Summary and Contributions: The paper presents an algorithm for k-clustering in a sliding window streaming model, where k-clustering means the generalization of k-median and k-means to any fixed l_p-norm. The main theoretical result is an algorithm that achieves O(1)-approximation for points in arbitrary metric space and thus includes the prevalent of Euclidean metric, which is also used in the experimental evaluation. This algorithm is for sliding window streaming, where the algorithm repeatedly solves the clustering problem on the w most recent points in the stream (for parameter w). While the minimal requirement is to estimate the cost of a k-clustering, this algorithm also reports k center points. The usual motivation for this model is to allow old data to expire, and analyze only recent data.

The paper considers k clustering problem in the sliding window streaming model. However, the authors are urged to consider the reviews when preparing the final version including explicitly stating a bound on the constant factor approximation obtained.

After Rebuttal: Thank you for the responses. I that believe the paper will be even stronger with the inclusion of the stochastic gradient-variant. This is a very valuable theorem, which will be useful for other theoreticians working in this field. On the other hand, to the best of my knowledge, this is the first paper that uses a stochastic Runge-Kutta integrator for sampling from strongly log-concave densities with explicit guarantees. The authors further show that their proposed numerical scheme improves upon the existing guarantees when applied to the overdamped Langevin dynamics.

The pre-train then fine-tune approach has advanced GNNs by enabling general knowledge capture without task-specific labels. However, an objective gap between pre-training and downstream tasks limits its effectiveness. Recent graph prompting methods aim to close this gap through task reformulations and learnable prompts. Despite this, they struggle with complex graphs like heterophily graphs. Freezing the GNN encoder can reduce the impact of prompting, while simple prompts fail to handle diverse hop-level distributions. This paper identifies two key challenges in adapting graph prompting methods for complex graphs: (1) adapting the model to new distributions in downstream tasks to mitigate pre-training and fine-tuning discrepancies from heterophily and (2) customizing prompts for hop-specific node requirements. To overcome these challenges, we propose Distribution-aware Graph Prompt Tuning (DAGPrompT), which integrates a GLoRA module for optimizing the GNN encoder's projection matrix and message-passing schema through low-rank adaptation. DAGPrompT also incorporates hop-specific prompts accounting for varying graph structures and distributions among hops. Evaluations on 10 datasets and 14 baselines demonstrate that DAGPrompT improves accuracy by up to 4.79 in node and graph classification tasks, setting a new state-of-the-art while preserving efficiency. Codes are available at GitHub.

We present a novel approach to anomaly detection by integrating Generalized Hyperbolic (GH) processes into kernel-based methods. The GH distribution, known for its flexibility in modeling skewness, heavy tails, and kurtosis, helps to capture complex patterns in data that deviate from Gaussian assumptions. We propose a GH-based kernel function and utilize it within Kernel Density Estimation (KDE) and One-Class Support Vector Machines (OCSVM) to develop anomaly detection frameworks. Theoretical results confirmed the positive semi-definiteness and consistency of the GH-based kernel, ensuring its suitability for machine learning applications. Empirical evaluation on synthetic and real-world datasets showed that our method improves detection performance in scenarios involving heavy-tailed and asymmetric or imbalanced distributions. https://github.com/paulinebourigault/GHKernelAnomalyDetect

Novelty Detection (ND) plays a crucial role in machine learning by identifying new or unseen data during model inference. This capability is especially important for the safe and reliable operation of automated systems. Despite advances in this field, existing techniques often fail to maintain their performance when subject to adversarial attacks. Our research addresses this gap by marrying the merits of nearest-neighbor algorithms with robust features obtained from models pretrained on ImageNet. We focus on enhancing the robustness and performance of ND algorithms. Experimental results demonstrate that our approach significantly outperforms current state-of-the-art methods across various benchmarks, particularly under adversarial conditions. By incorporating robust pretrained features into the k-NN algorithm, we establish a new standard for performance and robustness in the field of robust ND. This work opens up new avenues for research aimed at fortifying machine learning systems against adversarial vulnerabilities. Our implementation is publicly available at https://github.com/rohban-lab/ZARND.

