We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods consist of two consecutive stages, i.e., performing fair spectral embedding on a given graph and conducting $k$means to obtain discrete cluster labels. However, in practice, the graph is usually unknown, and we need to construct the underlying graph from potentially noisy data, the quality of which inevitably affects subsequent fair clustering performance. Furthermore, performing FSC through separate steps breaks the connections among these steps, leading to suboptimal results. To this end, we first theoretically analyze the effect of the constructed graph on FSC. Motivated by the analysis, we propose a novel graph construction method with a node-adaptive graph filter to learn graphs from noisy data. Then, all independent stages of conventional FSC are integrated into a single objective function, forming an end-to-end framework that inputs raw data and outputs discrete cluster labels. An algorithm is developed to jointly and alternately update the variables in each stage. Finally, we conduct extensive experiments on synthetic, benchmark, and real data, which show that our model is superior to state-of-the-art fair clustering methods.

We study the problem of allocating scarce societal resources of different types (e.g., permanent housing, deceased donor kidneys for transplantation, ventilators) to heterogeneous allocatees on a waitlist (e.g., people experiencing homelessness, individuals suffering from end-stage renal disease, Covid-19 patients) based on their observed covariates. We leverage administrative data collected in deployment to design an online policy that maximizes expected outcomes while satisfying budget constraints, in the long run. Our proposed policy waitlists each individual for the resource maximizing the difference between their estimated mean treatment outcome and the estimated resource dual-price or, roughly, the opportunity cost of using the resource. Resources are then allocated as they arrive, in a first-come first-serve fashion. We demonstrate that our data-driven policy almost surely asymptotically achieves the expected outcome of the optimal out-of-sample policy under mild technical assumptions. We extend our framework to incorporate various fairness constraints. We evaluate the performance of our approach on the problem of designing policies for allocating scarce housing resources to people experiencing homelessness in Los Angeles based on data from the homeless management information system. In particular, we show that using our policies improves rates of exit from homelessness by 1.9% and that policies that are fair in either allocation or outcomes by race come at a very low price of fairness.

This study employs Bayesian methodologies to explore the influence of player or positional factors in predicting the probability of a shot resulting in a goal, measured by the expected goals (xG) metric. Utilising publicly available data from StatsBomb, Bayesian hierarchical logistic regressions are constructed, analysing approximately 10,000 shots from the English Premier League to ascertain whether positional or player-level effects impact xG. The findings reveal positional effects in a basic model that includes only distance to goal and shot angle as predictors, highlighting that strikers and attacking midfielders exhibit a higher likelihood of scoring. However, these effects diminish when more informative predictors are introduced. Nevertheless, even with additional predictors, player-level effects persist, indicating that certain players possess notable positive or negative xG adjustments, influencing their likelihood of scoring a given chance. The study extends its analysis to data from Spain's La Liga and Germany's Bundesliga, yielding comparable results. Additionally, the paper assesses the impact of prior distribution choices on outcomes, concluding that the priors employed in the models provide sound results but could be refined to enhance sampling efficiency for constructing more complex and extensive models feasibly.

CP decomposition is a powerful tool for data science, especially gene analysis, deep learning, and quantum computation. However, the application of tensor decomposition is largely hindered by the exponential increment of the computational complexity and storage consumption with the size of tensors. While the data in our real world is usually presented as trillion- or even exascale-scale tensors, existing work can only support billion-scale scale tensors. In our work, we propose the Exascale-Tensor to mitigate the significant gap. Specifically, we propose a compression-based tensor decomposition framework, namely the exascale-tensor, to support exascale tensor decomposition. Then, we carefully analyze the inherent parallelism and propose a bag of strategies to improve computational efficiency. Last, we conduct experiments to decompose tensors ranging from million-scale to trillion-scale for evaluation. Compared to the baselines, the exascale-tensor supports 8,000x larger tensors and a speedup up to 6.95x. We also apply our method to two real-world applications, including gene analysis and tensor layer neural networks, of which the numeric results demonstrate the scalability and effectiveness of our method.

In this paper, a novel clustered FL framework that enables distributed edge devices with non-IID data to independently form several clusters in a distributed manner and implement FL training within each cluster is proposed. In particular, our designed clustered FL algorithm must overcome two challenges associated with FL training. First, the server has limited FL training information (i.e., the parameter server can only obtain the FL model information of each device) and limited computational power for finding the differences among a large amount of devices. Second, each device does not have the data information of other devices for device clustering and can only use global FL model parameters received from the server and its data information to determine its cluster identity, which will increase the difficulty of device clustering. To overcome these two challenges, we propose a joint gradient and loss based distributed clustering method in which each device determines its cluster identity considering the gradient similarity and training loss. The proposed clustering method not only considers how a local FL model of one device contributes to each cluster but also the direction of gradient descent thus improving clustering speed. By delegating clustering decisions to edge devices, each device can fully leverage its private data information to determine its own cluster identity, thereby reducing clustering overhead and improving overall clustering performance. Simulation results demonstrate that our proposed clustered FL algorithm can reduce clustering iterations by up to 99% compared to the existing baseline.

