Tensor is a natural way to represent the high-dimensional data, thus it preserves more intrinsic information than matrix when dealing with high-order data [1, 2, 3]. In practice, parts of the tensor entries are missing during data acquisition and transformation, tensor completion estimates the missing entries based on the assumption that most elements are correlated [4]. This correlation can be modeled as low-rank data structures which can be used in a series of applications, including signal processing [2], machine learning [5], remote sensing [6], computer vision [7], etc. There are two main frameworks for tensor completion, namely, variational energy minimization as well as tensor rank minimization [8, 9], where the energy is usually a recovery error in the context of tensor completion and the definition of rank varies with diverse tensor decompositions. The first method is realized by means of the alternating least square (ALS), in which each core tensor is updated one by one while others are fixed [8]. The ALSbased method requires a predefined tensor rank, while the rank minimization does not. Common forms of tensor decompositions are summarized as follows.

Adversarial training has been successfully applied to build robust models at a certain cost. While the robustness of a model increases, the standard classification accuracy declines. This phenomenon is suggested to be an inherent trade-off. We propose a model that employs feature prioritization by a nonlinear attention module and $L_2$ feature regularization to improve the adversarial robustness and the standard accuracy relative to adversarial training. The attention module encourages the model to rely heavily on robust features by assigning larger weights to them while suppressing non-robust features. The regularizer encourages the model to extract similar features for the natural and adversarial images, effectively ignoring the added perturbation. In addition to evaluating the robustness of our model, we provide justification for the attention module and propose a novel experimental strategy that quantitatively demonstrates that our model is almost ideally aligned with salient data characteristics. Additional experimental results illustrate the power of our model relative to the state of the art methods.

Data augmentation, a technique in which a training set is expanded with class-preserving transformations, is ubiquitous in modern machine learning pipelines. In this paper, we seek to establish a theoretical framework for understanding data augmentation. We approach this from two directions: First, we provide a general model of augmentation as a Markov process, and show that kernels appear naturally with respect to this model, even when we do not employ kernel classification. Next, we analyze more directly the effect of augmentation on kernel classifiers, showing that data augmentation can be approximated by first-order feature averaging and second-order variance regularization components. These frameworks both serve to illustrate the ways in which data augmentation affects the downstream learning model, and the resulting analyses provide novel connections between prior work in invariant kernels, tangent propagation, and robust optimization. Finally, we provide several proof-of-concept applications showing that our theory can be useful for accelerating machine learning workflows, such as reducing the amount of computation needed to train using augmented data, and predicting the utility of a transformation prior to training.

Training documents have a significant impact on the performance of predictive models in the legal domain. Yet, there is limited research that explores the effectiveness of the training document selection strategy - in particular, the strategy used to select the seed set, or the set of documents an attorney reviews first to establish an initial model. Since there is limited research on this important component of predictive coding, the authors of this paper set out to identify strategies that consistently perform well. Our research demonstrated that the seed set selection strategy can have a significant impact on the precision of a predictive model. Enabling attorneys with the results of this study will allow them to initiate the most effective predictive modeling process to comb through the terabytes of data typically present in modern litigation. This study used documents from four actual legal cases to evaluate eight different seed set selection strategies. Attorneys can use the results contained within this paper to enhance their approach to predictive coding.

Electroencephalograms (EEG) are often contaminated by artifacts which make interpreting them more challenging for clinicians. Hence, automated artifact recognition systems have the potential to aid the clinical workflow. In this abstract, we share the first results on applying various machine learning algorithms to the recently released world's largest open-source artifact recognition dataset. We envision that these results will serve as a benchmark for researchers who might work with this dataset in future. Introduction Removal of artifacts from electroencephalogram (EEG) is a necessary step in analyzing EEG signals since artifacts can lead to severe misinterpretation of these signals. However, manual removal of artifacts requires trained clinicians or neurophysiologists and is a procedure that is known to be both time and resource hungry.

