Background: Patient stratification in brain disorders remains a significant challenge, despite advances in machine learning and multimodal neuroimaging. Automated machine learning algorithms have been widely applied for identifying patient subtypes (biotypes), but results have been inconsistent across studies. These inconsistencies are often attributed to algorithmic limitations, yet an overlooked factor may be the statistical properties of the input data. This study investigates the contribution of data patterns on algorithm performance by leveraging synthetic brain morphometry data as an exemplar. Methods: Four widely used algorithms-SuStaIn, HYDRA, SmileGAN, and SurrealGAN were evaluated using multiple synthetic pseudo-patient datasets designed to include varying numbers and sizes of clusters and degrees of complexity of morphometric changes. Ground truth, representing predefined clusters, allowed for the evaluation of performance accuracy across algorithms and datasets. Results: SuStaIn failed to process datasets with more than 17 variables, highlighting computational inefficiencies. HYDRA was able to perform individual-level classification in multiple datasets with no clear pattern explaining failures. SmileGAN and SurrealGAN outperformed other algorithms in identifying variable-based disease patterns, but these patterns were not able to provide individual-level classification. Conclusions: Dataset characteristics significantly influence algorithm performance, often more than algorithmic design. The findings emphasize the need for rigorous validation using synthetic data before real-world application and highlight the limitations of current clustering approaches in capturing the heterogeneity of brain disorders. These insights extend beyond neuroimaging and have implications for machine learning applications in biomedical research.

Simulation-based Bayesian inference (SBI) methods are widely used for parameter estimation in complex models where evaluating the likelihood is challenging but generating simulations is relatively straightforward. However, these methods commonly assume that the simulation model accurately reflects the true data-generating process, an assumption that is frequently violated in realistic scenarios. In this paper, we focus on the challenges faced by SBI methods under model misspecification. We consolidate recent research aimed at mitigating the effects of misspecification, highlighting three key strategies: i) robust summary statistics, ii) generalised Bayesian inference, and iii) error modelling and adjustment parameters. To illustrate both the vulnerabilities of popular SBI methods and the effectiveness of misspecification-robust alternatives, we present empirical results on an illustrative example.

In this work, we study the training and generalization performance of two-layer neural networks (NNs) after one gradient descent step under structured data modeled by Gaussian mixtures. While previous research has extensively analyzed this model under isotropic data assumption, such simplifications overlook the complexities inherent in real-world datasets. Our work addresses this limitation by analyzing two-layer NNs under Gaussian mixture data assumption in the asymptotically proportional limit, where the input dimension, number of hidden neurons, and sample size grow with finite ratios. We characterize the training and generalization errors by leveraging recent advancements in Gaussian universality. Specifically, we prove that a high-order polynomial model performs equivalent to the nonlinear neural networks under certain conditions. The degree of the equivalent model is intricately linked to both the "data spread" and the learning rate employed during one gradient step. Through extensive simulations, we demonstrate the equivalence between the original model and its polynomial counterpart across various regression and classification tasks. Additionally, we explore how different properties of Gaussian mixtures affect learning outcomes. Finally, we illustrate experimental results on Fashion-MNIST classification, indicating that our findings can translate to realistic data.

Logistic regression models are widely used in the social and behavioral sciences and in high-stakes domains, due to their simplicity and interpretability properties. At the same time, such domains are permeated by distribution shifts, where the distribution generating the data changes between training and deployment. In this paper, we study a distributionally robust logistic regression problem that seeks the model that will perform best against adversarial realizations of the data distribution drawn from a suitably constructed Wasserstein ambiguity set. Our model and solution approach differ from prior work in that we can capture settings where the likelihood of distribution shifts can vary across features, significantly broadening the applicability of our model relative to the state-of-the-art. We propose a graph-based solution approach that can be integrated into off-the-shelf optimization solvers. We evaluate the performance of our model and algorithms on numerous publicly available datasets. Our solution achieves a 408x speed-up relative to the state-of-the-art. Additionally, compared to the state-of-the-art, our model reduces average calibration error by up to 36.19% and worst-case calibration error by up to 41.70%, while increasing the average area under the ROC curve (AUC) by up to 18.02% and worst-case AUC by up to 48.37%.

Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene expression, offering valuable insights into cellular states at a single time point. Recent advancements in temporally resolved scRNA-seq, spatial transcriptomics (ST), and time-series spatial transcriptomics (temporal-ST) have further revolutionized our ability to study the spatiotemporal dynamics of individual cells. These technologies, when combined with computational frameworks such as Markov chains, stochastic differential equations (SDEs), and generative models like optimal transport and Schr\"odinger bridges, enable the reconstruction of dynamic cellular trajectories and cell fate decisions. This review discusses how these dynamical system approaches offer new opportunities to model and infer cellular dynamics from a systematic perspective.

