Hypervariate Data google
Hypervariate data is Data with four or more dimensions in the dataset. …

Reluplex google
Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees about their behavior. We present a novel, scalable, and efficient technique for verifying properties of deep neural networks (or providing counter-examples). The technique is based on the simplex method, extended to handle the non-convex Rectified Linear Unit (ReLU) activation function, which is a crucial ingredient in many modern neural networks. The verification procedure tackles neural networks as a whole, without making any simplifying assumptions. We evaluated our technique on a prototype deep neural network implementation of the next-generation Airborne Collision Avoidance System for unmanned aircraft (ACAS Xu). Results show that our technique can successfully prove properties of networks that are an order of magnitude larger than the largest networks verified using existing methods. …

copCAR Regression Model (copCAR) google
Non-Gaussian spatial data are common in many fields. When fitting regressions for such data, one needs to account for spatial dependence to ensure reliable inference for the regression coefficients. The two most commonly used regression models for spatially aggregated data are the automodel and the areal generalized linear mixed model (GLMM). These models induce spatial dependence in different ways but share the smoothing approach, which is intuitive but problematic. This article develops a new regression model for areal data. The new model is called copCAR because it is copula-based and employs the areal GLMM#s conditional autoregression (CAR). copCAR overcomes many of the drawbacks of the automodel and the areal GLMM. Specifically, copCAR
(1) is flexible and intuitive,
(2) permits positive spatial dependence for all types of data,
(3) permits efficient computation, and
(4) provides reliable spatial regression inference and information about dependence strength.
An implementation is provided by R package copCAR, which is available from the Comprehensive R Archive Network, and supplementary materials are available online. …

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