Nonconvex optimization problems such as the ones in training deep neural networks suffer from a phenomenon called saddle point proliferation. This means that there are a vast number of high error saddle points present in the loss function. Second order methods have been tremendously successful and widely adopted in the convex optimization community, while their usefulness in deep learning remains limited. This is due to two problems: computational complexity and the methods being driven towards the high error saddle points. We introduce a novel algorithm specially designed to solve these two issues, providing a crucial first step to take the widely known advantages of Newton's method to the nonconvex optimization community, especially in high dimensional settings.

Boosting is one of the most significant developments in machine learning. This paper studies the rate of convergence of $L_2$Boosting, which is tailored for regression, in a high-dimensional setting. Moreover, we introduce so-called \textquotedblleft post-Boosting\textquotedblright. This is a post-selection estimator which applies ordinary least squares to the variables selected in the first stage by $L_2$Boosting. Another variant is \textquotedblleft Orthogonal Boosting\textquotedblright\ where after each step an orthogonal projection is conducted. We show that both post-$L_2$Boosting and the orthogonal boosting achieve the same rate of convergence as LASSO in a sparse, high-dimensional setting. We show that the rate of convergence of the classical $L_2$Boosting depends on the design matrix described by a sparse eigenvalue constant. To show the latter results, we derive new approximation results for the pure greedy algorithm, based on analyzing the revisiting behavior of $L_2$Boosting. We also introduce feasible rules for early stopping, which can be easily implemented and used in applied work. Our results also allow a direct comparison between LASSO and boosting which has been missing from the literature. Finally, we present simulation studies and applications to illustrate the relevance of our theoretical results and to provide insights into the practical aspects of boosting. In these simulation studies, post-$L_2$Boosting clearly outperforms LASSO.

Paul Daugherty is chief technology officer at Accenture. Cracking the Gender Code, a research report produced jointly by Accenture and Girls Who Code, can be downloaded here. The chasm between the number of job openings in today's digital economy and the number of skilled workers available is growing in the wrong direction and threatening the competitiveness of the U.S. economy. Fact No. 1: In 2015, there were 500,000 new computing jobs available in the U.S., but as recently as 2014, fewer than 40,000 new computer science graduates to fill them. This shortage will continue to grow as rapid advances in mobile, cloud, analytics and artificial intelligence technologies continue to redefine business, society and the global economy.

Fraud is a big problem in the cellular networking market, and machine learning is one potential solution to the problem. Mathematics-based cyberdefence firm claims Antigena can teach itself to fight off new malicious intrusions -- without human involvement. Fraudulent usage of cellular networks costs the industry an estimated $38 billion a year, according to the 2015 Global Fraud Loss Survey by the Communications Fraud Control Association (CFCA), an international organization that promotes revenue assurance, loss prevention, and fraud control in the industry. The CFCA says fraudsters use methods including PBX hacking, subscription fraud, dealer fraud, service abuse, and account takeover to steal from service providers. Current fraud detection approaches in the industry rely on static rules with pre-set volume or frequency thresholds, said Ole J. Mengshoel, associate research professor in the Department of Electrical and Computer Engineering and director of the Intelligent and High-Performing Systems Lab at Carnegie Mellon University.

One of Blizzard Entertainment's hottest video games is making the jump into a professional sports league. The studio, a division of video game publisher Activision Blizzard, announced Friday the launch of Overwatch League, a professional video gaming league kicking off its inaugural season during the second half of 2017. Details of the league were revealed during Blizzcon, the studio's annual fan event in Anaheim, Calif. Blizzard says the league will combine competitive video gaming -- better known as eSports -- with hallmarks of professional sports leagues like the National Football League, complete with teams based in various cities worldwide featuring owners who will cultivate team and player development. "Nothing like this has ever really been done before," said Activision Blizzard CEO Bobby Kotick during an interview with USA TODAY.

The 8.6 billion mobile devices on the planet have meant that quite often, getting a decent signal can be tough. However, researchers say a new drone could be the key. It can create an incredibly detailed 3D map of a city, allowing researchers to model how radio waves move through it. Researcher have devised a new method that involves taking aerial photographs of an area with a drone, which can be used as models to design radio links. Drones are equipped with a high quality cameras that can capture multiple points of view.

A team of scientists at IBM Research in Zurich, have created an artificial version of neurons using phase-change materials to store and process data. These phase change based artificial neurons can be used to detect patterns and discover correlations in the areas of big data and unsupervised machine learning. The results of the decade-long research to use phase-change materials for memory applications were recently published in the journal Nature Nanotechnology. The research team is led by Evangelos Eleftheriou. The development of energy-efficient, ultra-dense integrated neuromorphic technologies for applications in cognitive computing is getting a lot of attention.

Criteo is organizing the Machine Learning in the Real World workshop. This workshop aims at bringing together people from the industry and from academia to better understand which machine learning algorithms are used in practice and what we can do to improve them. Anyone who is involved in applying machine learning on real world data is welcome. This event is primarily intended for people with technical fluency in machine learning to help each other advance the state of the art. If you are interested in learning about the basics of the field, there are plenty of other great events in Paris which are probably more appropriate.

What Did You Miss at the Deep Learning Summit Last Week?

Natural language processing (NLP) is quickly becoming one of the foundational big data technologies that will allow healthcare to move forward with complex analytics, according to a series of market reports predicting significant growth for NLP products over the next few years. As healthcare organizations seek new strategies for extracting insights from unstructured data from electronic health records, Internet of Things devices, imaging studies, and elsewhere, they will create an NLP marketplace worth $2.65 billion by 2021, says ReportsnReports. "The market is growing rapidly because of the huge surge in clinical data, increasing use of connected devices, and evolving consumer needs," the report says. Natural language processing may play an instrumental role in precision medicine, predictive analytics, population health management, clinical decision support, and EHR documentation improvement. The NLP market is divided into several segments: interactive voice response and speech analytics technologies, optical character recognition (OCR), automatic coding, text analytics, and pattern and image recognition.