We study a setting in which a learner faces a sequence of A/B tests and has to make as many good decisions as possible within a given amount of time. Each A/B test $n$ is associated with an unknown (and potentially negative) reward $\mu_n \in [-1,1]$, drawn i.i.d. from an unknown and fixed distribution. For each A/B test $n$, the learner sequentially draws i.i.d. samples of a $\{-1,1\}$-valued random variable with mean $\mu_n$ until a halting criterion is met. The learner then decides to either accept the reward $\mu_n$ or to reject it and get zero instead. We measure the learner's performance as the sum of the expected rewards of the accepted $\mu_n$ divided by the total expected number of used time steps (which is different from the expected ratio between the total reward and the total number of used time steps). We design an algorithm and prove a data-dependent regret bound against any set of policies based on an arbitrary halting criterion and decision rule. Though our algorithm borrows ideas from multiarmed bandits, the two settings are significantly different and not directly comparable. In fact, the value of $\mu_n$ is never observed directly in our setting---unlike rewards in stochastic bandits. Moreover, the particular structure of our problem allows our regret bounds to be independent of the number of policies.

Graph embedding techniques allow to learn high-quality feature vectors from graph structures and are useful in a variety of tasks, from node classification to clustering. Existing approaches have only focused on learning feature vectors for the nodes in a (knowledge) graph. To the best of our knowledge, none of them has tackled the problem of embedding of graph edges, that is, knowledge graph triples. The approaches that are closer to this task have focused on homogeneous graphs involving only one type of edge and obtain edge embeddings by applying some operation (e.g., average) on the embeddings of the endpoint nodes. The goal of this paper is to introduce Triple2Vec, a new technique to directly embed edges in (knowledge) graphs. Trple2Vec builds upon three main ingredients. The first is the notion of line graph. The line graph of a graph is another graph representing the adjacency between edges of the original graph. In particular, the nodes of the line graph are the edges of the original graph. We show that directly applying existing embedding techniques on the nodes of the line graph to learn edge embeddings is not enough in the context of knowledge graphs. Thus, we introduce the notion of triple line graph. The second is an edge weighting mechanism both for line graphs derived from knowledge graphs and homogeneous graphs. The third is a strategy based on graph walks on the weighted triple line graph that can preserve proximity between nodes. Embeddings are finally generated by adopting the SkipGram model, where sentences are replaced with graph walks. We evaluate our approach on different real world (knowledge) graphs and compared it with related work.

Oja's algorithm has been the cornerstone of streaming methods in Principal Component Analysis (PCA) since it was first proposed in 1982. However, Oja's algorithm does not have a standardized choice of learning rate (step size) that both performs well in practice and truly conforms to the online streaming setting. In this paper, we propose a new learning rate scheme for Oja's method called AdaOja. This new algorithm requires only a single pass over the data and does not depend on knowing properties of the data set a priori. AdaOja is a novel variation of the Adagrad algorithm to Oja's algorithm in the single eigenvector case and extended to the multiple eigenvector case. We demonstrate for dense synthetic data, sparse real-world data and dense real-world data that AdaOja outperforms common learning rate choices for Oja's method. We also show that AdaOja performs comparably to state-of-the-art algorithms (History PCA and Streaming Power Method) in the same streaming PCA setting.

This paper studies how to sketch element-wise functions of low-rank matrices. Formally, given low-rank matrix A = [Aij ] and scalar non-linear function f, we aim for finding an approximated low-rank representation of (high-rank) matrix [f(A_{ij})]. To this end, we propose an efficient sketch algorithm whose complexity is significantly lower than the number of entries of A, i.e., it runs without accessing all entries of [f(A_{ij})] explicitly. Our main idea is to combine a polynomial approximation on f with the existing tensor sketch scheme approximating monomials of entries of A. To balance errors of the two approximation components in an optimal manner, we address a novel regression formula to find polynomial coefficients given A and f. We demonstrate the applicability and superiority of the proposed scheme under the tasks of kernel SVM classification and optimal transport.

