We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint. A novel Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry that exists in Tucker decomposition. The specific metric allows to use the versatile framework of Riemannian optimization on quotient manifolds to develop preconditioned nonlinear conjugate gradient and stochastic gradient descent algorithms for batch and online setups, respectively. Concrete matrix representations of various optimization-related ingredients are listed. Numerical comparisons suggest that our proposed algorithms robustly outperform state-of-the-art algorithms across different synthetic and real-world datasets.

Predicting user intentionality towards a certain product, or category, based on interactions within a website is crucial for e-commerce sites and ad display networks, especially for retargeting. By keeping track of the search patterns of the consumers, online merchants can have a better understanding of their behaviours and intentions [4]. In mobile e-commerce a rich set of data is available and potential consumers search for product information before making purchasing decisions, thus reflecting consumers purchase intentions. Users show different search patterns, i.e, time spent per item, search frequency and returning visits [1]. 1 2 DATA DESCRIPTION Clickstream data can be used to quantify search behavior using machine learning techniques [5], mostly focused on purchase records. While purchasing indicates consumers final preferences in the same category, search is also an essential component to measure intentionality towards a specific category.

First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and B\"olcskei, 2015. This paper considers the discrete case, introduces new convolutional neural network architectures, and proposes a mathematical framework for their analysis. Specifically, we establish deformation and translation sensitivity results of local and global nature, and we investigate how certain structural properties of the input signal are reflected in the corresponding feature vectors. Our theory applies to general filters and general Lipschitz-continuous non-linearities and pooling operators. Experiments on handwritten digit classification and facial landmark detection---including feature importance evaluation---complement the theoretical findings.

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized methods, that reduce the complexity in one of the matrix dimension, but not in both of them. In this paper, we tackle very large matrices in both dimensions. We propose a new factorization method that scales gracefully to terabyte-scale datasets. Those could not be processed by previous algorithms in a reasonable amount of time. We demonstrate the efficiency of our approach on massive functional Magnetic Resonance Imaging (fMRI) data, and on matrix completion problems for recommender systems, where we obtain significant speedups compared to state-of-the art coordinate descent methods. Matrix factorization is a flexible tool for uncovering latent factors in low-rank or sparse models. For instance, building on low-rank structure, it has proven very powerful for matrix completion, e.g. in recommender systems (Srebro et al., 2004; Candès & Recht, 2009). In signal processing and computer vision, matrix factorization with a sparse regularization is often called dictionary learning and has proven very effective for denoising and visual feature encoding (see Mairal, 2014, for a review).

The recent media frenzy about artificial intelligence (AI) has been unavoidable. This vision has perhaps come a step closer with the arrival of IBM Watsoni and Richard Susskind's latest book, The Future of the Professionsii, which predicts an internet society with greater virtual interaction with professional services such as doctors, teachers, accountants, architects and lawyers. In reality, is AI many years away from making any real impact in the legal sector? And should law firms see this technical advancement as an opportunity or threat? Broadly speaking, AI is the theory and development of computer systems which will perform tasks that normally require human intelligence.

The wildfire in Alberta, Canada, seems to be diminishing and residents should be able to return to the city of Fort McMurray over the next two weeks. The fire had appeared to be out of control just a few days ago but thanks to favourable weather conditions appears under control. The weather has played a huge part, but what about technology? AI, drones and satellites have all been used. Dr Guillermo Rein, from Imperial College, London and Editor-in-Chief of the journal Fire Technology explains how tech is now incorporated in fire management.

Apple and Samsung supplier Foxconn has reportedly replaced 60,000 factory workers with robots. One factory has "reduced employee strength from 110,000 to 50,000 thanks to the introduction of robots", a government official told the South China Morning Post. Xu Yulian, head of publicity for the Kunshan region, added: "More companies are likely to follow suit." In a statement to the BBC, Foxconn Technology Group confirmed that it was automating "many of the manufacturing tasks associated with our operations" but denied that it meant long-term job losses. "We are applying robotics engineering and other innovative manufacturing technologies to replace repetitive tasks previously done by employees, and through training, also enable our employees to focus on higher value-added elements in the manufacturing process, such as research and development, process control and quality control.

Even in the 1990s, when Australian banks copped a lot of flak for closing branches, consumer behaviour was changing. The banks may not have undertaken their branch network rationalisations in the most amenable fashion for the wider community but even then, as data from the Australian Prudential Regulation Authority show, actual points of representation didn't change as much as the headlines suggested. Indeed, points of representation actually increased for 11 straight years from 2001, the first year APRA started compiling proper data. The shift from traditional branch banking and physical currency has been immense. But the next generational shift in financial services – and services more generally – will be even more confronting.

One-fifth of the films and television shows offered in the European Union by on-demand providers like Netflix, iTunes and Amazon would have to be Europe-made under new proposals issued Wednesday. The quota would match one that already exists for TV networks in European countries and aims to protect the film industry, culture and national languages of the EU's 28 states in an increasingly globalized world dominated by programs in English and from the U.S. The proposal, however, is not popular in the industry and was immediately criticized by some. "Cultural quotas are outdated and unnecessary -- video-on-demand providers are already investing heavily into European local content," said James Waterworth, vice president of Europe operations for the CCIA computer and Internet industry association. Officials from the European Commission, the EU executive branch that made the proposal Wednesday, noted that Netflix's library is already made up of 21% European content, while other providers have up to 30%. "These percentages are not going to represent a major effort," said Guenther Oettinger, the commissioner responsible for Europe's digital market. "We are providing a certain degree of security for the European film industry."

The four founders, two of whom have resigned their professorships to devote their full attention to TwentyBN, met each other during studies at the University of Bielefeld in Germany. Each of the founders has over 15 years of experience in machine learning and the relatively young deep learning discipline. Prof. Dr. Roland Memisevic, Chief Scientist, received his doctorate in Toronto, studying with Geoffrey Hinton, one of the founding fathers of deep learning. Prior to co-founding Twenty Billion Neurons, Memisevic was a member of the faculty at the renowned Machine Learning Institute of the University of Montréal led by Yoshua Bengio. The institute counts Google, Facebook, and IBM amongst its most active donors.