Minimizing response times to meet legal requirements and serve patients in a timely manner is crucial for Emergency Medical Service (EMS) systems. Achieving this goal necessitates optimizing operational decision-making to efficiently manage ambulances. Against this background, we study a centrally controlled EMS system for which we learn an online ambulance dispatching and redeployment policy that aims at minimizing the mean response time of ambulances within the system by dispatching an ambulance upon receiving an emergency call and redeploying it to a waiting location upon the completion of its service. We propose a novel combinatorial optimization-augmented machine learning pipeline that allows to learn efficient policies for ambulance dispatching and redeployment. In this context, we further show how to solve the underlying full-information problem to generate training data and propose an augmentation scheme that improves our pipeline's generalization performance by mitigating a possible distribution mismatch with respect to the considered state space. Compared to existing methods that rely on augmentation during training, our approach offers substantial runtime savings of up to 87.9% while yielding competitive performance. To evaluate the performance of our pipeline against current industry practices, we conduct a numerical case study on the example of San Francisco's 911 call data. Results show that the learned policies outperform the online benchmarks across various resource and demand scenarios, yielding a reduction in mean response time of up to 30%.

FastMap was first introduced in the Data Mining community for generating Euclidean embeddings of complex objects. In this dissertation, we first present FastMap to generate Euclidean embeddings of graphs in near-linear time: The pairwise Euclidean distances approximate a desired graph-based distance function on the vertices. We then apply the graph version of FastMap to efficiently solve various graph-theoretic problems of significant interest in AI: including facility location, top-K centrality computations, community detection and block modeling, and graph convex hull computations. We also present a novel learning framework, called FastMapSVM, by combining FastMap and Support Vector Machines. We then apply FastMapSVM to predict the satisfiability of Constraint Satisfaction Problems and to classify seismograms in Earthquake Science.

Prognostic and Health Management (PHM) are crucial ways to avoid unnecessary maintenance for Cyber-Physical Systems (CPS) and improve system reliability. Predicting the Remaining Useful Life (RUL) is one of the most challenging tasks for PHM. Existing methods require prior knowledge about the system, contrived assumptions, or temporal mining to model the life cycles of machine equipment/devices, resulting in diminished accuracy and limited applicability in real-world scenarios. This paper proposes a Bi-directional Adversarial network with Covariate Encoding for machine Remaining Useful Life (BACE-RUL) prediction, which only adopts sensor measurements from the current life cycle to predict RUL rather than relying on previous consecutive cycle recordings. The current sensor measurements of mechanical devices are encoded to a conditional space to better understand the implicit inner mechanical status. The predictor is trained as a conditional generative network with the encoded sensor measurements as its conditions. Various experiments on several real-world datasets, including the turbofan aircraft engine dataset and the dataset collected from degradation experiments of Li-Ion battery cells, show that the proposed model is a general framework and outperforms state-of-the-art methods.

--Dynamic network embedding methods transform nodes in a dynamic network into low-dimensional vectors while preserving network characteristics, facilitating tasks such as node classification and community detection. Several embedding methods have been proposed to capture structural proximity among nodes in a network, where densely connected communities are preserved, while others have been proposed to preserve structural equivalence among nodes, capturing their structural roles regardless of their relative distance in the network. However, most existing methods that aim to preserve both network characteristics mainly focus on static networks and those designed for dynamic networks do not explicitly account for inter-snapshot structural properties. This paper proposes a novel unifying dynamic network embedding method that simultaneously preserves both structural proximity and equivalence while considering inter-snapshot structural relationships in a dynamic network. Specifically, to define structural equivalence in a dynamic network, we use temporal subgraphs, known as dynamic graphlets, to capture how a node's neighborhood structure evolves over time. We then introduce a temporal-structural random walk to flexibly sample time-respecting sequences of nodes, considering both their temporal proximity and similarity in evolving structures. The proposed method is evaluated using five real-world networks on node classification where it outperforms benchmark methods, showing its effectiveness and flexibility in capturing various aspects of a network. Network embedding transforms graph nodes into low-dimensional vectors while preserving network characteristics.

We introduce CVQBoost, a novel classification algorithm that leverages early hardware implementing Quantum Computing Inc's Entropy Quantum Computing (EQC) paradigm, Dirac-3 [Nguyen et. al. arXiv:2407.04512]. We apply CVQBoost to a fraud detection test case and benchmark its performance against XGBoost, a widely utilized ML method. Running on Dirac-3, CVQBoost demonstrates a significant runtime advantage over XGBoost, which we evaluate on high-performance hardware comprising up to 48 CPUs and four NVIDIA L4 GPUs using the RAPIDS AI framework. Our results show that CVQBoost maintains competitive accuracy (measured by AUC) while significantly reducing training time, particularly as dataset size and feature complexity increase. To assess scalability, we extend our study to large synthetic datasets ranging from 1M to 70M samples, demonstrating that CVQBoost on Dirac-3 is well-suited for large-scale classification tasks. These findings position CVQBoost as a promising alternative to gradient boosting methods, offering superior scalability and efficiency for high-dimensional ML applications such as fraud detection.