Graph-based semi-supervised learning is one of the most popular methods in machine learning. Some of its theoretical properties such as bounds for the generalization error and the convergence of the graph Laplacian regularizer have been studied in computer science and statistics literatures. However, a fundamental statistical property, the consistency of the estimator from this method has not been proved. In this article, we study the consistency problem under a non-parametric framework. We prove the consistency of graph-based learning in the case that the estimated scores are enforced to be equal to the observed responses for the labeled data. The sample sizes of both labeled and unlabeled data are allowed to grow in this result. When the estimated scores are not required to be equal to the observed responses, a tuning parameter is used to balance the loss function and the graph Laplacian regularizer. We give a counterexample demonstrating that the estimator for this case can be inconsistent. The theoretical findings are supported by numerical studies.

An important topic in the multi-label learning research is how to exploit the relationship between different classes of labels in order to improve the learning accuracy or reduce the number of required labels. When labels are partially observed, the low-rank matrix model is one of the most popular models to deal with missing labels. As human-labeling is usually expensive and time-consuming, it is critical to design a robust algorithm which is able to learn the underlying low-rank matrix model on datasets with noisy heavily missing labels. In this work, we consider an extreme scenario where each training instance only has one single label being annotated in binary set 1 out of multiple classes of labels. This scenario is often encountered in realworld systems but less discussed in literatures. For example, it is rare for a user to annotate a news article or a piece of music with many tags, especially when the user is not paid for his annotation. The problem becomes challenging when we have a large number of features and classes. Over the past decades, a number of multi-label learning approaches have been proposed under different settings.

Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling high dimensional constrained problems, as the projection step becomes computationally prohibitive to compute. To address this problem, this paper adopts a projection-free optimization approach, a.k.a.~the Frank-Wolfe (FW) or conditional gradient algorithm. We first develop a decentralized FW (DeFW) algorithm from the classical FW algorithm. The convergence of the proposed algorithm is studied by viewing the decentralized algorithm as an inexact FW algorithm. Using a diminishing step size rule and letting $t$ be the iteration number, we show that the DeFW algorithm's convergence rate is ${\cal O}(1/t)$ for convex objectives; is ${\cal O}(1/t^2)$ for strongly convex objectives with the optimal solution in the interior of the constraint set; and is ${\cal O}(1/\sqrt{t})$ towards a stationary point for smooth but non-convex objectives. We then show that a consensus-based DeFW algorithm meets the above guarantees with two communication rounds per iteration. Furthermore, we demonstrate the advantages of the proposed DeFW algorithm on low-complexity robust matrix completion and communication efficient sparse learning. Numerical results on synthetic and real data are presented to support our findings.

For most branching algorithms in Boolean logic "branching" means "variable-wise branching". We present the apparently novel technique of clause-wise branching, which is used to solve the ALLSAT problem for arbitrary Boolean functions in CNF format. Specifically, it converts a CNF into an orthogonal DNF, i.e. into an exclusive sum of products. Our method is enhanced by two ingredients: The use of a good SAT-solver and wildcards beyond the common don't-care symbol.

The California-based robot vacuum manufacturer has announced that Google Home support is coming to its Connected series vacuums. With the Botvac Connected already having Alexa integration, it was only a matter of time. If you are looking into getting a robot vacuum cleaner, you probably know the name. A California-based company that specializes in automated vacuums, Neato's Botvac series is arguably iRobot Roomba's biggest rival. I have the Botvac Connected for my apartment, and I personally thinks it's the best robot cleaner your money can buy right now.

A new report has proposed AI and Machine learning as a potential cure to the "Ransomware pandemic" making its way through the healthcare sector. The Institute of Critical Infrastructure Technology (ICIT) recently released a report called "How to Crush the Health Sector's Ransomware Pandemic". James Scott, senior fellow at ICIT and the author of the paper offers a plain solution to the worrying rash of cyber-attack on hospitals and healthcare providers that have held patient safety to ransom. He notes the proliferation of not only dynamic and adaptive malware, but the sheer number of adversaries that can find their way around defences no matter how resilient or well-resourced. But against this gloomy landscape, says Scott in a defiantly optimistic tone, what if healthcare organisations could use machine learning to overcome these threats?

For more on advances in machine learning, prediction, and technology, check out the Data science and advanced analytics sessions at Strata Hadoop World London, May 22-25, 2017. Early price ends April 7. You've probably heard by now that machine learning algorithms can use big data to predict whether a donor will give to a charity, whether an infant in a NICU will develop sepsis, whether a customer will respond to an ad, and on and on. Machine learning can even drive cars and predict elections. I believe it can, but these recent high-profile hiccups should leave everyone who works with data (big or not) and machine learning algorithms asking themselves some very hard questions: do I understand my data? Do I understand the model and answers my machine learning algorithm is giving me? And do I trust these answers? Unfortunately, the complexity that bestows the extraordinary predictive abilities on machine learning algorithms also makes the answers the algorithms produce hard to ...

The innovative ideas and social inspiration that flowed through SXSW Interactive will drive the state of technology in the coming year. Just like we saw at Mobile World Congress, autonomous cars were everywhere at SXSW. Though they weren't cruising on the road, there were plenty of showcases where you could gaze into the luxurious, self-driving future. One model from NIO featured lounge chairs and an interior that's fancier than my living room. Though aesthetic is certainly a big draw, it's important to keep in mind AI and deep learning will be necessary components to these vehicles.

Artificial intelligence will have a dramatic impact on business by 2020, according to study released this week by IT services, consulting and business solutions provider Tata Consultancy Services (TCS). The firm's study, "Getting Smarter by the Day: How AI is Elevating the Performance of Global Companies," shows that 84 percent of the 835 executives TCS surveyed from North America, Europe, Asia-Pacific and Latin America said their companies see the use of AI as "essential" to competitiveness. Artificial intelligence in the real world: What can it actually do? What are the limits of AI? And how do you go from managing data points to injecting AI in the enterprise?

The nose is one of humanity's most distinctive facial features, but exactly how we came to inherit such diverse shapes and sizes has remained a mystery. But new research which examined differences across populations around the world may have the answer. And it seems that the local climate may have helped to shape variations in the evolution of the nose. Researchers at Pennsylvania State University used 3D imaging to examine the nasal characteristics of 140 people. Dr Mark Shriver and his colleague Arslan Zaidi looked at the width of the nostrils, distance between nostrils, height of the nose, nose ridge length, nose protrusion, external area of the nose and the area of the nostrils. They examined the distribution of these traits across distinct global populations and compared them with temperatures and humidity in each area.