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We establish a simple connection between robust and differentially-private algorithms: private mechanisms which perform well with very high probability are automatically robust in the sense that they retain accuracy even if a constant fraction of the samples they receive are adversarially corrupted. Since optimal mechanisms typically achieve these high success probabilities, our results imply that optimal private mechanisms for many basic statistics problems are robust. We investigate the consequences of this observation for both algorithms and computational complexity across different statistical problems. Assuming the Brennan-Bresler secret-leakage planted clique conjecture, we demonstrate a fundamental tradeoff between computational efficiency, privacy leakage, and success probability for sparse mean estimation. Private algorithms which match this tradeoff are not yet known -- we achieve that (up to polylogarithmic factors) in a polynomially-large range of parameters via the Sum-of-Squares method. To establish an information-computation gap for private sparse mean estimation, we also design new (exponential-time) mechanisms using fewer samples than efficient algorithms must use. Finally, we give evidence for privacy-induced information-computation gaps for several other statistics and learning problems, including PAC learning parity functions and estimation of the mean of a multivariate Gaussian.

Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set $X$ of $n$ points and two integers $k$ and $m$, the clustering with outliers aims to exclude $m$ points from $X$ and partition the remaining points into $k$ clusters that minimizes a certain cost function. In this paper, we give a general approach for solving clustering with outliers, which results in a fixed-parameter tractable (FPT) algorithm in $k$ and $m$, that almost matches the approximation ratio for its outlier-free counterpart. As a corollary, we obtain FPT approximation algorithms with optimal approximation ratios for $k$-Median and $k$-Means with outliers in general metrics. We also exhibit more applications of our approach to other variants of the problem that impose additional constraints on the clustering, such as fairness or matroid constraints.

This article develops a new algorithm named TTRISK to solve high-dimensional risk-averse optimization problems governed by differential equations (ODEs and/or PDEs) under uncertainty. As an example, we focus on the so-called Conditional Value at Risk (CVaR), but the approach is equally applicable to other coherent risk measures. Both the full and reduced space formulations are considered. The algorithm is based on low rank tensor approximations of random fields discretized using stochastic collocation. To avoid non-smoothness of the objective function underpinning the CVaR, we propose an adaptive strategy to select the width parameter of the smoothed CVaR to balance the smoothing and tensor approximation errors. Moreover, unbiased Monte Carlo CVaR estimate can be computed by using the smoothed CVaR as a control variate. To accelerate the computations, we introduce an efficient preconditioner for the KKT system in the full space formulation.The numerical experiments demonstrate that the proposed method enables accurate CVaR optimization constrained by large-scale discretized systems. In particular, the first example consists of an elliptic PDE with random coefficients as constraints. The second example is motivated by a realistic application to devise a lockdown plan for United Kingdom under COVID-19. The results indicate that the risk-averse framework is feasible with the tensor approximations under tens of random variables.

Multifidelity methods are widely used for estimating quantities of interest (QoI) in computational science by employing numerical simulations of differing costs and accuracies. Many methods approximate numerical-valued statistics that represent only limited information, e.g., scalar statistics, about the QoI. Further quantification of uncertainty, e.g., for risk assessment, failure probabilities, or confidence intervals, requires estimation of the full distributions. In this paper, we generalize the ideas in [Xu et al., SIAM J. Sci. Comput. 44.1 (2022), A150-A175] to develop a multifidelity method that approximates the full distribution of scalar-valued QoI. The main advantage of our approach compared to alternative methods is that we require no particular relationships among the high and lower-fidelity models (e.g. model hierarchy), and we do not assume any knowledge of model statistics including correlations and other cross-model statistics before the procedure starts. Under suitable assumptions in the framework above, we achieve provable 1-Wasserstein metric convergence of an algorithmically constructed distributional emulator via an exploration-exploitation strategy. We also prove that crucial policy actions taken by our algorithm are budget-asymptotically optimal. Numerical experiments are provided to support our theoretical analysis.

