Hypothesis testing for small-sample scenarios is a practically important problem. In this paper, we investigate the robust hypothesis testing problem in a data-driven manner, where we seek the worst-case detector over distributional uncertainty sets centered around the empirical distribution from samples using Sinkhorn distance. Compared with the Wasserstein robust test, the corresponding least favorable distributions are supported beyond the training samples, which provides a more flexible detector. Various numerical experiments are conducted on both synthetic and real datasets to validate the competitive performances of our proposed method. As a fundamental problem in statistics, hypothesis testing plays a key role in general scientific discovery areas such as anomaly detection and model criticism. The goal of hypothesis testing is to determine which one among given hypotheses is true within a certain error probability level.

It is known that when the statistical models are singular, i.e., the Fisher information matrix at the true parameter is degenerate, the fixed step-size gradient descent algorithm takes polynomial number of steps in terms of the sample size $n$ to converge to a final statistical radius around the true parameter, which can be unsatisfactory for the application. To further improve that computational complexity, we consider the utilization of the second-order information in the design of optimization algorithms. Specifically, we study the normalized gradient descent (NormGD) algorithm for solving parameter estimation in parametric statistical models, which is a variant of gradient descent algorithm whose step size is scaled by the maximum eigenvalue of the Hessian matrix of the empirical loss function of statistical models. When the population loss function, i.e., the limit of the empirical loss function when $n$ goes to infinity, is homogeneous in all directions, we demonstrate that the NormGD iterates reach a final statistical radius around the true parameter after a logarithmic number of iterations in terms of $n$. Therefore, for fixed dimension $d$, the NormGD algorithm achieves the optimal overall computational complexity $\mathcal{O}(n)$ to reach the final statistical radius. This computational complexity is cheaper than that of the fixed step-size gradient descent algorithm, which is of the order $\mathcal{O}(n^{\tau})$ for some $\tau > 1$, to reach the same statistical radius. We illustrate our general theory under two statistical models: generalized linear models and mixture models, and experimental results support our prediction with general theory.

We consider stochastic optimization problems where data is drawn from a Markov chain. Existing methods for this setting crucially rely on knowing the mixing time of the chain, which in real-world applications is usually unknown. We propose the first optimization method that does not require the knowledge of the mixing time, yet obtains the optimal asymptotic convergence rate when applied to convex problems. We further show that our approach can be extended to: (i) finding stationary points in non-convex optimization with Markovian data, and (ii) obtaining better dependence on the mixing time in temporal difference (TD) learning; in both cases, our method is completely oblivious to the mixing time. Our method relies on a novel combination of multi-level Monte Carlo (MLMC) gradient estimation together with an adaptive learning method.

In this paper, we consider the problem of non-linear dimensionality reduction under uncertainty, both from a theoretical and algorithmic perspectives. Since real-world data usually contain measurements with uncertainties and artifacts, the input space in the proposed framework consists of probability distributions to model the uncertainties associated with each sample. We propose a new dimensionality reduction framework, called NGEU, which leverages uncertainty information and directly extends several traditional approaches, e.g., KPCA, MDA/KMFA, to receive as inputs the probability distributions instead of the original data. We show that the proposed NGEU formulation exhibits a global closed-form solution, and we analyze, based on the Rademacher complexity, how the underlying uncertainties theoretically affect the generalization ability of the framework. Empirical results on different datasets show the effectiveness of the proposed framework.

Cardiovascular disease is one of the most challenging diseases in middle-aged and older people, which causes high mortality. Coronary artery disease (CAD) is known as a common cardiovascular disease. A standard clinical tool for diagnosing CAD is angiography. The main challenges are dangerous side effects and high angiography costs. Today, the development of artificial intelligence-based methods is a valuable achievement for diagnosing disease. Hence, in this paper, artificial intelligence methods such as neural network (NN), deep neural network (DNN), and Fuzzy C-Means clustering combined with deep neural network (FCM-DNN) are developed for diagnosing CAD on a cardiac magnetic resonance imaging (CMRI) dataset. The original dataset is used in two different approaches. First, the labeled dataset is applied to the NN and DNN to create the NN and DNN models. Second, the labels are removed, and the unlabeled dataset is clustered via the FCM method, and then, the clustered dataset is fed to the DNN to create the FCM-DNN model. By utilizing the second clustering and modeling, the training process is improved, and consequently, the accuracy is increased. As a result, the proposed FCM-DNN model achieves the best performance with a 99.91% accuracy specifying 10 clusters, i.e., 5 clusters for healthy subjects and 5 clusters for sick subjects, through the 10-fold cross-validation technique compared to the NN and DNN models reaching the accuracies of 92.18% and 99.63%, respectively. To the best of our knowledge, no study has been conducted for CAD diagnosis on the CMRI dataset using artificial intelligence methods. The results confirm that the proposed FCM-DNN model can be helpful for scientific and research centers.

