Traditional models reliant solely on pairwise associations often prove insufficient in capturing the complex statistical structure inherent in multivariate data. Yet existing methods for identifying information shared among groups of $d>3$ variables are often intractable; asymmetric around a target variable; or unable to consider all factorisations of the joint probability distribution. Here, we present a framework that systematically derives high-order measures using lattice and operator function pairs, whereby the lattice captures the algebraic relational structure of the variables and the operator function computes measures over the lattice. We show that many existing information-theoretic high-order measures can be derived by using divergences as operator functions on sublattices of the partition lattice, thus preventing the accurate quantification of all interactions for $d>3$. Similarly, we show that using the KL divergence as the operator function also leads to unwanted cancellation of interactions for $d>3$. To characterise all interactions among $d$ variables, we introduce the Streitberg information defined on the full partition lattice using generalisations of the KL divergence as operator functions. We validate our results numerically on synthetic data, and illustrate the use of the Streitberg information through applications to stock market returns and neural electrophysiology data.

The top priority of a Housing and Homelessness System of Care (HHSC) is to connect people experiencing homelessness to supportive housing. An HHSC typically consists of many agencies serving the same population. Information technology platforms differ in type and quality between agencies, so their data are usually isolated from one agency to another. Larger agencies may have sufficient data to train and test artificial intelligence (AI) tools but smaller agencies typically do not. To address this gap, we introduce a Federated Learning (FL) approach enabling all agencies to train a predictive model collaboratively without sharing their sensitive data. We demonstrate how FL can be used within an HHSC to provide all agencies equitable access to quality AI and further assist human decision-makers in the allocation of resources within HHSC. This is achieved while preserving the privacy of the people within the data by not sharing identifying information between agencies without their consent. Our experimental results using real-world HHSC data from Calgary, Alberta, demonstrate that our FL approach offers comparable performance with the idealized scenario of training the predictive model with data fully shared and linked between agencies.

We consider the problem of asynchronous stochastic optimization, where an optimization algorithm makes updates based on stale stochastic gradients of the objective that are subject to an arbitrary (possibly adversarial) sequence of delays. We present a procedure which, for any given $q \in (0,1]$, transforms any standard stochastic first-order method to an asynchronous method with convergence guarantee depending on the $q$-quantile delay of the sequence. This approach leads to convergence rates of the form $O(\tau_q/qT+\sigma/\sqrt{qT})$ for non-convex and $O(\tau_q^2/(q T)^2+\sigma/\sqrt{qT})$ for convex smooth problems, where $\tau_q$ is the $q$-quantile delay, generalizing and improving on existing results that depend on the average delay. We further show a method that automatically adapts to all quantiles simultaneously, without any prior knowledge of the delays, achieving convergence rates of the form $O(\inf_{q} \tau_q/qT+\sigma/\sqrt{qT})$ for non-convex and $O(\inf_{q} \tau_q^2/(q T)^2+\sigma/\sqrt{qT})$ for convex smooth problems. Our technique is based on asynchronous mini-batching with a careful batch-size selection and filtering of stale gradients.

We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent work (Na et al. 2023) demonstrated that Hessian averaging can be utilized to achieve fast $\mathcal{O}\left(\sqrt{\tfrac{\log k}{k}}\right)$ local superlinear convergence for strongly convex functions in high probability, while maintaining fixed per-iteration Hessian costs. These methods, however, require gradient exactness and strong convexity, which poses challenges for their practical implementation. To address this concern we consider Hessian-averaged methods that allow gradient inexactness via norm condition based adaptive-sampling strategies. For the finite-sum problem we utilize deterministic sampling techniques which lead to global linear and sublinear convergence rates for strongly convex and nonconvex functions respectively. In this setting we are able to derive an improved deterministic local superlinear convergence rate of $\mathcal{O}\left(\tfrac{1}{k}\right)$. For the %expected risk expectation problem we utilize stochastic sampling techniques, and derive global linear and sublinear rates for strongly convex and nonconvex functions, as well as a $\mathcal{O}\left(\tfrac{1}{\sqrt{k}}\right)$ local superlinear convergence rate, all in expectation. We present novel analysis techniques that differ from the previous probabilistic results. Additionally, we propose scalable and efficient variations of these methods via diagonal approximations and derive the novel diagonally-averaged Newton (Dan) method for large-scale problems. Our numerical results demonstrate that the Hessian averaging not only helps with convergence, but can lead to state-of-the-art performance on difficult problems such as CIFAR100 classification with ResNets.

Graph neural networks (GNNs) take as input the graph structure and the feature vectors associated with the nodes. Both contain noisy information about the labels. Here we propose joint denoising and rewiring (JDR)--an algorithm to jointly denoise the graph structure and features, which can improve the performance of any downstream algorithm. We do this by defining and maximizing the alignment between the leading eigenspaces of graph and feature matrices. To approximately solve this computationally hard problem, we propose a heuristic that efficiently handles real-world graph datasets with many classes and different levels of homophily or heterophily. We experimentally verify the effectiveness of our approach on synthetic data and real-world graph datasets. The results show that JDR consistently outperforms existing rewiring methods on node classification tasks using GNNs as downstream models.