Intensive Care Units usually carry patients with a serious risk of mortality. Recent research has shown the ability of Machine Learning to indicate the patients' mortality risk and point physicians toward individuals with a heightened need for care. Nevertheless, healthcare data is often subject to privacy regulations and can therefore not be easily shared in order to build Centralized Machine Learning models that use the combined data of multiple hospitals. Federated Learning is a Machine Learning framework designed for data privacy that can be used to circumvent this problem. In this study, we evaluate the ability of deep Federated Learning to predict the risk of Intensive Care Unit mortality at an early stage. We compare the predictive performance of Federated, Centralized, and Local Machine Learning in terms of AUPRC, F1-score, and AUROC. Our results show that Federated Learning performs equally well as the centralized approach and is substantially better than the local approach, thus providing a viable solution for early Intensive Care Unit mortality prediction. In addition, we show that the prediction performance is higher when the patient history window is closer to discharge or death. Finally, we show that using the F1-score as an early stopping metric can stabilize and increase the performance of our approach for the task at hand.

Clustering has been extensively studied in centralized settings, but relatively unexplored in federated ones that data are distributed among multiple clients and can only be kept local at the clients. The necessity to invest more resources in improving federated clustering methods is twofold: 1) The performance of supervised federated learning models can benefit from clustering. 2) It is non-trivial to extend centralized ones to perform federated clustering tasks. In centralized settings, various deep clustering methods that perform dimensionality reduction and clustering jointly have achieved great success. To obtain high-quality cluster information, it is natural but non-trivial to extend these methods to federated settings. For this purpose, we propose a simple but effective federated deep clustering method. It requires only one communication round between the central server and clients, can run asynchronously, and can handle device failures. Moreover, although most studies have highlighted adverse effects of the non-independent and identically distributed (non-IID) data across clients, experimental results indicate that the proposed method can significantly benefit from this scenario.

With the explosive growth of information technology, multi-view graph data have become increasingly prevalent and valuable. Most existing multi-view clustering techniques either focus on the scenario of multiple graphs or multi-view attributes. In this paper, we propose a generic framework to cluster multi-view attributed graph data. Specifically, inspired by the success of contrastive learning, we propose multi-view contrastive graph clustering (MCGC) method to learn a consensus graph since the original graph could be noisy or incomplete and is not directly applicable. Our method composes of two key steps: we first filter out the undesirable high-frequency noise while preserving the graph geometric features via graph filtering and obtain a smooth representation of nodes; we then learn a consensus graph regularized by graph contrastive loss. Results on several benchmark datasets show the superiority of our method with respect to state-of-the-art approaches. In particular, our simple approach outperforms existing deep learning-based methods.

In this paper, we propose a one-stage online clustering method called Contrastive Clustering (CC) which explicitly performs the instance- and cluster-level contrastive learning. To be specific, for a given dataset, the positive and negative instance pairs are constructed through data augmentations and then projected into a feature space. Therein, the instance- and cluster-level contrastive learning are respectively conducted in the row and column space by maximizing the similarities of positive pairs while minimizing those of negative ones. Our key observation is that the rows of the feature matrix could be regarded as soft labels of instances, and accordingly the columns could be further regarded as cluster representations. By simultaneously optimizing the instance- and cluster-level contrastive loss, the model jointly learns representations and cluster assignments in an end-to-end manner. Extensive experimental results show that CC remarkably outperforms 17 competitive clustering methods on six challenging image benchmarks. In particular, CC achieves an NMI of 0.705 (0.431) on the CIFAR-10 (CIFAR-100) dataset, which is an up to 19\% (39\%) performance improvement compared with the best baseline.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

Deep learning models on graphs have achieved remarkable performance in various graph analysis tasks, e.g., node classification, link prediction and graph clustering. However, they expose uncertainty and unreliability against the well-designed inputs, i.e., adversarial examples. Accordingly, various studies have emerged for both attack and defense addressed in different graph analysis tasks, leading to the arms race in graph adversarial learning. For instance, the attacker has poisoning and evasion attack, and the defense group correspondingly has preprocessing- and adversarial- based methods. Despite the booming works, there still lacks a unified problem definition and a comprehensive review. To bridge this gap, we investigate and summarize the existing works on graph adversarial learning tasks systemically. Specifically, we survey and unify the existing works w.r.t. attack and defense in graph analysis tasks, and give proper definitions and taxonomies at the same time. Besides, we emphasize the importance of related evaluation metrics, and investigate and summarize them comprehensively. Hopefully, our works can serve as a reference for the relevant researchers, thus providing assistance for their studies. More details of our works are available at //github.com/gitgiter/Graph-Adversarial-Learning.