We define a novel family of algorithms for the adversarial multi-armed bandit problem, and provide a simple analysis technique based on convex smoothing. We prove two main results. First, we show that regularization via the \emph{Tsallis entropy}, which includes EXP3 as a special case, achieves the $\Theta(\sqrt{TN})$ minimax regret. Second, we show that a wide class of perturbation methods achieve a near-optimal regret as low as $O(\sqrt{TN \log N})$ if the perturbation distribution has a bounded hazard rate. For example, the Gumbel, Weibull, Frechet, Pareto, and Gamma distributions all satisfy this key property.

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations, and dimensions are all unknown. In practice one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from undersampling due to complexity and speed constraints on the acquisition device or mechanism. More pertinently, even if the high-dimensional data set is available it is often desirable to first project the data points into a lower-dimensional space and to perform clustering there; this reduces storage requirements and computational cost. The purpose of this paper is to quantify the impact of dimensionality reduction through random projection on the performance of three subspace clustering algorithms, all of which are based on principles from sparse signal recovery. Specifically, we analyze the thresholding based subspace clustering (TSC) algorithm, the sparse subspace clustering (SSC) algorithm, and an orthogonal matching pursuit variant thereof (SSC-OMP). We find, for all three algorithms, that dimensionality reduction down to the order of the subspace dimensions is possible without incurring significant performance degradation. Moreover, these results are order-wise optimal in the sense that reducing the dimensionality further leads to a fundamentally ill-posed clustering problem. Our findings carry over to the noisy case as illustrated through analytical results for TSC and simulations for SSC and SSC-OMP. Extensive experiments on synthetic and real data complement our theoretical findings.

The strength of association between a pair of data vectors is represented by a nonnegative real number, called matching weight. For dimensionality reduction, we consider a linear transformation of data vectors, and define a matching error as the weighted sum of squared distances between transformed vectors with respect to the matching weights. Given data vectors and matching weights, the optimal linear transformation minimizing the matching error is solved by the spectral graph embedding of Yan et al. (2007). This method is a generalization of the canonical correlation analysis, and will be called as matching correlation analysis (MCA). In this paper, we consider a novel sampling scheme where the observed matching weights are randomly sampled from underlying true matching weights with small probability, whereas the data vectors are treated as constants. We then investigate a cross-validation by resampling the matching weights. Our asymptotic theory shows that the cross-validation, if rescaled properly, computes an unbiased estimate of the matching error with respect to the true matching weights. Existing ideas of cross-validation for resampling data vectors, instead of resampling matching weights, are not applicable here. MCA can be used for data vectors from multiple domains with different dimensions via an embarrassingly simple idea of coding the data vectors. This method will be called as cross-domain matching correlation analysis (CDMCA), and an interesting connection to the classical associative memory model of neural networks is also discussed.

Introduction Influenza is a leading cause of death in the United States (US), where up to 50,000 are killed each year by influenza- ‐like illnesses (ILI) [1]. Therefore, monitoring, early detection, and prediction of influenza outbreaks are crucial to public health. Disease detection and surveillance systems provide epidemiologic intelligence that allows health officials to deploy preventive measures and help clinic and hospital administrators make optimal staffing and stocking decisions [2]. The US Centers for Disease Control and Prevention (CDC) monitors ILI in the US by gathering information from physicians' reports about patients with ILI seeking medical attention [3]. CDC's ILI data provides useful estimates of influenza activity; however, its availability has a known time lag of one to two weeks. This time lag is far from optimal since public health decisions need to be made based on information that is two weeks old. Systems capable of providing real- ‐time estimates of influenza activity are, thus, critical. Many attempts have been made to design methods capable of providing real- ‐time estimates of ILI activity in the US by leveraging Internet- ‐based data sources that could potentially measure ILI in an indirect manner [4, 5, 6, 7, 8, 9, 10, 11].

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. We show that the quantum linear systems algorithm [Harrow et al., Phys. We show that even in some cases not ideally suited to the quantum linear systems algorithm, a polynomial increase in efficiency still occurs. Gaussian processes (GP) are commonly used as powerful models for regression problems in the field of supervised machine learning, and have been widely applied across a broad spectrum of applications, ranging from robotics, data mining, geophysics (where they are referred to as kriging) and climate modelling all the way to predicting price behaviour of commodities in financial markets. Although GP models are becoming increasingly popular in the community of machine learning, it is known to be computationally expensive, hindering their widespread adoption.