Multi-objective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multi-objective optimization problems. In fact, many real-world multi-objective problems contain a number of constraints. To promote research on constrained multi-objective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multi-objective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness and diversity-hardness. We then develop a general toolkit to construct difficulty-adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. Based on this toolkit, we suggest nine difficulty-adjustable and scalable CMOPs and nine CMaOPs. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility- and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.

We introduce deep scale-spaces (DSS), a generalization of convolutional neural networks, exploiting the scale symmetry structure of conventional image recognition tasks. Put plainly, the class of an image is invariant to the scale at which it is viewed. We construct scale equivariant cross-correlations based on a principled extension of convolutions, grounded in the theory of scale-spaces and semigroups. As a very basic operation, these cross-correlations can be used in almost any modern deep learning architecture in a plug-and-play manner. We demonstrate our networks on the Patch Camelyon and Cityscapes datasets, to prove their utility and perform introspective studies to further understand their properties.

This work investigates how context should be taken into account when performing continuous authentication of a smartphone user based on touchscreen and accelerometer readings extracted from swipe gestures. The study is conducted on the publicly available HMOG dataset consisting of 100 study subjects performing pre-defined reading and navigation tasks while sitting and walking. It is shown that context-specific models are needed for different smartphone usage and human activity scenarios to minimize authentication error. Also, the experimental results suggests that utilization of phone movement improves swipe gesture-based verification performance only when the user is moving.

Machine learning theory has mostly focused on generalization to samples from the same distribution as the training data. Whereas a better understanding of generalization beyond the training distribution where the observed distribution changes is also fundamentally important to achieve a more powerful form of generalization. In this paper, we attempt to study through the lens of information measures how a particular architecture behaves when the true probability law of the samples is potentially different at training and testing times. Our main result is that the testing gap between the empirical cross-entropy and its statistical expectation (measured with respect to the testing probability law) can be bounded with high probability by the mutual information between the input testing samples and the corresponding representations, generated by the encoder obtained at training time. These results of theoretical nature are supported by numerical simulations showing that the mentioned mutual information is representative of the testing gap, capturing qualitatively the dynamic in terms of the hyperparameters of the network.

Convolution is a central operation in Convolutional Neural Networks (CNNs), which applies a kernel or mask to overlapping regions shifted across the image. In this work we show that the underlying kernels are trained with highly correlated data, which leads to co-adaptation of model weights. To address this issue we propose what we call network deconvolution, a procedure that aims to remove pixel-wise and channel-wise correlations before the data is fed into each layer. We show that by removing this correlation we are able to achieve better convergence rates during model training with superior results without the use of batch normalization on the CIFAR-10, CIFAR-100, MNIST, Fashion-MNIST datasets, as well as against reference models from "model zoo" on the ImageNet standard benchmark.

The level sets of neural networks represent fundamental properties such as decision boundaries of classifiers and are used to model non-linear manifold data such as curves and surfaces. Thus, methods for controlling the neural level sets could find many applications in machine learning. In this paper we present a simple and scalable approach to directly control level sets of a deep neural network. Our method consists of two parts: (i) sampling of the neural level sets, and (ii) relating the samples' positions to the network parameters. The latter is achieved by a \emph{sample network} that is constructed by adding a single fixed linear layer to the original network. In turn, the sample network can be used to incorporate the level set samples into a loss function of interest. We have tested our method on three different learning tasks: training networks robust to adversarial attacks, improving generalization to unseen data, and curve and surface reconstruction from point clouds. Notably, we increase robust accuracy to the level of standard classification accuracy in off-the-shelf networks, improving it by 2\% in MNIST and 27\% in CIFAR10 compared to state-of-the-art methods. For surface reconstruction, we produce high fidelity surfaces directly from raw 3D point clouds.