Predicative machine learning models are frequently being used by companies, institutes and organizations to make choices about humans. Strategic classification studies learning in settings where self-interested users can strategically modify their features to obtain favorable predictive outcomes. A key working assumption, however, is that 'favorable' always means 'positive'; this may be appropriate in some applications (e.g., loan approval, university admissions and hiring), but reduces to a fairly narrow view what user interests can be. In this work we argue for a broader perspective on what accounts for strategic user behavior, and propose and study a flexible model of generalized strategic classification. Our generalized model subsumes most current models, but includes other novel settings; among these, we identify and target one intriguing sub-class of problems in which the interests of users and the system are aligned. For this cooperative setting, we provide an in-depth analysis, and propose a practical learning approach that is effective and efficient. We compare our approach to existing learning methods and show its statistical and optimization benefits. Returning to our fully generalized model, we show how our results and approach can extend to the most general case. We conclude with a set of experiments that empirically demonstrate the utility of our approach.

The distributed nature and privacy-preserving characteristics of federated learning make it prone to the threat of poisoning attacks, especially backdoor attacks, where the adversary implants backdoors to misguide the model on certain attacker-chosen sub-tasks. In this paper, we present a novel method ARIBA to accurately and robustly identify backdoor attacks in federated learning. By empirical study, we observe that backdoor attacks are discernible by the filters of CNN layers. Based on this finding, we employ unsupervised anomaly detection to evaluate the pre-processed filters and calculate an anomaly score for each client. We then identify the most suspicious clients according to their anomaly scores. Extensive experiments are conducted, which show that our method ARIBA can effectively and robustly defend against multiple state-of-the-art attacks without degrading model performance.

We argue that when comparing two graphs, the distribution of node structural features is more informative than global graph statistics which are often used in practice, especially to evaluate graph generative models. Thus, we present GraphDCA - a framework for evaluating similarity between graphs based on the alignment of their respective node representation sets. The sets are compared using a recently proposed method for comparing representation spaces, called Delaunay Component Analysis (DCA), which we extend to graph data. To evaluate our framework, we generate a benchmark dataset of graphs exhibiting different structural patterns and show, using three node structure feature extractors, that GraphDCA recognizes graphs with both similar and dissimilar local structure. We then apply our framework to evaluate three publicly available real-world graph datasets and demonstrate, using gradual edge perturbations, that GraphDCA satisfyingly captures gradually decreasing similarity, unlike global statistics. Finally, we use GraphDCA to evaluate two state-of-the-art graph generative models, NetGAN and CELL, and conclude that further improvements are needed for these models to adequately reproduce local structural features.

We introduce L0Learn: an open-source package for sparse regression and classification using L0 regularization. L0Learn implements scalable, approximate algorithms, based on coordinate descent and local combinatorial optimization. The package is built using C++ and has a user-friendly R interface. Our experiments indicate that L0Learn can scale to problems with millions of features, achieving competitive run times with state-of-the-art sparse learning packages. L0Learn is available on both CRAN and GitHub.

In a number of application domains, one observes a sequence of network data; for example, repeated measurements between users interactions in social media platforms, financial correlation networks over time, or across subjects, as in multi-subject studies of brain connectivity. One way to analyze such data is by stacking networks into a third-order array or tensor. We propose a principal components analysis (PCA) framework for sequence network data, based on a novel decomposition for semi-symmetric tensors. We derive efficient algorithms for computing our proposed "Coupled CP" decomposition and establish estimation consistency of our approach under an analogue of the spiked covariance model with rates the same as the matrix case up to a logarithmic term. Our framework inherits many of the strengths of classical PCA and is suitable for a wide range of unsupervised learning tasks, including identifying principal networks, isolating meaningful changepoints or outliers across observations, and for characterizing the "variability network" of the most varying edges. Finally, we demonstrate the effectiveness of our proposal on simulated data and on examples from political science and financial economics. The proof techniques used to establish our main consistency results are surprisingly straight-forward and may find use in a variety of other matrix and tensor decomposition problems.