Dynamic graph learning aims to uncover evolutionary laws in real-world systems, enabling accurate social recommendation (link prediction) or early detection of cancer cells (classification). Inspired by the success of state space models, e.g., Mamba, for efficiently capturing long-term dependencies in language modeling, we propose DyG-Mamba, a new continuous state space model (SSM) for dynamic graph learning. Specifically, we first found that using inputs as control signals for SSM is not suitable for continuous-time dynamic network data with irregular sampling intervals, resulting in models being insensitive to time information and lacking generalization properties. Drawing inspiration from the Ebbinghaus forgetting curve, which suggests that memory of past events is strongly correlated with time intervals rather than specific details of the events themselves, we directly utilize irregular time spans as control signals for SSM to achieve significant robustness and generalization. Through exhaustive experiments on 12 datasets for dynamic link prediction and dynamic node classification tasks, we found that DyG-Mamba achieves state-of-the-art performance on most of the datasets, while also demonstrating significantly improved computation and memory efficiency.

With the increasing number of patients diagnosed with Alzheimer's Disease, prognosis models have the potential to aid in early disease detection. However, current approaches raise dependability concerns as they do not account for uncertainty. In this work, we compare the performance of Monte Carlo Dropout, Variational Inference, Markov Chain Monte Carlo, and Ensemble Learning trained on 512 patients to predict 4-year cognitive score trajectories with confidence bounds. We show that MC Dropout and MCMC are able to produce well-calibrated, and accurate predictions under noisy training data.

The explainability of black-box machine learning algorithms, commonly known as Explainable Artificial Intelligence (XAI), has become crucial for financial and other regulated industrial applications due to regulatory requirements and the need for transparency in business practices. Among the various paradigms of XAI, Explainable Case-Based Reasoning (XCBR) stands out as a pragmatic approach that elucidates the output of a model by referencing actual examples from the data used to train or test the model. Despite its potential, XCBR has been relatively underexplored for many algorithms such as tree-based models until recently. We start by observing that most XCBR methods are defined based on the distance metric learned by the algorithm. By utilizing a recently proposed technique to extract the distance metric learned by Random Forests (RFs), which is both geometry- and accuracy-preserving, we investigate various XCBR methods. These methods amount to identify special points from the training datasets, such as prototypes, critics, counter-factuals, and semi-factuals, to explain the predictions for a given query of the RF. We evaluate these special points using various evaluation metrics to assess their explanatory power and effectiveness.

Nature disasters play a key role in shaping human-urban infrastructure interactions. Effective and efficient response to natural disasters is essential for building resilience and a sustainable urban environment. Two types of information are usually the most necessary and difficult to gather in disaster response. The first information is about disaster damage perception, which shows how badly people think that urban infrastructure has been damaged. The second information is geolocation awareness, which means how people whereabouts are made available. In this paper, we proposed a novel disaster mapping framework, namely CVDisaster, aiming at simultaneously addressing geolocalization and damage perception estimation using cross-view Street-View Imagery (SVI) and Very High-Resolution satellite imagery. CVDisaster consists of two cross-view models, where CVDisaster-Geoloc refers to a cross-view geolocalization model based on a contrastive learning objective with a Siamese ConvNeXt image encoder, and CVDisaster-Est is a cross-view classification model based on a Couple Global Context Vision Transformer (CGCViT). Taking Hurricane IAN as a case study, we evaluate the CVDisaster framework by creating a novel cross-view dataset (CVIAN) and conducting extensive experiments. As a result, we show that CVDisaster can achieve highly competitive performance (over 80% for geolocalization and 75% for damage perception estimation) with even limited fine-tuning efforts, which largely motivates future cross-view models and applications within a broader GeoAI research community. The data and code are publicly available at: https://github.com/tum-bgd/CVDisaster.

The availability of performant pre-trained models has led to a proliferation of fine-tuned expert models that are specialized to a particular domain or task. Model MoErging methods aim to recycle expert models to create an aggregate system with improved performance or generalization. A key component of MoErging methods is the creation of a router that decides which expert model(s) to use for a particular input or application. The promise, effectiveness, and large design space of MoErging has spurred the development of many new methods over the past few years. This rapid pace of development has made it challenging to compare different MoErging methods, which are rarely compared to one another and are often validated in different experimental setups. To remedy such gaps, we present a comprehensive survey of MoErging methods that includes a novel taxonomy for cataloging key design choices and clarifying suitable applications for each method. Apart from surveying MoErging research, we inventory software tools and applications that make use of MoErging. We additionally discuss related fields of study such as model merging, multitask learning, and mixture-of-experts models. Taken as a whole, our survey provides a unified overview of existing MoErging methods and creates a solid foundation for future work in this burgeoning field.