This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with an expectation constraint on either decision variables or problem parameters. We first present a new stochastic approximation (SA) type algorithm, namely the cooperative SA (CSA), to handle problems with the expectation constraint on devision variables. We show that this algorithm exhibits the optimal ${\cal O}(1/\sqrt{N})$ rate of convergence, in terms of both optimality gap and constraint violation, when the objective and constraint functions are generally convex, where $N$ denotes the number of iterations. Moreover, we show that this rate of convergence can be improved to ${\cal O}(1/N)$ if the objective and constraint functions are strongly convex. We then present a variant of CSA, namely the cooperative stochastic parameter approximation (CSPA) algorithm, to deal with the situation when the expectation constraint is defined over problem parameters and show that it exhibits similar optimal rate of convergence to CSA. It is worth noting that CSA and CSPA are primal methods which do not require the iterations on the dual space and/or the estimation on the size of the dual variables. To the best of our knowledge, this is the first time that such optimal SA methods for solving expectation constrained stochastic optimization are presented in the literature.

We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of theoretical analyses of deep learning has revealed its high expressive power and universal approximation capability. Although these analyses are highly nonparametric, existing generalization error analyses have been developed mainly in a fixed dimensional parametric model. To compensate this gap, we develop an infinite dimensional model that is based on an integral form as performed in the analysis of the universal approximation capability. This allows us to define a reproducing kernel Hilbert space corresponding to each layer. Our point of view is to deal with the ordinary finite dimensional deep neural network as a finite approximation of the infinite dimensional one. The approximation error is evaluated by the degree of freedom of the reproducing kernel Hilbert space in each layer. To estimate a good finite dimensional model, we consider both of empirical risk minimization and Bayesian deep learning. We derive its generalization error bound and it is shown that there appears bias-variance trade-off in terms of the number of parameters of the finite dimensional approximation. We show that the optimal width of the internal layers can be determined through the degree of freedom and the convergence rate can be faster than $O(1/\sqrt{n})$ rate which has been shown in the existing studies.

Increasingly, companies are turning to artificial intelligence to understand what people say about their products and services on Twitter or Facebook. The goal is to react more quickly to complainers and perhaps sell more stuff to happy customers. But with sarcasm, there is a big gap between what people say and what they mean. And, because computers tend to take everything literally, they simply don't get the joke. For example, "You look wonderful" can mean two very different things depending on the context and the speaker.

Summary: This new study claims to be able to identify criminals based on their facial characteristics. Even if the data science is good has AI pushed too far into areas of societal taboos? This isn't the first time data science has been restricted in favor of social goals, but this study may be a trip wire that starts a long and difficult discussion about the role of AI. Has AI gone too far? This might seem like a nonsensical question to data scientists who strive every day to expand the capabilities of AI until you read the headlines created by this just released peer reviewed scientific paper: Automated Inference on Criminality Using Face Images (Xiaolin Wu, McMaster Univ.

Garry Kasparov, one of the greatest chess players of all time, is famous for his pair of faceoffs against the IBM supercomputer Deep Blue. Kasparov won the first match against the computer, 4-2, in 1996, but lost in the rematch, 3½-2½, in 1997. He recently published a book, "Deep Thinking," about the experience. Business Insider recently spoke with Kasparov about Deep Blue, his thoughts on AI, and machine advancements over the past 20 years -- and how he sees the interplay between machine intelligence and humanity. This interview has been edited for clarity and length. Garry Kasparov: AI as a concept is surrounded by mythology. Most of the things we mention we understand. You know, if we say "white," we all see it's white. If we talk about elements of computer science or some general items, we are in agreement.

Samsung Electronics may invest $1 billion into acquisitions of artificial intelligence (AI) companies. South Korean outlet Chosun Biz reported on Tuesday that the Seoul-based tech giant is currently considering the idea of establishing a $1 billion fund for that purpose. An anonymous source from the U.S. branch of Samsung Electronics allegedly said that the company may even inject more money into the fund as the aforementioned figure is apparently just the bare minimum that the largest business conglomerate in South Korea believes is worth investing. Apart from direct acquisitions and mergers, the report says that the fund would also be used to purchase stakes in AI companies. Despite the fact that Samsung Electronics recently made some significant investments into AI, the company's management still thinks more similar initiatives are necessary, the source revealed.

Sören Schwertfeger finished his postdoctorate research on autonomous robots in Germany, and seemed set to go to Europe or the United States, where artificial intelligence was pioneered and established. Instead, he went to China. "You couldn't have started a lab like mine elsewhere," Mr. Schwertfeger said. The balance of power in technology is shifting. China, which for years watched enviously as the West invented the software and the chips powering today's digital age, has become a major player in artificial intelligence, what some think may be the most important technology of the future.

Facebook Data Science Blog, the official blog of interesting insights presented by Facebook data scientists. Your bridge to careers in Data Science and Data Engineering Information is Beautiful, by Independent data journalist and information designer David McCandless who is also the author of his book'Information is Beautiful'. Large Scale ML & other Animals, by Danny Bickson, started the GraphLab, an award winning large scale open source project. Perpetual Enigma by Prateek Joshi, a computer vision enthusiast writes question-style compelling story reads on machine learning. Facebook Data Science Blog, the official blog of interesting insights presented by Facebook data scientists.

Inequality goes back to the Stone Age. Thirty thousand years ago, bands of hunter-gatherers in Russia buried some members in sumptuous graves replete with thousands of ivory beads, bracelets, jewels and art objects, while other members had to settle for a bare hole in the ground. Nevertheless, ancient hunter-gatherer groups were still more egalitarian than any subsequent human society, because they had very little property. Property is a pre-requisite for long-term inequality. Following the agricultural revolution, property multiplied and with it inequality.

Antwerp (Belgium) – May 16, 2017 – Today, at the imec technology forum (ITF2017), imec, the world-leading research and innovation hub in nano-electronics and digital technologies, demonstrated the world's first self-learning neuromorphic chip. The brain-inspired chip, based on OxRAM technology, has the capability of self-learning and has been demonstrated to have the ability to compose music. The human brain is a dream for computer scientists: it has a huge computing power while consuming only a few tens of Watts. Imec researchers are combining state-of-the-art hardware and software to design chips that feature these desirable characteristics of a self-learning system. Imec's ultimate goal is to design the process technology and building blocks to make artificial intelligence to be energy efficient so that that it can be integrated into sensors.