This study forms the basis of a digital twin system of the knee joint, using advanced quantitative MRI (qMRI) and machine learning to advance precision health in osteoarthritis (OA) management and knee replacement (KR) prediction. We combined deep learning-based segmentation of knee joint structures with dimensionality reduction to create an embedded feature space of imaging biomarkers. Through cross-sectional cohort analysis and statistical modeling, we identified specific biomarkers, including variations in cartilage thickness and medial meniscus shape, that are significantly associated with OA incidence and KR outcomes. Integrating these findings into a comprehensive framework represents a considerable step toward personalized knee-joint digital twins, which could enhance therapeutic strategies and inform clinical decision-making in rheumatological care. This versatile and reliable infrastructure has the potential to be extended to broader clinical applications in precision health.

The vast repositories of Electronic Health Records (EHR) and medical claims hold untapped potential for studying rare but critical events, such as suicide attempt. Conventional setups often model suicide attempt as a univariate outcome and also exclude any ``single-record'' patients with a single documented encounter due to a lack of historical information. However, patients who were diagnosed with suicide attempts at the only encounter could, to some surprise, represent a substantial proportion of all attempt cases in the data, as high as 70--80%. We innovate a hybrid and integrative learning framework to leverage concurrent outcomes as surrogates and harness the forbidden yet precious information from single-record data. Our approach employs a supervised learning component to learn the latent variables that connect primary (e.g., suicide) and surrogate outcomes (e.g., mental disorders) to historical information. It simultaneously employs an unsupervised learning component to utilize the single-record data, through the shared latent variables. As such, our approach offers a general strategy for information integration that is crucial to modeling rare conditions and events. With hospital inpatient data from Connecticut, we demonstrate that single-record data and concurrent diagnoses indeed carry valuable information, and utilizing them can substantially improve suicide risk modeling.

In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to preserve the inherent structure of such data. However, existing approaches, such as tensor autoregression and tensor decomposition, often have consistently failed to provide clear assertions regarding the number of samples that can be exactly predicted. While matrix-based methods using nuclear norms address this limitation, their reliance on matrices limits accuracy and increases computational costs when handling multidimensional data. To overcome these challenges, we reformulate multidimensional time series prediction as a deterministic tensor completion problem and propose a novel theoretical framework. Specifically, we develop a deterministic tensor completion theory and introduce the Temporal Convolutional Tensor Nuclear Norm (TCTNN) model. By convolving the multidimensional time series along the temporal dimension and applying the tensor nuclear norm, our approach identifies the maximum forecast horizon for exact predictions. Additionally, TCTNN achieves superior performance in prediction accuracy and computational efficiency compared to existing methods across diverse real-world datasets, including climate temperature, network flow, and traffic ride data. Our implementation is publicly available at https://github.com/HaoShu2000/TCTNN.

Contextual pricing strategies are prevalent in online retailing, where the seller adjusts prices based on products' attributes and buyers' characteristics. Although such strategies can enhance seller's profits, they raise concerns about fairness when significant price disparities emerge among specific groups, such as gender or race. These disparities can lead to adverse perceptions of fairness among buyers and may even violate the law and regulation. In contrast, price differences can incentivize disadvantaged buyers to strategically manipulate their group identity to obtain a lower price. In this paper, we investigate contextual dynamic pricing with fairness constraints, taking into account buyers' strategic behaviors when their group status is private and unobservable from the seller. We propose a dynamic pricing policy that simultaneously achieves price fairness and discourages strategic behaviors. Our policy achieves an upper bound of $O(\sqrt{T}+H(T))$ regret over $T$ time horizons, where the term $H(T)$ arises from buyers' assessment of the fairness of the pricing policy based on their learned price difference. When buyers are able to learn the fairness of the price policy, this upper bound reduces to $O(\sqrt{T})$. We also prove an $\Omega(\sqrt{T})$ regret lower bound of any pricing policy under our problem setting. We support our findings with extensive experimental evidence, showcasing our policy's effectiveness. In our real data analysis, we observe the existence of price discrimination against race in the loan application even after accounting for other contextual information. Our proposed pricing policy demonstrates a significant improvement, achieving 35.06% reduction in regret compared to the benchmark policy.