**GraphMP**

Recent studies showed that single-machine graph processing systems can be as highly competitive as cluster-based approaches on large-scale problems. While several out-of-core graph processing systems and computation models have been proposed, the high disk I/O overhead could significantly reduce performance in many practical cases. In this paper, we propose GraphMP to tackle big graph analytics on a single machine. GraphMP achieves low disk I/O overhead with three techniques. First, we design a vertex-centric sliding window (VSW) computation model to avoid reading and writing vertices on disk. Second, we propose a selective scheduling method to skip loading and processing unnecessary edge shards on disk. Third, we use a compressed edge cache mechanism to fully utilize the available memory of a machine to reduce the amount of disk accesses for edges. Extensive evaluations have shown that GraphMP could outperform existing single-machine out-of-core systems such as GraphChi, X-Stream and GridGraph by up to 51, and can be as highly competitive as distributed graph engines like Pregel+, PowerGraph and Chaos. … **Prediction Interval**

In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which future observations will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis. Prediction intervals are used in both frequentist statistics and Bayesian statistics: a prediction interval bears the same relationship to a future observation that a frequentist confidence interval or Bayesian credible interval bears to an unobservable population parameter: prediction intervals predict the distribution of individual future points, whereas confidence intervals and credible intervals of parameters predict the distribution of estimates of the true population mean or other quantity of interest that cannot be observed.

Prediction Interval, the wider sister of Confidence Interval … **Snapshot Ensembles**

Ensembles of neural networks are known to be much more robust and accurate than individual networks. However, training multiple deep networks for model averaging is computationally expensive. In this paper, we propose a method to obtain the seemingly contradictory goal of ensembling multiple neural networks at no additional training cost. We achieve this goal by training a single neural network, converging to several local minima along its optimization path and saving the model parameters. To obtain repeated rapid convergence, we leverage recent work on cyclic learning rate schedules. The resulting technique, which we refer to as Snapshot Ensembling, is simple, yet surprisingly effective. We show in a series of experiments that our approach is compatible with diverse network architectures and learning tasks. It consistently yields lower error rates than state-of-the-art single models at no additional training cost, and compares favorably with traditional network ensembles. On CIFAR-10 and CIFAR-100 our DenseNet Snapshot Ensembles obtain error rates of 3.4% and 17.4% respectively.

Snapshot Ensembles in Keras … **INDIAN**

We devise a learning algorithm for possibly nonsmooth deep neural networks featuring inertia and Newtonian directional intelligence only by means of a back-propagation oracle. Our algorithm, called INDIAN, has an appealing mechanical interpretation, making the role of its two hyperparameters transparent. An elementary phase space lifting allows both for its implementation and its theoretical study under very general assumptions. We handle in particular a stochastic version of our method (which encompasses usual mini-batch approaches) for nonsmooth activation functions (such as ReLU). Our algorithm shows high efficiency and reaches state of the art on image classification problems. …

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