We present a global optimization algorithm for clustering data given the ratio of likelihoods that each pair of data points is in the same cluster or in different clusters. To define a clustering solution in terms of pairwise relationships, a necessary and sufficient condition is that belonging to the same cluster satisfies transitivity. We define a global objective function based on pairwise likelihood ratios and a transitivity constraint over all triples, assigning an equal prior probability to all clustering solutions. We maximize the objective function by implementing max-sum message passing on the corresponding factor graph to arrive at an O(N^3) algorithm. Lastly, we demonstrate an application inspired by mutational sequencing for decoding random binary words transmitted through a noisy channel.

Syntactic constituency parsing is a fundamental problem in natural language processing and has been the subject of intensive research and engineering for decades. As a result, the most accurate parsers are domain specific, complex, and inefficient. In this paper we show that the domain agnostic attention-enhanced sequence-to-sequence model achieves state-of-the-art results on the most widely used syntactic constituency parsing dataset, when trained on a large synthetic corpus that was annotated using existing parsers. It also matches the performance of standard parsers when trained only on a small human-annotated dataset, which shows that this model is highly data-efficient, in contrast to sequence-to-sequence models without the attention mechanism. Our parser is also fast, processing over a hundred sentences per second with an unoptimized CPU implementation.

We consider the problem of modelling noisy but highly symmetric shapes that can be viewed as hierarchies of whole-part relationships in which higher level objects are composed of transformed collections of lower level objects. To this end, we propose the stochastic wreath process, a fully generative probabilistic model of drawings. Following Leyton's "Generative Theory of Shape", we represent shapes as sequences of transformation groups composed through a wreath product. This representation emphasizes the maximization of transfer --- the idea that the most compact and meaningful representation of a given shape is achieved by maximizing the re-use of existing building blocks or parts. The proposed stochastic wreath process extends Leyton's theory by defining a probability distribution over geometric shapes in terms of noise processes that are aligned with the generative group structure of the shape. We propose an inference scheme for recovering the generative history of given images in terms of the wreath process using reversible jump Markov chain Monte Carlo methods and Approximate Bayesian Computation. In the context of sketching we demonstrate the feasibility and limitations of this approach on model-generated and real data.

We propose an efficient nonparametric strategy for learning a message operator in expectation propagation (EP), which takes as input the set of incoming messages to a factor node, and produces an outgoing message as output. This learned operator replaces the multivariate integral required in classical EP, which may not have an analytic expression. We use kernel-based regression, which is trained on a set of probability distributions representing the incoming messages, and the associated outgoing messages. The kernel approach has two main advantages: first, it is fast, as it is implemented using a novel two-layer random feature representation of the input message distributions; second, it has principled uncertainty estimates, and can be cheaply updated online, meaning it can request and incorporate new training data when it encounters inputs on which it is uncertain. In experiments, our approach is able to solve learning problems where a single message operator is required for multiple, substantially different data sets (logistic regression for a variety of classification problems), where it is essential to accurately assess uncertainty and to efficiently and robustly update the message operator.

Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large datasets typical of modern machine learning. The recently proposed consensus Monte Carlo algorithm removes this limitation by partitioning the data and drawing samples conditional on each partition in parallel (Scott et al, 2013). A fixed aggregation function then combines these samples, yielding approximate posterior samples. We introduce variational consensus Monte Carlo (VCMC), a variational Bayes algorithm that optimizes over aggregation functions to obtain samples from a distribution that better approximates the target. The resulting objective contains an intractable entropy term; we therefore derive a relaxation of the objective and show that the relaxed problem is blockwise concave under mild conditions. We illustrate the advantages of our algorithm on three inference tasks from the literature, demonstrating both the superior quality of the posterior approximation and the moderate overhead of the optimization step. Our algorithm achieves a relative error reduction (measured against serial MCMC) of up to 39% compared to consensus Monte Carlo on the task of estimating 300-dimensional probit regression parameter expectations; similarly, it achieves an error reduction of 92% on the task of estimating cluster comembership probabilities in a Gaussian mixture model with 8 components in 8 dimensions. Furthermore, these gains come at moderate cost compared to the runtime of serial MCMC, achieving near-ideal speedup in some instances.

