Given partially observed pairwise comparison data generated by the Bradley-Terry-Luce (BTL) model, we study the problem of top-$k$ ranking. That is, to optimally identify the set of top-$k$ players. We derive the minimax rate with respect to a normalized Hamming loss. This provides the first result in the literature that characterizes the partial recovery error in terms of the proportion of mistakes for top-$k$ ranking. We also derive the optimal signal to noise ratio condition for the exact recovery of the top-$k$ set. The maximum likelihood estimator (MLE) is shown to achieve both optimal partial recovery and optimal exact recovery. On the other hand, we show another popular algorithm, the spectral method, is in general sub-optimal. Our results complement the recent work by Chen et al. (2019) that shows both the MLE and the spectral method achieve the optimal sample complexity for exact recovery. It turns out the leading constants of the sample complexity are different for the two algorithms. Another contribution that may be of independent interest is the analysis of the MLE without any penalty or regularization for the BTL model. This closes an important gap between theory and practice in the literature of ranking.

Network embedding is a very important method for network data. However, most of the algorithms can only deal with static networks. In this paper, we propose an algorithm Recurrent Neural Network Embedding (RNNE) to deal with dynamic network, which can be typically divided into two categories: a) topologically evolving graphs whose nodes and edges will increase (decrease) over time; b) temporal graphs whose edges contain time information. In order to handle the changing size of dynamic networks, RNNE adds virtual node, which is not connected to any other nodes, to the networks and replaces it when new node arrives, so that the network size can be unified at different time. On the one hand, RNNE pays attention to the direct links between nodes and the similarity between the neighborhood structures of two nodes, trying to preserve the local and global network structure. On the other hand, RNNE reduces the influence of noise by transferring the previous embedding information. Therefore, RNNE can take into account both static and dynamic characteristics of the network.We evaluate RNNE on five networks and compare with several state-of-the-art algorithms. The results demonstrate that RNNE has advantages over other algorithms in reconstruction, classification and link predictions.

It is abundantly clear that time dependent data is a vital source of information in the world. The challenge has been for applications in machine learning to gain access to a considerable amount of quality data needed for algorithm development and analysis. Modeling synthetic data using a Generative Adversarial Network (GAN) has been at the heart of providing a viable solution. Our work focuses on one dimensional times series and explores the few shot approach, which is the ability of an algorithm to perform well with limited data. This work attempts to ease the frustration by proposing a new architecture, Time Series GAN (TSGAN), to model realistic time series data. We evaluate TSGAN on 70 data sets from a benchmark time series database. Our results demonstrate that TSGAN performs better than the competition both quantitatively using the Frechet Inception Score (FID) metric, and qualitatively when classification is used as the evaluation criteria.

We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals how the tensor dimensions (features) interact with each other. However, since the factors are a priori unknown, the corresponding optimization problems are inherently non-convex. The existing guaranteed algorithms which handle this non-convexity incur an irreducible error (bias), and only apply to cases where all factors have the same structure. To this end, we develop a provable algorithm for online structured tensor factorization, wherein one of the factors obeys some incoherence conditions, and the others are sparse. Specifically we show that, under some relatively mild conditions on initialization, rank, and sparsity, our algorithm recovers the factors exactly (up to scaling and permutation) at a linear rate. Complementary to our theoretical results, our synthetic and real-world data evaluations showcase superior performance compared to related techniques. Moreover, its scalability and ability to learn on-the-fly makes it suitable for real-world tasks.

Ordered Weighted $L_{1}$ (OWL) regularized regression is a new regression analysis for high-dimensional sparse learning. Proximal gradient methods are used as standard approaches to solve OWL regression. However, it is still a burning issue to solve OWL regression due to considerable computational cost and memory usage when the feature or sample size is large. In this paper, we propose the first safe screening rule for OWL regression by exploring the order of the primal solution with the unknown order structure via an iterative strategy, which overcomes the difficulties of tackling the non-separable regularizer. It effectively avoids the updates of the parameters whose coefficients must be zero during the learning process. More importantly, the proposed screening rule can be easily applied to standard and stochastic proximal gradient methods. Moreover, we prove that the algorithms with our screening rule are guaranteed to have identical results with the original algorithms. Experimental results on a variety of datasets show that our screening rule leads to a significant computational gain without any loss of accuracy, compared to existing competitive algorithms.