Recent years have witnessed amazing outcomes from "Big Models" trained by "Big Data". Most popular algorithms for model training are iterative. Due to the surging volumes of data, we can usually afford to process only a fraction of the training data in each iteration. Typically, the data are either uniformly sampled or sequentially accessed. In this paper, we study how the data access pattern can affect model training. We propose an Active Sampler algorithm, where training data with more "learning value" to the model are sampled more frequently. The goal is to focus training effort on valuable instances near the classification boundaries, rather than evident cases, noisy data or outliers. We show the correctness and optimality of Active Sampler in theory, and then develop a light-weight vectorized implementation. Active Sampler is orthogonal to most approaches optimizing the efficiency of large-scale data analytics, and can be applied to most analytics models trained by stochastic gradient descent (SGD) algorithm. Extensive experimental evaluations demonstrate that Active Sampler can speed up the training procedure of SVM, feature selection and deep learning, for comparable training quality by 1.6-2.2x.

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry of the resulting vectors followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as "data-driven multiscale windowed power spectra," "data-driven multiscale windowed absolute spectra," "data-driven multiwavelet absolute values," or (in their most general configuration) "data-driven nonlinear multiwavelet packets." Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (for example, logistic or tanh) nonlinearities, max. pooling, etc., do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.

In the context of embodied artificial intelligence, morphological computation refers to processes which are conducted by the body (and environment) that otherwise would have to be performed by the brain. Exploiting environmental and morphological properties is an important feature of embodied systems. The main reason is that it allows to significantly reduce the controller complexity. An important aspect of morphological computation is that it cannot be assigned to an embodied system per se, but that it is, as we show, behavior- and state-dependent. In this work, we evaluate two different measures of morphological computation that can be applied in robotic systems and in computer simulations of biological movement. As an example, these measures were evaluated on muscle and DC-motor driven hopping models. We show that a state-dependent analysis of the hopping behaviors provides additional insights that cannot be gained from the averaged measures alone. This work includes algorithms and computer code for the measures.

Deep neural networks are a powerful tool for feature learning and extraction given their ability to model high-level abstractions in highly complex data. One area worth exploring in feature learning and extraction using deep neural networks is efficient neural connectivity formation for faster feature learning and extraction. Motivated by findings of stochastic synaptic connectivity formation in the brain as well as the brain's uncanny ability to efficiently represent information, we propose the efficient learning and extraction of features via StochasticNets, where sparsely-connected deep neural networks can be formed via stochastic connectivity between neurons. To evaluate the feasibility of such a deep neural network architecture for feature learning and extraction, we train deep convolutional StochasticNets to learn abstract features using the CIFAR-10 dataset, and extract the learned features from images to perform classification on the SVHN and STL-10 datasets. Experimental results show that features learned using deep convolutional StochasticNets, with fewer neural connections than conventional deep convolutional neural networks, can allow for better or comparable classification accuracy than conventional deep neural networks: relative test error decrease of ~4.5% for classification on the STL-10 dataset and ~1% for classification on the SVHN dataset. Furthermore, it was shown that the deep features extracted using deep convolutional StochasticNets can provide comparable classification accuracy even when only 10% of the training data is used for feature learning. Finally, it was also shown that significant gains in feature extraction speed can be achieved in embedded applications using StochasticNets. As such, StochasticNets allow for faster feature learning and extraction performance while facilitate for better or comparable accuracy performances.

Exponential growth in Electronic Healthcare Records (EHR) has resulted in new opportunities and urgent needs for discovery of meaningful data-driven representations and patterns of diseases in Computational Phenotyping research. Deep Learning models have shown superior performance for robust prediction in computational phenotyping tasks, but suffer from the issue of model interpretability which is crucial for clinicians involved in decision-making. In this paper, we introduce a novel knowledge-distillation approach called Interpretable Mimic Learning, to learn interpretable phenotype features for making robust prediction while mimicking the performance of deep learning models. Our framework uses Gradient Boosting Trees to learn interpretable features from deep learning models such as Stacked Denoising Autoencoder and Long Short-Term Memory. Exhaustive experiments on a real-world clinical time-series dataset show that our method obtains similar or better performance than the deep learning models, and it provides interpretable phenotypes for clinical decision making.