 with 90\% probability, and given that they are performing one task during this slot, they may take on a second concurrent task with 60\% probability. We propose algorithms to discover probabilistic calendars and probabilistic multitasking capacities from event logs. An evaluation shows that, with these enhancements, simulation models discovered from event logs better replicate the distribution of activities and cycle times, relative to approaches with crisp calendars and monotasking assumptions.

Dimensionality reduction (DR) offers a useful representation of complex high-dimensional data. Recent DR methods focus on hyperbolic geometry to derive a faithful low-dimensional representation of hierarchical data. However, existing methods are based on neighbor embedding, frequently ruining the continual relation of the hierarchies. This paper presents hyperboloid Gaussian process (GP) latent variable models (hGP-LVMs) to embed high-dimensional hierarchical data with implicit continuity via nonparametric estimation. We adopt generative modeling using the GP, which brings effective hierarchical embedding and executes ill-posed hyperparameter tuning. This paper presents three variants that employ original point, sparse point, and Bayesian estimations. We establish their learning algorithms by incorporating the Riemannian optimization and active approximation scheme of GP-LVM. For Bayesian inference, we further introduce the reparameterization trick to realize Bayesian latent variable learning. In the last part of this paper, we apply hGP-LVMs to several datasets and show their ability to represent high-dimensional hierarchies in low-dimensional spaces.

Intervention intuition is often used in model explanation where the intervention effect of a feature on the outcome is quantified by the difference of a model prediction when the feature value is changed from the current value to the baseline value. Such a model intervention effect of a feature is inherently association. In this paper, we will study the conditions when an intuitive model intervention effect has a causal interpretation, i.e., when it indicates whether a feature is a direct cause of the outcome. This work links the model intervention effect to the causal interpretation of a model. Such an interpretation capability is important since it indicates whether a machine learning model is trustworthy to domain experts. The conditions also reveal the limitations of using a model intervention effect for causal interpretation in an environment with unobserved features. Experiments on semi-synthetic datasets have been conducted to validate theorems and show the potential for using the model intervention effect for model interpretation.

We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as domain adaptation and algorithmic fairness, where comparing two groups is essential while controlling for confounding variables. We begin by establishing a hardness result for conditional two-sample testing, demonstrating that no valid test can have significant power against any single alternative without proper assumptions. We then introduce two general frameworks that implicitly or explicitly target specific classes of distributions for their validity and power. Our first framework allows us to convert any conditional independence test into a conditional two-sample test in a black-box manner, while preserving the asymptotic properties of the original conditional independence test. The second framework transforms the problem into comparing marginal distributions with estimated density ratios, which allows us to leverage existing methods for marginal two-sample testing. We demonstrate this idea in a concrete manner with classification and kernel-based methods. Finally, simulation studies are conducted to illustrate the proposed frameworks in finite-sample scenarios.

Infectious diseases occur when pathogens from other individuals or animals infect a person, resulting in harm to both individuals and society as a whole. The outbreak of such diseases can pose a significant threat to human health. However, early detection and tracking of these outbreaks have the potential to reduce the mortality impact. To address these threats, public health authorities have endeavored to establish comprehensive mechanisms for collecting disease data. Many countries have implemented infectious disease surveillance systems, with the detection of epidemics being a primary objective. The clinical healthcare system, local/state health agencies, federal agencies, academic/professional groups, and collaborating governmental entities all play pivotal roles within this system. Moreover, nowadays, search engines and social media platforms can serve as valuable tools for monitoring disease trends. The Internet and social media have become significant platforms where users share information about their preferences and relationships. This real-time information can be harnessed to gauge the influence of ideas and societal opinions, making it highly useful across various domains and research areas, such as marketing campaigns, financial predictions, and public health, among others. This article provides a review of the existing standard methods developed by researchers for detecting outbreaks using time series data. These methods leverage various data sources, including conventional data sources and social media data or Internet data sources. The review particularly concentrates on works published within the timeframe of 2015 to 2022.