Apple on Monday served up a veritable smorgasbord of digital delights for its fans, unveiling at its annual developers conference upgrades to its mobile and desktop software, showing off a gussied-up Siri with a new bag of tricks, and firing a shot over Spotify's bow with its new streaming Apple Music subscription service. "This is a truly revolutionary music service," Eddy Cue, Apple's senior vice president of Internet software and services, told the crowd of several thousand developers, designers and product managers at the 26th Worldwide Developers Conference, the annual Apple love fest at Moscone Center in San Francisco. "Apple Music will bring you all of your music all in one place." Revealed toward the end of a nearly three-hour extravaganza, the music feature was clearly Apple's rabbit out of a hat. It had been widely expected for months, ever since May last year when Apple bought subscription streaming music service Beats Music, and Beats Electronics, which makes the popular Beats headphones, speakers and audio software.

Apple on Monday served up a veritable smorgasbord of digital delights for its fans, unveiling at its annual developers conference upgrades to its mobile and desktop software, showing off a gussied-up Siri with a new bag of tricks, and firing a shot over Spotify's bow with its new streaming Apple Music subscription service. "This is a truly revolutionary music service," Eddy Cue, Apple's senior vice president of Internet software and services, told the crowd of several thousand developers, designers and product managers at the 26th Worldwide Developers Conference, the annual Apple love fest at Moscone Center in San Francisco. "Apple Music will bring you all of your music all in one place." Revealed toward the end of a nearly three-hour extravaganza, the music feature was clearly Apple's rabbit out of a hat. It had been widely expected for months, ever since May last year when Apple bought subscription streaming music service Beats Music, and Beats Electronics, which makes the popular Beats headphones, speakers and audio software.

At Apple's WWDC developers' conference keynote in San Francisco, the company's senior vice president of software engineering, Craig Federighi, highlighted a number of new tools coming to Apple's iOS 9 update. Some of these features include a native news aggregator (aptly called News); a refreshed user interface for the more "proactive" digital voice assistant Siri, and split-screen capabilities for the iPad. But similar to past WWDC events, Apple only spent time going through what it considered key upgrades. The other, less high-profile features were thrown onto a keynote slide and glossed over almost completely. Below are the 30 features Apple did not parse through during the presentation: One notable item on the list is "app thinning," which lets users download apps that are tailored to their iOS device.

A robot that evoked a human form paused in front of a door leading to a simulated nuclear power plant accident and inexplicably stood motionless. Suddenly, from the grandstands overlooking the scene, a group of schoolchildren began to chant: "Go Robot! What has long been thought of as a brave new world in which mobile robots freely move about in factories, towns and cities is now approaching. Robots will advance from the dull, dirty and dangerous work that they do today to take on a range of tasks, from rescue work to elder care in close contact with humans. Just as software robots such as Apple's Siri and Microsoft's Cortana have rapidly become useful personal assistants, physical robots will occupy a place in the near future. That is the world imagined by government officials and technologists at the Defense Advanced Research Projects Agency, the American military organization that is charged with the mission of avoiding a Sputnik-style technology threat to national security. Last weekend at the sprawling Los Angeles County Fairgrounds, Darpa concluded the Robotics Challenge, a two-year-long effort to jump start this next generation of smart and presumably helpful robots by offering a cash prize for the designers of a machine that could work in concert with human controllers in a hazardous environment. The $3.5 million competition was won by a South Korean team from the Korean Advanced Institute of Science and Technology. The technology may still seem far-fetched, but betting against the agency that has had a remarkably far-reaching effect on the modern world -- from funding the work that led to both the personal computer and the Internet, to setting expectations that self-driving vehicles are only a matter of years away -- might be a mistake. Darpa officials have taken pains to assure anyone who would listen that it was not primarily interested in designing Terminators, or killer robots. The agency is an arm of the Pentagon, and its futuristic robots are an example of what is described as a "dual use" technology that will have both military and civilian uses. Darpa, which is also known for pioneering the Internet surveillance system that was exposed last year by Edward J. Snowden, has, under its current director, Arati Prabhakar, expanded its watchfulness over the potential effect of the technologies it helps foster. In introducing a workshop for discussion on the effect of robotics held at the end of the challenge competition on Sunday, Dr. Prabhakar described the agency as being committed to a broader mission: "We work together to build the future of robots that can help extend the capabilities that we have and build the technologies that will aid humanity in the future.

During Apple's annual developers keynote at WWDC, Senior Vice President of Software Engineering Craig Federighi announced the company's latest mobile operating system, iOS 9. In addition to a refreshed user interface for the digital voice assistant Siri and a native News app, the update features a number of new tools specifically tailored for the iPad, Apple's tablet line. One notable change is the iPad's digital QuickType keyboard, which can now switch to a digital trackpad. Using a two-finger swipe, you can select, drag and paste large chunks of text more quickly and easily. Multitasking capabilities have also improved.