Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data and their hidden generation process, respectively. It has been pointed out that conventional statistical analysis is not applicable to these models, because redundancy of the latent variable produces singularities in the parameter space. In recent years, a method based on algebraic geometry has allowed us to analyze the accuracy of predicting observable variables when using Bayesian estimation. However, how to analyze latent variables has not been sufficiently studied, even though one of the main issues in unsupervised learning is to determine how accurately the latent variable is estimated. A previous study proposed a method that can be used when the range of the latent variable is redundant compared with the model generating data. The present paper extends that method to the situation in which the latent variables have redundant dimensions. We formulate new error functions and derive their asymptotic forms. Calculation of the error functions is demonstrated in two-layered Bayesian networks.

A lot of people have inhibitions regarding artificial intelligence taking over the world, and inevitably their jobs. And we've been seeing that in almost every sector. For example, a lot of jobs that were previously being done by humans are now increasingly becoming automated, and AI – like it or hate it - seems to be the way forward for many industries. But quite contrary to our fears, the increased adoption of AI, machine learning and the Internet of Things (IoT) in business strategies and analytics will only increase jobs for human beings, according to recruitment experts. Human resource and search experts estimate that the AI buzz could generate a 50-60 percent higher demand for AI and robotics professionals in 2018, even as machines will take over repetitive manual work.

SPOILER ALERT: This piece contains extensive spoilers for the new season of "Black Mirror." "Black Mirror," and its creator Charlie Brooker, are sometimes spoken about in terms of prophetic ability. That 2011 episode about a prime minister and a pig resonated in the real world. There's "The Waldo Moment," which generated viral headlines crediting the episode with predicting President Trump's rise to power. And then there's "Nosedive," the episode set in a world where a person's life depends on their rating out of five on a social media app -- enter China's idea for a "social credit" system.

Farmers Business Network, a San Carlos, Calif.-based farmer-to-farmer network raised $110 million in Series D funding. T. Rowe Price Associates Inc and Temasek led the round, and were joined by investors includingAcre Venture Partners, Kleiner Perkins Caufield & Byers, GV and DBL Partners. Ripcord, a Hayward, CA robotic digitization company, raised $59.5 million this year in a March Series A and Aug/Dec Series B equity funding led by GV and Icon Ventures with Lux Capital, Telstra Ventures, Silicon Valley Bank, Kleiner Perkins, Google and Baidu Ventures. Ripcord has developed and is providing as a service a digitization service using AI, scanning and robotics to go from cardboard storage boxes full of tagged manila folders, to scanable pdf files available through ERP and other office systems. JingChi, a Chinese-funded Beijing and Silicon Valley self-driving AI systems startup, raised $52 million (in September) in a seed round led by Qiming Venture Partners.

Information technology in 2018 is expected to be more exciting as technologies that were just a concept or in the trial stages in the past years will become a reality, according to technology companies. Commentaries submitted by technology companies had five common predictions related to artificial intelligence, Internet of Things, blockchain, cloud computing, and IT security. According to IDC, revenue growth from information-based products will double the rest of the product and services portfolio for a third of Fortune 500 companies by the end of 2017. "AI became mainstream with consumer products like Amazon Alexa and Apple Siri, and Hitachi believes that it is the collaboration of AI and humans that will bring real benefits to society," said Hitachi Vantara's Hubert Yoshida, chief technology officer, and Russell Skingsley, chief technology officer of Asia Pacific. "Through tools like Pentaho Data Integration, our aim is to democratize the data engineering and data science process to make Machine Intelligence – a combination of Machine Learning and AI – more accessible to a wider variety of developers and engineers. Zakir Ahmed, General Manager of Asia at Oracle NetSuite, notes that to date, AI has mostly been following simple rules. If A B then C else D. This proved to be sufficient for powering devices like smart fridges or cars. On the downside, this predictability also meant that people could easily outsmart AI, often with dire consequences. "Thankfully, in 2018 we will reach a pivoting point, where deep learning will fast become an integral component of AI," said Ahmed, noting that these new intelligent AI 2.0 systems will learn, suggest and automate processes by analysing business patterns and behaviours. "For example, banks can provide tailored financial services based on their customers' investment portfolio and risk appetite.

The Chinese armies are now able to use robots to fire ballistic missiles after successfully developing an automated launching system, Chinese military media claimed. The advanced system would help China fire warheads three times faster and halve the number of soldiers involved. The news emerged as tensions between Beijing and Washington have escalated over the claims that China had allowed oil into North Korea, which violated a United Nations embargo. Beijing has denied the allegations. Beijing's next-generation intercontinental ballistic missile, Dongfeng-41 (pictured) could allegedly strike anywhere in the world.

In Nagoya, Japan, a city that once held an entire museum dedicated to robotics, a hospital will soon add robots developed by Toyota to its medical staff. No, they won't be scrubbing in for surgery: In February, the Nagoya University Hospital will deploy four bots to ferry medicine and test samples between floors for a year. The robots are essentially mobile refrigerators with a 90-liter capacity that rely on radar and cameras to zoom through the hospital. Should they run into humans, they're programmed to dodge them or politely voice'Excuse me, please let me pass,' according to The Asahi Shimbun. Staff can summon the robots and assign a destination for their medical payload using a tablet.

Where AI, robots, IoT and the so-called Fourth Industrial Revolution are taking us, and how we should prepare for it are some of the hottest topics being discussed today. Perhaps the most striking thing about these discussions is how different people's conclusions are. Some picture a utopia where machines do all work, where all people receive a universal basic income from the revenues machines generate and where, being freed from a need to work for wages, all people devote their time to altruism, art and culture. Others picture a dystopia where a tiny elite class uses their control of AI to horde all the world's wealth and trap everyone else in inescapable poverty. Others take a broad view that sees minimal disruption beyond adopting new workplace paradigms.

The hotel and hospitality industry, enabled with advanced technology and more collaboration with associated businesses, will see some important trends in 2018 as hotel brands reinvent themselves to cater to a new type of clientele. Millennial guests will dominate the landscape, and reshape the industry with demands for more automated options and conveniences and the ability to do everything from a smartphone, and hotels - eager to deliver more conveniences to this younger audience - will forge closer alliances with retailers and community destinations. Hotel guests will place increasing priority on booking rooms that are totally connected, fully automated, and with an ability to seamlessly check in, check out, and access services, all through a smartphone app and without the need for human interaction. Human travel agents have long since gone out of style, and online booking platforms provide a more convenient and often less expensive option. "In 2018, we will continue to see hotel booking platforms continue to advance," said Chris Rivett, travel expert at HotelsCombined.com.

CENTRAL bankers around the world have set up or are creating departments to embrace Big Data in the quest for deeper insight into the economies they manage. David Hardoon, chief data officer at the Monetary Authority of Singapore, in a recent speech said: "Isaac Asimov once said, 'I do not fear computers. I fear the lack of them.'" "We are now starting to put in place the necessary tools, infrastructure and skillsets to harness the power of data science to unlock insights, sharpen surveillance of risks, enhance regulatory compliance and transform the way we do work." Authorities like Mr Hardoon are tapping publicly available sources such as Google Trends and jobs websites to help "nowcast" their economies, and confidential data like credit registers that can help identify a stressed bank.