One of the beauties of the projected gradient descent method lies in its rather simple mechanism and yet stable behavior with inexact, stochastic gradients, which has led to its wide-spread use in many machine learning applications. However, once we replace the projection operator with a simpler linear program, as is done in the Frank-Wolfe method, both simplicity and stability take a serious hit. The aim of this paper is to bring them back without sacrificing the efficiency. In this paper, we propose the first one-sample stochastic Frank-Wolfe algorithm, called 1-SFW, that avoids the need to carefully tune the batch size, step size, learning rate, and other complicated hyper parameters. In particular, 1-SFW achieves the optimal convergence rate of $\mathcal{O}(1/\epsilon^2)$ for reaching an $\epsilon$-suboptimal solution in the stochastic convex setting, and a $(1-1/e)-\epsilon$ approximate solution for a stochastic monotone DR-submodular maximization problem. Moreover, in a general non-convex setting, 1-SFW finds an $\epsilon$-first-order stationary point after at most $\mathcal{O}(1/\epsilon^3)$ iterations, achieving the current best known convergence rate. All of this is possible by designing a novel unbiased momentum estimator that governs the stability of the optimization process while using a single sample at each iteration.

Generative adversarial networks (GANs) are a powerful approach to unsupervised learning. They have achieved state-of-the-art performance in the image domain. However, GANs are limited in two ways. They often learn distributions with low support---a phenomenon known as mode collapse---and they do not guarantee the existence of a probability density, which makes evaluating generalization using predictive log-likelihood impossible. In this paper, we develop the prescribed GAN (PresGAN) to address these shortcomings. PresGANs add noise to the output of a density network and optimize an entropy-regularized adversarial loss. The added noise renders tractable approximations of the predictive log-likelihood and stabilizes the training procedure. The entropy regularizer encourages PresGANs to capture all the modes of the data distribution. Fitting PresGANs involves computing the intractable gradients of the entropy regularization term; PresGANs sidestep this intractability using unbiased stochastic estimates. We evaluate PresGANs on several datasets and found they mitigate mode collapse and generate samples with high perceptual quality. We further found that PresGANs reduce the gap in performance in terms of predictive log-likelihood between traditional GANs and variational autoencoders (VAEs).

Adversarial training, in which a network is trained on both adversarial and clean examples, is one of the most trusted defense methods against adversarial attacks. However, there are three major practical difficulties in implementing and deploying this method - expensive in terms of extra memory and computation costs; accuracy trade-off between clean and adversarial examples; and lack of diversity of adversarial perturbations. Classical adversarial training uses fixed, precomputed perturbations in adversarial examples (input space). In contrast, we introduce dynamic adversarial perturbations into the parameter space of the network, by adding perturbation biases to the fully connected layers of deep convolutional neural network. During training, using only clean images, the perturbation biases are updated in the Fast Gradient Sign Direction to automatically create and store adversarial perturbations by recycling the gradient information computed. The network learns and adjusts itself automatically to these learned adversarial perturbations. Thus, we can achieve adversarial training with negligible cost compared to requiring a training set of adversarial example images. In addition, if combined with classical adversarial training, our perturbation biases can alleviate accuracy trade-off difficulties, and diversify adversarial perturbations.

This paper is concerned with estimating the column space of an unknown low-rank matrix $\boldsymbol{A}^{\star}\in\mathbb{R}^{d_{1}\times d_{2}}$, given noisy and partial observations of its entries. There is no shortage of scenarios where the observations --- while being too noisy to support faithful recovery of the entire matrix --- still convey sufficient information to enable reliable estimation of the column space of interest. This is particularly evident and crucial for the highly unbalanced case where the column dimension $d_{2}$ far exceeds the row dimension $d_{1}$, which is the focal point of the current paper. We investigate an efficient spectral method, which operates upon the sample Gram matrix with diagonal deletion. We establish statistical guarantees for this method in terms of both $\ell_{2}$ and $\ell_{2,\infty}$ estimation accuracy, which improve upon prior results if $d_{2}$ is substantially larger than $d_{1}$. To illustrate the effectiveness of our findings, we develop consequences of our general theory for three applications of practical importance: (1) tensor completion from noisy data, (2) covariance estimation with missing data, and (3) community recovery in bipartite graphs. Our theory leads to improved performance guarantees for all three cases.

With the increasing adoption of AI, inherent security and privacy vulnerabilities formachine learning systems are being discovered. One such vulnerability makes itpossible for an adversary to obtain private information about the types of instancesused to train the targeted machine learning model. This so-called model inversionattack is based on sequential leveraging of classification scores towards obtaininghigh confidence representations for various classes. However, for deep networks,such procedures usually lead to unrecognizable representations that are uselessfor the adversary. In this paper, we introduce a more realistic definition of modelinversion, where the adversary is aware of the general purpose of the attackedmodel (for instance, whether it is an OCR system or a facial recognition system),and the goal is to find realistic class representations within the corresponding lower-dimensional manifold (of, respectively, general symbols or general faces). To thatend, we leverage properties of generative adversarial networks for constructinga connected lower-dimensional manifold, and demonstrate the efficiency of ourmodel inversion attack that is carried out within that manifold.

