The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propagated by the chain rule through the graph are low variance unbiased estimators of the gradients of the expected loss. While many continuous random variables have such reparameterizations, discrete random variables lack useful reparameterizations due to the discontinuous nature of discrete states. In this work we introduce Concrete random variables---continuous relaxations of discrete random variables. The Concrete distribution is a new family of distributions with closed form densities and a simple reparameterization. Whenever a discrete stochastic node of a computation graph can be refactored into a one-hot bit representation that is treated continuously, Concrete stochastic nodes can be used with automatic differentiation to produce low-variance biased gradients of objectives (including objectives that depend on the log-probability of latent stochastic nodes) on the corresponding discrete graph. We demonstrate the effectiveness of Concrete relaxations on density estimation and structured prediction tasks using neural networks.

Recent advances in deep learning (dl; LeCun et al., 2015) have revolutionized the application of machine learning in areas such as computer vision (Krizhevsky et al., 2012), speech recognition (Hinton et al., 2012) and natural language processing (Collobert and Weston, 2008). Although certain kernel-based methods have also been successful in such domains (Cho and Saul, 2009; Mairal et al., 2014), it is still unclear whether these methods can indeed catch up with the recent dl breakthroughs. Aside from the benefits obtained from using compositional representations, we believe that the main components contributing to the success of dl techniques are: (i) their scalability to large datasets and efficient computation via gpus; (ii) their large representational power; and (iii) the use of well-targeted objective functions for the problem at hand. In the kernel world, Gaussian process (gp; Rasmussen and Williams, 2006) models are attractive because they are elegant Bayesian nonparametric approaches to learning from data. Nevertheless, besides the limitations intrinsic to local kernel machines (Bengio et al., 2005), it is clear that gp-based methods have not fully explored the desirable criteria highlighted above. Firstly, with regards to (i) scalability, despite recent advances in inducing-variable approaches and variational inference in gp models (Titsias, 2009; Hensman et al., 2013, 2015a; Dezfouli and Bonilla, 2015), the study of truly large datasets in problems other than regression and the investigation of gpu-based acceleration in gp models are still under-explored areas. We note that these issues are also shared by non-probabilistic kernel methods such as support vector machines (svms; Scholkopf and Smola, 2001). Furthermore, concerning (ii) their representational power, kernel methods have been plagued by the overuse of very limited kernels such as the squared exponential kernel, also known as the radial-basisfunction (rbf) kernel.

Power spectral density (PSD) maps providing the distribution of RF power across space and frequency are constructed using power measurements collected by a network of low-cost sensors. By introducing linear compression and quantization to a small number of bits, sensor measurements can be communicated to the fusion center with minimal bandwidth requirements. Strengths of data- and model-driven approaches are combined to develop estimators capable of incorporating multiple forms of spectral and propagation prior information while fitting the rapid variations of shadow fading across space. To this end, novel nonparametric and semiparametric formulations are investigated. It is shown that PSD maps can be obtained using support vector machine-type solvers. In addition to batch approaches, an online algorithm attuned to real-time operation is developed. Numerical tests assess the performance of the novel algorithms.

The highly intelligent machines that will be unleashed in the near future won't be coming for our lives. They'll be coming for our jobs. Being rendered obsolete by technology has been a concern among the flesh-and-blood set for hundreds of years -- cars put many in the horse industry out of work, for example -- but the speed and types of recent advances are about to give the issue an exceptional urgency. Previously, it was repetitive blue-collar jobs that were at risk, such as those in manufacturing. In the near future, however, the leaps in artificial intelligence will soon make it possible for machines to do all sorts of jobs, including those that require thinking skills we once believed beyond the reach of machines.

The all- new test vehicle will be used to explore a full range of autonomous driving capabilities. Toyota's work on autonomous vehicles in the United States began in 2005 at its technical center in Ann Arbor, Mich.-- The company secured its first U.S. patents in the field in 2006.-- According to a report last year by the Intellectual Property and Science division of Thomson Reuters, Toyota holds more patents in the field than any other company. "This new advanced safety research vehicle is the first autonomous testing platform developed entirely by TRI, and reflects the rapid progress of our autonomous driving program," said TRI CEO Gill Pratt.

If you've ever wondered how two or more things relate to each other, or if you've ever had your boss ask you to create a forecast or analyze relationships between variables, then learning regression would be worth your time. In this article, you'll learn the basics of simple linear regression - a tool commonly used in forecasting and financial analysis. We will begin by learning the core principles of regression, first learning about covariance and correlation, and then moving on to building and interpreting a regression output. A lot of software such as Microsoft Excel can do all the regression calculations and outputs for you, but it is still important to learn the underlying mechanics. At the center of regression is the relationship between two variables called the dependent and independent variables.

From helping you take care of email to creating personalized online shopping experiences, AI promises to transform the way we live and work. But with all the hype out there, how do we know which benefits we'll actually see? We're inviting 250 to exhibit at TNW Conference and pitch on stage! What is the top benefit you predict emerging from AI, and do you think the overall benefits will live up to the hype? The greatest benefit of AI -- which is already emerging -- is the elimination of repetitive tasks.

Economists may be underestimating the impact on labor markets of increasing automation and the rise of artificial intelligence, according to a post published on the Bank of England's staff blog on March 1. RELATED: Starsky Robotics sees'last mile' solution for driverless trucks "The potential for simultaneous and rapid disruption, coupled with the breadth of human functions that AI might replicate, may have profound implications for labor markets," BOE regional agents Mauricio Armellini and Tim Pike wrote in the Bank Underground post. "Economists should seriously consider the possibility that millions of people may be at risk of unemployment, should these technologies be widely adopted." RELATED: Robots could replace 1.7 million American truckers in the next decade Robots and intelligent machines threaten to replace workers in industries from finance to retail to haulage, with BOE Chief Economist Andrew Haldane estimating in 2015 that 15 million British jobs and 80 million in the U.S. could be lost to automation. Past periods of technological upheaval, such as the industrial revolution, may not be a useful guide as the pace of change was slower, giving society longer to mitigate the potential consequences of increasing job displacement and inequality, according to Armellini and Pike.

Scientists have used a unique computational technique that sifts through big data to identify a subset of concussion patients with normal brain scans, who may deteriorate months after diagnosis and develop confusion, personality changes and differences in vision and hearing, as well as post-traumatic stress disorder. This finding, which is corroborated by the identification of molecular biomarkers, is paving the way to a precision medicine approach to the diagnosis and treatment of patients with traumatic brain injury. Investigators headed by scientists at UC San Francisco and its partner institution Zuckerberg San Francisco General Hospital and Trauma Center (ZSFG) analyzed an unprecedented array of data, using a machine learning technology called topological data analysis (TDA), which "visualizes" diverse datasets across multiple scales, a technique that has never before been used to study traumatic brain injury. TDA, which employs mathematics derived from topology, draws on the philosophy that all data has an underlying shape. It creates a summary or compressed representation of all the data points using algorithms that map patient data into a multidimensional space.

Artificial intelligence is already gaining steam as one of the most-talked-about tech trends of 2017. It's one of those umbrella terms that's easy to throw around. But away from the big conferences and debates about tech's role in society, the hard work to develop the predictive technology is happening. One of those spots is the Eastern Campus of the Emerging Technology Centers, where Insilico Medicine is working to develop algorithms that can help select and develop the right drugs. The company sees artificial intelligence as a path to reduce the use of animal testing in developing pharmaceuticals, and is even working on a virtual human to simulate how drugs affect the body.