While traditional federated learning (FL) typically focuses on a star topology where clients are directly connected to a central server, real-world distributed systems often exhibit hierarchical architectures. Hierarchical FL (HFL) has emerged as a promising solution to bridge this gap, leveraging aggregation points at multiple levels of the system. However, existing algorithms for HFL encounter challenges in dealing with multi-timescale model drift, i.e., model drift occurring across hierarchical levels of data heterogeneity. In this paper, we propose a multi-timescale gradient correction (MTGC) methodology to resolve this issue. Our key idea is to introduce distinct control variables to (i) correct the client gradient towards the group gradient, i.e., to reduce client model drift caused by local updates based on individual datasets, and (ii) correct the group gradient towards the global gradient, i.e., to reduce group model drift caused by FL over clients within the group. We analytically characterize the convergence behavior of MTGC under general non-convex settings, overcoming challenges associated with couplings between correction terms. We show that our convergence bound is immune to the extent of data heterogeneity, confirming the stability of the proposed algorithm against multi-level non-i.i.d.

Constructing confidence intervals (CIs) for the average treatment effect (ATE) from patient records is crucial to assess the effectiveness and safety of drugs. However, patient records typically come from different hospitals, thus raising the question of how multiple observational datasets can be effectively combined for this purpose. In our paper, we propose a new method that estimates the ATE from multiple observational datasets and provides valid CIs. Our method makes little assumptions about the observational datasets and is thus widely applicable in medical practice. The key idea of our method is that we leverage predictionpowered inferences and thereby essentially'shrink' the CIs so that we offer more precise uncertainty quantification as compared to naïve approaches. We further prove the unbiasedness of our method and the validity of our CIs. We confirm our theoretical results through various numerical experiments. Finally, we provide an extension of our method for constructing CIs from combinations of experimental and observational datasets. Estimating the average treatment effect (ATE) together with confidence intervals (CIs) is relevant in many fields, such as medicine, where the ATE is used to assess the effectiveness and safety of drugs (Glass et al., 2013; Feuerriegel et al., 2024). Nowadays, there is a growing interest in using observational datasets for this purpose, for example, electronic health records (EHRs) and clinical registries (Johnson et al., 2016; Corrigan-Curay et al., 2018; Hong, 2021). Importantly, such observational datasets typically originate from different hospitals, different health providers, or even different countries (Colnet et al., 2024), thus raising the question of how to construct CIs for ATE estimation from multiple observational datasets. Motivating example: During the COVID-19 pandemic, the effectiveness and safety of potential drugs and vaccines were often assessed from electronic health records that originated from different hospitals to rapidly generate new evidence with treatment guidelines (Tacconelli et al., 2022). For example, one study (Wong et al., 2024) estimated the effect of nirmatrelvir/ritonavir (also known under the commercial name "paxlovid") in patients with COVID-19 diagnosis on 28-day all-cause hospitalizations from data obtained through a retrospective, multi-center study.

The Mapper algorithm is an essential tool for visualizing complex, high dimensional data in topology data analysis (TDA) and has been widely used in biomedical research. It outputs a combinatorial graph whose structure implies the shape of the data. However,the need for manual parameter tuning and fixed intervals, along with fixed overlapping ratios may impede the performance of the standard Mapper algorithm. Variants of the standard Mapper algorithms have been developed to address these limitations, yet most of them still require manual tuning of parameters. Additionally, many of these variants, including the standard version found in the literature, were built within a deterministic framework and overlooked the uncertainty inherent in the data. To relax these limitations, in this work, we introduce a novel framework that implicitly represents intervals through a hidden assignment matrix, enabling automatic parameter optimization via stochastic gradient descent. In this work, we develop a soft Mapper framework based on a Gaussian mixture model(GMM) for flexible and implicit interval construction. We further illustrate the robustness of the soft Mapper algorithm by introducing the Mapper graph mode as a point estimation for the output graph. Moreover, a stochastic gradient descent algorithm with a specific topological loss function is proposed for optimizing parameters in the model. Both simulation and application studies demonstrate its effectiveness in capturing the underlying topological structures. In addition, the application to an RNA expression dataset obtained from the Mount Sinai/JJ Peters VA Medical Center Brain Bank (MSBB) successfully identifies a distinct subgroup of Alzheimer's Disease.

Network data often represent multiple types of relations, which can also denote exchanged quantities, and are typically encompassed in a weighted multiplex. Such data frequently exhibit clustering structures, however, traditional clustering methods are not well-suited for multiplex networks. Additionally, standard methods treat edge weights in their raw form, potentially biasing clustering towards a node's total weight capacity rather than reflecting cluster-related interaction patterns. To address this, we propose transforming edge weights into a compositional format, enabling the analysis of connection strengths in relative terms and removing the impact of nodes' total weights. We introduce a multiplex Dirichlet stochastic block model designed for multiplex networks with compositional layers. This model accounts for sparse compositional networks and enables joint clustering across different types of interactions. We validate the model through a simulation study and apply it to the international export data from the Food and Agriculture Organization of the United Nations.

Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be computationally infeasible. During training, surrogate parameters are fitted such that the surrogate reproduces the simulation model's outputs as closely as possible. However, the simulation model itself is merely a simplification of the real-world system, often missing relevant processes or suffering from misspecifications e.g., in inputs or boundary conditions. Hints about these might be captured in real-world measurement data, and yet, we typically ignore those hints during surrogate building. In this paper, we propose two novel probabilistic approaches to integrate simulation data and real-world measurement data during surrogate training. The first method trains separate surrogate models for each data source and combines their predictive distributions, while the second incorporates both data sources by training a single surrogate. We show the conceptual differences and benefits of the two approaches through both synthetic and real-world case studies. The results demonstrate the potential of these methods to improve predictive accuracy, predictive coverage, and to diagnose problems in the underlying simulation model. These insights can improve system understanding and future model development.

