Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric variational family, which adapts its shape to match complex posterior distributions. The VGP generates approximate posterior samples by generating latent inputs and warping them through random non-linear mappings; the distribution over random mappings is learned during inference, enabling the transformed outputs to adapt to varying complexity. We prove a universal approximation theorem for the VGP, demonstrating its representative power for learning any model. For inference we present a variational objective inspired by auto-encoders and perform black box inference over a wide class of models. The VGP achieves new state-of-the-art results for unsupervised learning, inferring models such as the deep latent Gaussian model and the recently proposed DRAW.

Abstract--A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, todays denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, we develop an extension of the approximate message passing (AMP) framework, called Denoising-based AMP (DAMP), that can integrate a wide class of denoisers within its iterations. We demonstrate that, when used with a high performance denoiser for natural images, DAMP offers state-of-the-art CS recovery performance while operating tens of times faster than competing methods. We explain the exceptional performance of DAMP by analyzing some of its theoretical features. A key element in DAMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove. The fundamental challenge faced by a compressed sensing (CS) reconstruction algorithm is to reconstruct a highdimensional signal from a small number of measurements. In a single pixel camera, Φ might be a sequence of 1s and 0s representing the modulation of a micromirror array [3]. " Ψu with sparse u, where Ψ represents the inverse transform matrix. C. Metzler and R. Baraniuk are with the Department of Electrical and Computer Engineering, Rice University, Houston, TX 77023 USA (email: chris.metzler@rice.edu and richb@rice.edu). A. Maleki is with the Department of Statistics, Columbia University, New York, NY 10023 USA (email: arian@stat.columbia.edu). The work of C. Metzler supported by the NSF GRF Program and the DoD NDSEG Program. The work of A. Maleki was supported by the grant NSF CCF-1420328. However, when dealing with large signals, such as images, these convex programs are extremely computationally demanding. Therefore, lower cost iterative algorithms were developed; including matching pursuit [6], orthogonal matching pursuit [7], iterative hard-thresholding [8], compressive sampling matching pursuit [9], approximate message passing [10], and iterative soft-thresholding [11]-[16], to name just a few. See [17], [18] for a complete set of references. Here, δ " m{n is a measure of the under-determinacy of the problem, x y denotes the average of a vector, and The role of this term is illustrated in Figure 1. A QQplot is a visual inspection tool for checking the Gaussianity of the data. In a QQplot, deviation from a straight line is an evidence of non-Gaussianity.

In keeping with its vision of an era of cognitive computing enabled by acceleration technology, IBM Research (NYSE: IBM) today announced plans for a multi-year collaboration with the University of Illinois Urbana-Champaign to create the Center for Cognitive Computing Systems Research (C3SR) which will be housed within the College of Engineering on the Urbana campus. IBM has big ambitions for the center: "C3SR will build and optimize integrated systems such as state-of-the-art cognitive computing systems modeled on IBM's Watson technology that can master a subject area by learning from multimedia and multi-modal educational content. Such systems will efficiently ingest vast amounts of data including videos, lecture notes, homework, and textbooks, and reason through this knowledge effectively enough to be able to eventually pass a college level exam." Many details are yet to be worked out. The level of funding and size of installation will be announced this summer when the new center formally opens, said Hillery Hunter, a project driver and the director for systems acceleration and memory at IBM Research.

With a paralyzing spinal cord injury, the biological wiring that hooks up our controlling brains to our useful limbs gets snipped, leading to permanent loss of sensation and control and usually a lifetime of extra health care. Researchers have spent years working to repair those lost connections, allowing paralyzed patients to sip coffee and enjoy a beer with robotic limbs controlled by just their minds. Now, researchers have gone a step further, allowing a paralyzed person to control his own hand with just his mind. In a study published Wednesday in Nature, researchers report using a "neural bypass" that reconnects a patient's mental commands for movement to responsive muscles in his limbs, creating somewhat of a synthetic nervous system. The pioneering patient, Ian Burkhart, a 24-year-old man left with quadriplegia after a diving accident almost six years ago, can once again move his hand.

More than 70 years ago, Isaac Asimov dreamed up his three laws of robotics, which insisted, above all, that "a robot may not injure a human being or, through inaction, allow a human being to come to harm". Now, after Stephen Hawking warned that "the development of full artificial intelligence could spell the end of the human race", two academics have come up with a way of teaching ethics to computers: telling them stories. Mark Riedl and Brent Harrison from the School of Interactive Computing at the Georgia Institute of Technology have just unveiled Quixote, a prototype system that is able to learn social conventions from simple stories. Or, as they put in their paper Using Stories to Teach Human Values to Artificial Agents, revealed at the AAAI-16 Conference in Phoenix, Arizona this week, the stories are used "to generate a value-aligned reward signal for reinforcement learning agents that prevents psychotic-appearing behaviour". A simple version of a story could be about going to get prescription medicine from a chemist, laying out what a human would typically do and encounter in this situation.

Are you skeptical about machines' ability to effectively aid social science decision making? Machines are becoming ever more intelligent, increasingly able to help humans make decisions across the social science spectrum, but cognitive computing is still in its infancy, with much unexplored ground ahead. Accordingly, government leaders who harness the power of cognitive computing are helping usher in a renaissance of simplified operations and enhanced constituent engagement. The secret to effectively using cognitive computing to aid human decision making lies in teaching computers to ask the right questions while taking account context and staying focused on what computers do well. Computers operate at great speed.

Microsoft is the world's most valuable company, with a 261 billion market cap. And an IBM computer named Deep Blue defeats Garry Kasparov, reigning world chess champion and, at the time, the highest-ranked chess player to have ever lived.

The days when a Facebook post would reach 90 percent of a page's audience have come and gone. In 2011, I was managing operations for Coca-Cola's global Facebook page, which had just surpassed Starbucks to become the largest CPG brand page on Facebook. The page was shared among dozens of markets because Facebook did not yet support regional pages. And each post was geotargeted to reach the right audience. One fine August day, Facebook dropped the targeting from a post specific to our Brazilian audience.

Machine learning has crossed from the lab to the business world. Machine learning provides insights that help to create more intelligent data-driven applications that improve business processes, operation, and easier decision making. In a conversation at Structure Data 2016 conference in San Francisco, Dr. Peter Lee, Corporate Vice President, Microsoft Research and Jack Clark, Bloomberg News – San Francisco, talked about the advances we made in Artificial Intelligence (AI) and machine learning in recent years. Dr. Lee is responsible for Microsoft Research New Experiences and Technologies. He said that AI is essentially used to really understand what customers want.

"Although messaging is the way users communicate with each other, it's not how they interact with businesses. Of all the ways humans communicate, texting might be the most direct. Text carries less superfluous information than other ways of sending information. With text, there are no voice intonations to decipher or accents to understand, no facial gestures to interpret, and no body language to translate. Text is something computers can understand and process quickly and it's why messaging is a great place for humans and A.I. to work together to serve customer needs.