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Deep learning has proven to be successful in various domains and for different tasks. However, when it comes to private data several restrictions are making it difficult to use deep learning approaches in these application fields. Recent approaches try to generate data privately instead of applying a privacy-preserving mechanism directly, on top of the classifier. The solution is to create public data from private data in a manner that preserves the privacy of the data. In this work, two very prominent GAN-based architectures were evaluated in the context of private time series classification. In contrast to previous work, mostly limited to the image domain, the scope of this benchmark was the time series domain. The experiments show that especially GSWGAN performs well across a variety of public datasets outperforming the competitor DPWGAN. An analysis of the generated datasets further validates the superiority of GSWGAN in the context of time series generation.

We study multiclass online prediction where the learner can predict using a list of multiple labels (as opposed to just one label in the traditional setting). We characterize learnability in this model using the $b$-ary Littlestone dimension. This dimension is a variation of the classical Littlestone dimension with the difference that binary mistake trees are replaced with $(k+1)$-ary mistake trees, where $k$ is the number of labels in the list. In the agnostic setting, we explore different scenarios depending on whether the comparator class consists of single-labeled or multi-labeled functions and its tradeoff with the size of the lists the algorithm uses. We find that it is possible to achieve negative regret in some cases and provide a complete characterization of when this is possible. As part of our work, we adapt classical algorithms such as Littlestone's SOA and Rosenblatt's Perceptron to predict using lists of labels. We also establish combinatorial results for list-learnable classes, including an list online version of the Sauer-Shelah-Perles Lemma. We state our results within the framework of pattern classes -- a generalization of hypothesis classes which can represent adaptive hypotheses (i.e. functions with memory), and model data-dependent assumptions such as linear classification with margin.

We develop a Distributionally Robust Optimization (DRO) formulation for Multiclass Logistic Regression (MLR), which could tolerate data contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of distributions that are close to the empirical distribution of the training set in the sense of the Wasserstein metric. We relax the DRO formulation into a regularized learning problem whose regularizer is a norm of the coefficient matrix. We establish out-of-sample performance guarantees for the solutions to our model, offering insights on the role of the regularizer in controlling the prediction error. We apply the proposed method in rendering deep Vision Transformer (ViT)-based image classifiers robust to random and adversarial attacks. Specifically, using the MNIST and CIFAR-10 datasets, we demonstrate reductions in test error rate by up to 83.5% and loss by up to 91.3% compared with baseline methods, by adopting a novel random training method.

A novel methodology is proposed for clustering multivariate time series data using energy distance defined in Sz\'ekely and Rizzo (2013). Specifically, a dissimilarity matrix is formed using the energy distance statistic to measure separation between the finite dimensional distributions for the component time series. Once the pairwise dissimilarity matrix is calculated, a hierarchical clustering method is then applied to obtain the dendrogram. This procedure is completely nonparametric as the dissimilarities between stationary distributions are directly calculated without making any model assumptions. In order to justify this procedure, asymptotic properties of the energy distance estimates are derived for general stationary and ergodic time series. The method is illustrated in a simulation study for various component time series that are either linear or nonlinear. Finally the methodology is applied to two examples; one involves GDP of selected countries and the other is population size of various states in the U.S.A. in the years 1900 -1999.

Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or empirically, to converge to the underlying PDE solution with arbitrarily high accuracy. The primary difficulty lies in solving the highly non-convex optimization problems resulting from the neural network discretization, which are difficult to treat both theoretically and practically. It is our goal in this work to take a step toward remedying this. For this purpose, we develop a novel greedy training algorithm for shallow neural networks. Our method is applicable to both the variational formulation of the PDE and also to the residual minimization formulation pioneered by physics informed neural networks (PINNs). We analyze the method and obtain a priori error bounds when solving PDEs from the function class defined by shallow networks, which rigorously establishes the convergence of the method as the network size increases. Finally, we test the algorithm on several benchmark examples, including high dimensional PDEs, to confirm the theoretical convergence rate. Although the method is expensive relative to traditional approaches such as finite element methods, we view this work as a proof of concept for neural network-based methods, which shows that numerical methods based upon neural networks can be shown to rigorously converge.

Deep learning techniques have achieved superior performance in computer-aided medical image analysis, yet they are still vulnerable to imperceptible adversarial attacks, resulting in potential misdiagnosis in clinical practice. Oppositely, recent years have also witnessed remarkable progress in defense against these tailored adversarial examples in deep medical diagnosis systems. In this exposition, we present a comprehensive survey on recent advances in adversarial attack and defense for medical image analysis with a novel taxonomy in terms of the application scenario. We also provide a unified theoretical framework for different types of adversarial attack and defense methods for medical image analysis. For a fair comparison, we establish a new benchmark for adversarially robust medical diagnosis models obtained by adversarial training under various scenarios. To the best of our knowledge, this is the first survey paper that provides a thorough evaluation of adversarially robust medical diagnosis models. By analyzing qualitative and quantitative results, we conclude this survey with a detailed discussion of current challenges for adversarial attack and defense in medical image analysis systems to shed light on future research directions.

Electrocardiography analysis is widely used in various clinical applications and Deep Learning models for classification tasks are currently in the focus of research. Due to their data-driven character, they bear the potential to handle signal noise efficiently, but its influence on the accuracy of these methods is still unclear. Therefore, we benchmark the influence of four types of noise on the accuracy of a Deep Learning-based method for atrial fibrillation detection in 12-lead electrocardiograms. We use a subset of a publicly available dataset (PTBXL) and use the metadata provided by human experts regarding noise for assigning a signal quality to each electrocardiogram. Furthermore, we compute a quantitative signal-to-noise ratio for each electrocardiogram. We analyze the accuracy of the Deep Learning model with respect to both metrics and observe that the method can robustly identify atrial fibrillation, even in cases signals are labelled by human experts as being noisy on multiple leads. False positive and false negative rates are slightly worse for data being labelled as noisy. Interestingly, data annotated as showing baseline drift noise results in an accuracy very similar to data without. We conclude that the issue of processing noisy electrocardiography data can be addressed successfully by Deep Learning methods that might not need preprocessing as many conventional methods do.

Botnet attacks are a major threat to networked systems because of their ability to turn the network nodes that they compromise into additional attackers, leading to the spread of high volume attacks over long periods. The detection of such Botnets is complicated by the fact that multiple network IP addresses will be simultaneously compromised, so that Collective Classification of compromised nodes, in addition to the already available traditional methods that focus on individual nodes, can be useful. Thus this work introduces a collective Botnet attack classification technique that operates on traffic from an n-node IP network with a novel Associated Random Neural Network (ARNN) that identifies the nodes which are compromised. The ARNN is a recurrent architecture that incorporates two mutually associated, interconnected and architecturally identical n-neuron random neural networks, that act simultneously as mutual critics to reach the decision regarding which of n nodes have been compromised. A novel gradient learning descent algorithm is presented for the ARNN, and is shown to operate effectively both with conventional off-line training from prior data, and with on-line incremental training without prior off-line learning. Real data from a 107 node packet network is used with over 700,000 packets to evaluate the ARNN, showing that it provides accurate predictions. Comparisons with other well-known state of the art methods using the same learning and testing datasets, show that the ARNN offers significantly better performance.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.