Systems that can automatically analyze EEG signals can aid neurologists by reducing heavy workload and delays. However, such systems need to be first trained using a labeled dataset. While large corpuses of EEG data exist, a fraction of them are labeled. Hand-labeling data increases workload for the very neurologists we try to aid. This paper proposes a semi-supervised learning algorithm that can not only extract meaningful information from large unlabeled EEG datasets but also perform task-specific learning on labeled datasets as small as 5 examples. Introduction Brain-related disorders such as epilepsy can be diagnosed by analyzing electroencephalograms (EEGs).

Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of features required to achieve optimal learning bounds. Leverage scores introduce an optimized distribution for features based on an infinite-dimensional integral operator (depending on input distribution), which is impractical to sample from. Focusing on empirical leverage scores in this paper, we establish an out-of-sample performance bound, revealing an interesting trade-off between the approximated kernel and the eigenvalue decay of another kernel in the domain of random features defined based on data distribution. Our experiments verify that the empirical algorithm consistently outperforms vanilla Monte Carlo sampling, and with a minor modification the method is even competitive to supervised data-dependent kernel learning, without using the output (label) information.

The past few years have seen several works establishing PAC frameworks for solving various problems in economic domains; these include optimal auction design, approximate optima of submodular functions, stable partitions and payoff divisions in cooperative games and more. In this work, we provide a unified learning-theoretic methodology for modeling these problems, and establish some useful tools for determining whether a given economic solution concept can be learned from data. Our learning theoretic framework generalizes a notion of function space dimension --- the graph dimension --- adapting it to the solution concept learning domain. We identify sufficient conditions for the PAC learnability of solution concepts, and show that results in existing works can be immediately derived using our general methodology. Finally, we apply our methods in other economic domains, yielding a novel notion of PAC competitive equilibrium and PAC Condorcet winners.

Despite a large amount of attention on adversarial examples, very few works have demonstrated an effective defense against this threat. We examine Deep k-Nearest Neighbor (DkNN), a proposed defense that combines k-Nearest Neighbor (kNN) and deep learning to improve the model's robustness to adversarial examples. It is challenging to evaluate the robustness of this scheme due to a lack of efficient algorithm for attacking kNN classifiers with large k and high-dimensional data. We propose a heuristic attack that allows us to use gradient descent to find adversarial examples for kNN classifiers, and then apply it to attack the DkNN defense as well. Results suggest that our attack is moderately stronger than any naive attack on kNN and significantly outperforms other attacks on DkNN.

Farhad Bulbul is with the Department of Mathematics, Jessore University of Science and Technology, Bangladesh (email: farhad@just.edu.bd). Saiful Islam is with the Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science & Technology University, Bangladesh. Dr. Hazrat Ali is with the Department of Electrical and Computer Engineering, COMSATS University Islamabad, Abbottabad Campus, Pakistan (email: hazratali@cuiatd.edu.pk). Abstract-- In this paper, we present an approach for identification of actions within depth action videos. First, we process the video to get motion history images (MHIs) and static history images (SHIs) corresponding to an action video based on the use of 3D Motion Trail Model (3DMTM). We then characterize the action video by extracting the Gradient Local Auto-Correlations (GLAC) features from the SHIs and the MHIs. The two sets of features i.e., GLAC features from MHIs and GLAC features from SHIs are concatenated to obtain a representation vector for action. Finally, we perform the classification on all the action samples by using the l2-regularized Collaborative Representation Classifier (l2-CRC) to recognize different human actions in an effective way. We perform evaluation of the proposed method on three action datasets, MSR-Action3D, DHA and UTD-MHAD. Through experimental results, we observe that the proposed method performs superior to other approaches. I. INTRODUCTION Research in human action recognition (HAR) is considered as one of the most interesting domains of computer vision. The action recognition system is being extensively applied in human security system, medical science, social awareness, and entertainment [1], [2], [3], [4].. Indeed, to develop an applicable action recognition system, researchers still need to win against the odds due to diversity in human body sizes, appearances, postures, motions, clothing, camera motions, viewing angles, and illumination. In the early stage, the human action recognition system was developed by researchers based on RGB data [5], [6], [7], [8].