In this work, we have proposed a generative model for density estimation, called VAE-KRnet, which combines the canonical variational autoencoder (VAE) with our recently developed flow-based generative model, called KRnet. VAE is used as a dimension reduction technique to capture the latent space, and KRnet is used to model the distribution of the latent variables. Using a linear model between the data and the latent variables, we show that VAE-KRnet can be more effective and robust than the canonical VAE. As an application, we apply VAE-KRnet to variational Bayes to approximate the posterior. The variational Bayes approaches are usually based on the minimization of the Kullback-Leibler (KL) divergence between the model and the posterior, which often underestimates the variance if the model capability is not sufficiently strong. However, for high-dimensional distributions, it is very challenging to construct an accurate model since extra assumptions are often needed for efficiency, e.g., the mean-field approach assumes mutual independence between dimensions. When the number of dimensions is relatively small, KRnet can be used to approximate the posterior effectively with respect to the original random variable. For high-dimensional cases, we consider VAE-KRnet to incorporate with the dimension reduction. To alleviate the underestimation of the variance, we include the maximization of the mutual information between the latent random variable and the original one when seeking an approximate distribution with respect to the KL divergence. Numerical experiments have been presented to demonstrate the effectiveness of our model.

A convolutional neural network strongly robust to adversarial perturbations at reasonable computational and performance cost has not yet been demonstrated. The primate visual ventral stream seems to be robust to small perturbations in visual stimuli but the underlying mechanisms that give rise to this robust perception are not understood. In this work, we investigate the role of two biologically plausible mechanisms in adversarial robustness. We demonstrate that the non-uniform sampling performed by the primate retina and the presence of multiple receptive fields with a range of receptive field sizes at each eccentricity improve the robustness of neural networks to small adversarial perturbations. We verify that these two mechanisms do not suffer from gradient obfuscation and study their contribution to adversarial robustness through ablation studies.

A probabilistic model is said to be calibrated if its predicted probabilities match the corresponding empirical frequencies. Calibration is important for uncertainty quantification and decision making in safety-critical applications. While calibration of classifiers has been widely studied, we find that calibration is brittle and can be easily lost under minimal covariate shifts. Existing techniques, including domain adaptation ones, primarily focus on prediction accuracy and do not guarantee calibration neither in theory nor in practice. In this work, we formally introduce the problem of calibration under domain shift, and propose an importance Figure 1: Reliability diagram for a LeNet-5 model sampling based approach to address trained using CDAN (SOTA domain adaptation technique) it. We evaluate and discuss the efficacy of our on MNIST and tested on USPS as target data.

Adversarial robustness has become a fundamental requirement in modern machine learning applications. Yet, there has been surprisingly little statistical understanding so far. In this paper, we provide the first result of the optimal minimax guarantees for the excess risk for adversarially robust classification, under Gaussian mixture model proposed by \cite{schmidt2018adversarially}. The results are stated in terms of the Adversarial Signal-to-Noise Ratio (AdvSNR), which generalizes a similar notion for standard linear classification to the adversarial setting. For the Gaussian mixtures with AdvSNR value of $r$, we establish an excess risk lower bound of order $\Theta(e^{-(\frac{1}{8}+o(1)) r^2} \frac{d}{n})$ and design a computationally efficient estimator that achieves this optimal rate. Our results built upon minimal set of assumptions while cover a wide spectrum of adversarial perturbations including $\ell_p$ balls for any $p \ge 1$.

Robustness issues arise in a variety of forms and are studied through multiple lenses in the machine learning literature. Neural networks lack adversarial robustness -- they are vulnerable to adversarial examples that through small perturbations to inputs cause incorrect predictions. Further, trust is undermined when models give miscalibrated or unstable uncertainty estimates, i.e. the predicted probability is not a good indicator of how much we should trust our model and could vary greatly over multiple independent runs. In this paper, we study the connection between adversarial robustness, predictive uncertainty (calibration) and model uncertainty (stability) on multiple classification networks and datasets. We find that the inputs for which the model is sensitive to small perturbations (are easily attacked) are more likely to have poorly calibrated and unstable predictions. Based on this insight, we examine if calibration and stability can be improved by addressing those adversarially unrobust inputs. To this end, we propose Adversarial Robustness based Adaptive Label Smoothing (AR-AdaLS) that integrates the correlations of adversarial robustness and uncertainty into training by adaptively softening labels conditioned on how easily it can be attacked by adversarial examples. We find that our method, taking the adversarial robustness of the in-distribution data into consideration, leads to better calibration and stability over the model even under distributional shifts. In addition, AR-AdaLS can also be applied to an ensemble model to achieve the best calibration performance.