We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the Johnson-Lindenstrauss transform and the angular kernel, we show that we can select matrices yielding guaranteed improved performance in accuracy and/or speed compared to earlier methods. We introduce matrices with complex entries which give significant further accuracy improvement. We provide geometric and Markov chain-based perspectives to help understand the benefits, and empirical results which suggest that the approach is helpful in a wider range of applications.

Transfer learning leverages the knowledge in one domain, the source domain, to improve learning efficiency in another domain, the target domain. Existing transfer learning research is relatively well-progressed, but only in situations where the feature spaces of the domains are homogeneous and the target domain contains at least a few labeled instances. However, transfer learning has not been well-studied in heterogeneous settings with an unlabeled target domain. To contribute to the research in this emerging field, this paper presents: (1) an unsupervised knowledge transfer theorem that prevents negative transfer; and (2) a principal angle-based metric to measure the distance between two pairs of domains. The metric shows the extent to which homogeneous representations have preserved the information in original source and target domains. The unsupervised knowledge transfer theorem sets out the transfer conditions necessary to prevent negative transfer. Linear monotonic maps meet the transfer conditions of the theorem and, hence, are used to construct homogeneous representations of the heterogeneous domains, which in principle prevents negative transfer. The metric and the theorem have been implemented in an innovative transfer model, called a Grassmann-LMM-geodesic flow kernel (GLG), that is specifically designed for knowledge transfer across heterogeneous domains. The GLG model learns homogeneous representations of heterogeneous domains by minimizing the proposed metric. Knowledge is transferred through these learned representations via a geodesic flow kernel. Notably, the theorem presented in this paper provides the sufficient transfer conditions needed to guarantee that knowledge is transferred from a source domain to an unlabeled target domain with correctness.

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.

Keywords: EEG, electroencephalogram, seizure detection, machine learning The electroencephalogram (EEG), which has been in clinical use for over 70 years, is still an essential tool for diagnosis of neural functioning (Kennett, 2012). Well-known applications of EEGs include identification of epilepsy and epileptic seizures, anoxic and hypoxic damage to the brain, and identification of neural disorders such as hemorrhagic stroke, ischemia and toxic metabolic encephalopathy (Drury, 1988). More recently there has been interest in diagnosing Alzheimer's (Tsolaki et al., 2014), head trauma (Rapp et al., 2015) and sleep disorders (Younes, 2017). Many of these clinical applications now involve the collection of large amounts of data (e.g., 72-hour continuous EEG recordings), which makes manual interpretation challenging. Similarly, the increased use of EEGs in critical care has created a significant demand for high-performance automatic interpretation software (e.g., real-time seizure detection).

Most of the data science use cases are relatively well established by now: a goal is defined, a target class is selected, a model is trained to recognize/predict the target, and the same model is applied to new never-seen-before productive data. An anomaly is an event that is not part of the system's past; an event that cannot be found in the system's historical data. In the case of network data, an anomaly can be an intrusion, in medicine a sudden pathological status, in sales or credit card businesses a fraudulent payment, and, finally, in machinery a mechanical piece breakdown. In the manufacturing industry, the goal is to keep a mechanical pieceworking as long as possible–mechanical pieces are expensive – and at the same time to predict its breaking point before it actually occurs–a machine breakoften triggers a chain reaction of expensive damages. Therefore, a high value is usually associated with the early discovery, warning, prediction, and/or prevention of anomalies.Specifically, the prediction of "unknown" disruptive events in the field of mechanical maintenance takes the name of "anomaly detection".

We study conditional risk minimization (CRM), i.e. the problem of learning a hypothesis of minimal risk for prediction at the next step of a sequentially arriving dependent data. Despite it being a fundamental problem, successful learning in the CRM sense has so far only been demonstrated using theoretical algorithms that cannot be used for real problems as they would require storing all incoming data. In this work, we introduce MACRO, a meta-algorithm for CRM that does not suffer from this shortcoming, as instead of storing all data it maintains and iteratively updates a set of learning subroutines. Using suitable approximations, MACRO can be implemented and applied to real data, leading, as we illustrate experimentally, to improved prediction performance compared to traditional non-conditional learning.

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been observed that when using large batch sizes there is a persistent degradation in generalization performance - known as the "generalization gap" phenomena. Identifying the origin of this gap and closing it had remained an open problem. Contributions: We examine the initial high learning rate training phase. We find that the weight distance from its initialization grows logarithmically with the number of weight updates. We therefore propose a "random walk on random landscape" statistical model which is known to exhibit similar "ultra-slow" diffusion behavior. Following this hypothesis we conducted experiments to show empirically that the "generalization gap" stems from the relatively small number of updates rather than the batch size, and can be completely eliminated by adapting the training regime used. We further investigate different techniques to train models in the large-batch regime and present a novel algorithm named "Ghost Batch Normalization" which enables significant decrease in the generalization gap without increasing the number of updates. To validate our findings we conduct several additional experiments on MNIST, CIFAR-10, CIFAR-100 and ImageNet. Finally, we reassess common practices and beliefs concerning training of deep models and suggest they may not be optimal to achieve good generalization.

We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smaller than that of the full log-likelihood in standard MCMC. The likelihood estimate is bias-corrected and used in two dependent pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to $n$ and $m$, respectively. We propose a practical estimator of the error and show that the error is negligible even for a very small $m$ in our applications. We demonstrate that Subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature.

Wind energy is a clean resource, and one that is growing worldwide, since it is the most efficient renewable energy source [1,2].