Instead, we propose to integrate a generative inpainter into three representative attribution methods to remove an input feature. Compared to the original counterparts, our methods (1) generate more plausible counterfactual samples under the true data generating process; (2) are more robust to hyperparameter settings; and (3) localize objects more accurately. Our findings were consistent across both ImageNet and Places365 datasets and two different pairs of classifiers and inpainters. Explaining a classifier's outputs given a certain input is increasingly important, especially for life-critical applications (Doshi-V elez & Kim, 2017). A popular means for visually explaining an image classifier's decisions is an attribution map i.e. a heatmap that highlights the input pixels that are the evidence for and against the classification outputs (Montavon et al., 2018). To construct an attribution map, many methods approximate the attribution value of an input region by the classification probability change when that region is absent i.e. removed from the image. That is, most perturbation-based attribution methods implement the absence of an input feature by replacing it with (a) mean pixels; (b) random noise; or (c) blurred versions of the original content. While removing an input feature to measure its attribution is a principle method in causal reasoning, the existing removal (i.e. To combat these two issues, we propose to harness a state-of-the-art generative inpainting model (hereafter, an inpainter) to remove features from an input image and fill in with content that is plausible under the true data distribution. We test our approach on three representative attribution methods of Sliding-Patch (SP) (Zeiler & Fergus, 2014), LIME (Ribeiro et al., 2016), and Meaningful-Perturbation (MP) (Fong & V edaldi, 2017) across two large-scale datasets of ImageNet (Russakovsky et al., 2015) and Places365 (Zhou et al., 2017). For each dataset, we use a separate pair of pre-trained image classifiers and inpainters. Work done during CA's internship at Auburn University.

Diagnostic stroke imaging with C-arm cone-beam computed tomography (CBCT) enables reduction of time-to-therapy for endovascular procedures. However, the prolonged acquisition time compared to helical CT increases the likelihood of rigid patient motion. Rigid motion corrupts the geometry alignment assumed during reconstruction, resulting in image blurring or streaking artifacts. To reestablish the geometry, we estimate the motion trajectory by an autofocus method guided by a neural network, which was trained to regress the reprojection error, based on the image information of a reconstructed slice. The network was trained with CBCT scans from 19 patients and evaluated using an additional test patient. It adapts well to unseen motion amplitudes and achieves superior results in a motion estimation benchmark compared to the commonly used entropy-based method.

By design, discriminatively trained neural network classifiers produce reliable predictions only for in-distribution samples. For their real-world deployments, detecting out-of-distribution (OOD) samples is essential. Assuming OOD to be outside the closed boundary of in-distribution, typical neural classifiers do not contain the knowledge of this boundary for OOD detection during inference. There have been recent approaches to instill this knowledge in classifiers by explicitly training the classifier with OOD samples close to the in-distribution boundary. However, these generated samples fail to cover the entire in-distribution boundary effectively, thereby resulting in a sub-optimal OOD detector. In this paper, we analyze the feasibility of such approaches by investigating the complexity of producing such "effective" OOD samples. We also propose a novel algorithm to generate such samples using a manifold learning network (e.g., variational autoencoder) and then train an n+1 classifier for OOD detection, where the $n+1^{th}$ class represents the OOD samples. We compare our approach against several recent classifier-based OOD detectors on MNIST and Fashion-MNIST datasets. Overall the proposed approach consistently performs better than the others.

--Recently, reducing the communication time between machines becomes the main focus of the distributed data mining. Previous methods propose to make workers do more computation locally before aggregating local solutions in the server such that fewer communication rounds between server and workers are required. However, these methods do not consider reducing the communication time per round and work very poor under certain conditions, for example, when there are straggler problems or the dataset is of high dimension. In this paper, we target to reduce communication time per round as well as the required communication rounds. We propose a communication-efficient distributed primal-dual method with straggler-agnostic server and bandwidth-efficient workers. We analyze the convergence property and prove that the proposed method guarantees linear convergence rate to the optimal solution for convex problems. Finally, we conduct large-scale experiments in simulated and real distributed systems and experimental results demonstrate that the proposed method is much faster than compared methods. Distributed optimization methods are nontrivial when we optimize a data mining problem when the data or model is distributed across multiple machines. When data are distributed, parameter server [6], [14] or decentralized methods [15], [16] were proposed for parallel computation and linear speedup.

We investigate time-dependent data analysis from the perspective of recurrent kernel machines, from which models with hidden units and gated memory cells arise naturally. By considering dynamic gating of the memory cell, a model closely related to the long short-term memory (LSTM) recurrent neural network is derived. Extending this setup to $n$-gram filters, the convolutional neural network (CNN), Gated CNN, and recurrent additive network (RAN) are also recovered as special cases. Our analysis provides a new perspective on the LSTM, while also extending it to $n$-gram convolutional filters. Experiments are performed on natural language processing tasks and on analysis of local field potentials (neuroscience). We demonstrate that the variants we derive from kernels perform on par or even better than traditional neural methods. For the neuroscience application, the new models demonstrate significant improvements relative to the prior state of the art.