The Deep Leakage from Gradient (DLG) attack has emerged as a prevalent and highly effective method for extracting sensitive training data by inspecting exchanged gradients. This approach poses a substantial threat to the privacy of individuals and organizations alike. This research presents a comprehensive analysis of the gradient leakage method when applied specifically to transformer-based models. Through meticulous examination, we showcase the capability to accurately recover data solely from gradients and rigorously investigate the conditions under which gradient attacks can be executed, providing compelling evidence. Furthermore, we reevaluate the approach of introducing additional noise on gradients as a protective measure against gradient attacks. To address this, we outline a theoretical proof that analyzes the associated privacy costs within the framework of differential privacy. Additionally, we affirm the convergence of the Stochastic Gradient Descent (SGD) algorithm under perturbed gradients. The primary objective of this study is to augment the understanding of gradient leakage attack and defense strategies while actively contributing to the development of privacy-preserving techniques specifically tailored for transformer-based models. By shedding light on the vulnerabilities and countermeasures associated with gradient leakage, this research aims to foster advancements in safeguarding sensitive data and upholding privacy in the context of transformer-based models.

Data sampling is an effective method to improve the training speed of neural networks, with recent results demonstrating that it can even break the neural scaling laws. These results critically rely on high-quality scores to estimate the importance of an input to the network. We observe that there are two dominant strategies: static sampling, where the scores are determined before training, and dynamic sampling, where the scores can depend on the model weights. Static algorithms are computationally inexpensive but less effective than their dynamic counterparts, which can cause end-to-end slowdown due to their need to explicitly compute losses. To address this problem, we propose a novel sampling distribution based on nonparametric kernel regression that learns an effective importance score as the neural network trains. However, nonparametric regression models are too computationally expensive to accelerate end-to-end training. Therefore, we develop an efficient sketch-based approximation to the Nadaraya-Watson estimator. Using recent techniques from high-dimensional statistics and randomized algorithms, we prove that our Nadaraya-Watson sketch approximates the estimator with exponential convergence guarantees. Our sampling algorithm outperforms the baseline in terms of wall-clock time and accuracy on four datasets.

Motor impairments, frequently caused by neurological incidents like strokes or traumatic brain injuries, present substantial obstacles in rehabilitation therapy. This research aims to elevate the field by optimizing motor imagery classification algorithms within Brain-Computer Interfaces (BCIs). By improving the efficiency of BCIs, we offer a novel approach that holds significant promise for enhancing motor rehabilitation outcomes. Utilizing unsupervised techniques for dimensionality reduction, namely Uniform Manifold Approximation and Projection (UMAP) coupled with K-Nearest Neighbors (KNN), we evaluate the necessity of employing supervised methods such as Long Short-Term Memory (LSTM) and Convolutional Neural Networks (CNNs) for classification tasks. Importantly, participants who exhibited high KNN scores following UMAP dimensionality reduction also achieved high accuracy in supervised deep learning (DL) models. Due to individualized model requirements and massive neural training data, dimensionality reduction becomes an effective preprocessing step that minimizes the need for extensive data labeling and supervised deep learning techniques. This approach has significant implications not only for targeted therapies in motor dysfunction but also for addressing regulatory, safety, and reliability concerns in the rapidly evolving BCI field.

This paper presents a comprehensive evaluation of three distinct computational algorithms applied to the decision-making process of real estate purchases. Specifically, we analyze the efficacy of Linear Regression from Scikit-learn library, Gaussian Elimination with partial pivoting, and LU Decomposition in predicting the advisability of buying a house in the State of Connecticut based on a set of financial and market-related parameters. The algorithms' performances were compared using a dataset encompassing town-specific details, yearly data, interest rates, and median sale ratios. Our results demonstrate significant differences in predictive accuracy, with Linear Regression and LU Decomposition providing the most reliable recommendations and Gaussian Elimination showing limitations in stability and performance. The study's findings emphasize the importance of algorithm selection in predictive analytic and offer insights into the practical applications of computational methods in real estate investment strategies. By evaluating model efficacy through metrics such as R-squared scores and Mean Squared Error, we provide a nuanced understanding of each method's strengths and weaknesses, contributing valuable knowledge to the fields of real estate analysis and predictive modeling.

Classifying patterns of known classes and rejecting ambiguous and novel (also called as out-of-distribution (OOD)) inputs are involved in open world pattern recognition. Deep neural network models usually excel in closed-set classification while performing poorly in rejecting OOD. To tackle this problem, numerous methods have been designed to perform open set recognition (OSR) or OOD rejection/detection tasks. Previous methods mostly take post-training score transformation or hybrid models to ensure low scores on OOD inputs while separating known classes. In this paper, we attempt to build a unified framework for building open set classifiers for both classification and OOD rejection. We formulate the open set recognition of $ K $-known-class as a $ (K + 1) $-class classification problem with model trained on known-class samples only. By decomposing the $ K $-class problem into $ K $ one-versus-all (OVA) binary classification tasks and binding some parameters, we show that combining the scores of OVA classifiers can give $ (K + 1) $-class posterior probabilities, which enables classification and OOD rejection in a unified framework. To maintain the closed-set classification accuracy of the OVA trained classifier, we propose a hybrid training strategy combining OVA loss and multi-class cross-entropy loss. We implement the OVA framework and hybrid training strategy on the recently proposed convolutional prototype network. Experiments on popular OSR and OOD detection datasets demonstrate that the proposed framework, using a single multi-class classifier, yields competitive performance in closed-set classification, OOD detection, and misclassification detection.