Next-generation reservoir computing (NG-RC) has attracted much attention due to its excellent performance in spatio-temporal forecasting of complex systems and its ease of implementation. This paper shows that NG-RC can be encoded as a kernel ridge regression that makes training efficient and feasible even when the space of chosen polynomial features is very large. Additionally, an extension to an infinite number of covariates is possible, which makes the methodology agnostic with respect to the lags into the past that are considered as explanatory factors, as well as with respect to the number of polynomial covariates, an important hyperparameter in traditional NG-RC. We show that this approach has solid theoretical backing and good behavior based on kernel universality properties previously established in the literature. Various numerical illustrations show that these generalizations of NG-RC outperform the traditional approach in several forecasting applications.

Backdoor attacks inject poisoning samples during training, with the goal of forcing a machine learning model to output an attacker-chosen class when presented a specific trigger at test time. Although backdoor attacks have been demonstrated in a variety of settings and against different models, the factors affecting their effectiveness are still not well understood. In this work, we provide a unifying framework to study the process of backdoor learning under the lens of incremental learning and influence functions. We show that the effectiveness of backdoor attacks depends on: (i) the complexity of the learning algorithm, controlled by its hyperparameters; (ii) the fraction of backdoor samples injected into the training set; and (iii) the size and visibility of the backdoor trigger. These factors affect how fast a model learns to correlate the presence of the backdoor trigger with the target class. Our analysis unveils the intriguing existence of a region in the hyperparameter space in which the accuracy on clean test samples is still high while backdoor attacks are ineffective, thereby suggesting novel criteria to improve existing defenses.

Extracting anomaly causality facilitates diagnostics once monitoring systems detect system faults. Identifying anomaly causes in large systems involves investigating a more extensive set of monitoring variables across multiple subsystems. However, learning causal graphs comes with a significant computational burden that restrains the applicability of most existing methods in real-time and large-scale deployments. In addition, modern monitoring applications for large systems often generate large amounts of binary alarm flags, and the distinct characteristics of binary anomaly data -- the meaning of state transition and data sparsity -- challenge existing causality learning mechanisms. This study proposes an anomaly causal discovery approach (AnomalyCD), addressing the accuracy and computational challenges of generating causal graphs from binary flag data sets. The AnomalyCD framework presents several strategies, such as anomaly flag characteristics incorporating causality testing, sparse data and link compression, and edge pruning adjustment approaches. We validate the performance of this framework on two datasets: monitoring sensor data of the readout-box system of the Compact Muon Solenoid experiment at CERN, and a public data set for information technology monitoring. The results demonstrate the considerable reduction of the computation overhead and moderate enhancement of the accuracy of temporal causal discovery on binary anomaly data sets.

Time series forecasting always faces the challenge of concept drift, where data distributions evolve over time, leading to a decline in forecast model performance. Existing solutions are based on online learning, which continually organize recent time series observations as new training samples and update model parameters according to the forecasting feedback on recent data. However, they overlook a critical issue: obtaining ground-truth future values of each sample should be delayed until after the forecast horizon. This delay creates a temporal gap between the training samples and the test sample. Our empirical analysis reveals that the gap can introduce concept drift, causing forecast models to adapt to outdated concepts. In this paper, we present \textsc{Proceed}, a novel proactive model adaptation framework for online time series forecasting. \textsc{Proceed} first estimates the concept drift between the recently used training samples and the current test sample. It then employs an adaptation generator to efficiently translate the estimated drift into parameter adjustments, proactively adapting the model to the test sample. To enhance the generalization capability of the framework, \textsc{Proceed} is trained on synthetic diverse concept drifts. Extensive experiments on five real-world datasets across various forecast models demonstrate that \textsc{Proceed} brings more performance improvements than the state-of-the-art online learning methods, significantly facilitating forecast models' resilience against concept drifts. Code is available at \url{https://github.com/SJTU-DMTai/OnlineTSF}.

Machine learning (ML) algorithms play a crucial role in decision making across diverse fields such as healthcare, finance, education, and law enforcement. Despite their widespread adoption, these systems raise ethical and social concerns due to potential biases and fairness issues. This study focuses on evaluating and improving the fairness of Computer Vision and Natural Language Processing (NLP) models applied to unstructured datasets, emphasizing how biased predictions can reinforce existing systemic inequalities. A publicly available dataset from Kaggle was utilized to simulate a practical scenario for examining fairness in ML workflows. To address and mitigate biases, the study employed two leading fairness libraries: Fairlearn by Microsoft, and AIF360 by IBM. These tools offer comprehensive frameworks for fairness analysis, including metrics evaluation, result visualization, and bias mitigation techniques. The research aims to measure bias levels in ML models, compare the effectiveness of these fairness libraries, and provide actionable recommendations for practitioners. The results demonstrate that each library possesses distinct strengths and limitations in evaluating and mitigating fairness. By systematically analyzing these tools, the study contributes valuable insights to the growing field of ML fairness, offering practical guidance for integrating fairness solutions into real world applications. This research underscores the importance of building more equitable and responsible machine learning systems.