This work considers low-rank canonical polyadic decomposition (CPD) under a class of non-Euclidean loss functions that frequently arise in statistical machine learning and signal processing. These loss functions are often used for certain types of tensor data, e.g., count and binary tensors, where the least squares loss is considered unnatural.Compared to the least squares loss, the non-Euclidean losses are generally more challenging to handle. Non-Euclidean CPD has attracted considerable interests and a number of prior works exist. However, pressing computational and theoretical challenges, such as scalability and convergence issues, still remain. This work offers a unified stochastic algorithmic framework for large-scale CPD decomposition under a variety of non-Euclidean loss functions. Our key contribution lies in a tensor fiber sampling strategy-based flexible stochastic mirror descent framework. Leveraging the sampling scheme and the multilinear algebraic structure of low-rank tensors, the proposed lightweight algorithm ensures global convergence to a stationary point under reasonable conditions. Numerical results show that our framework attains promising non-Euclidean CPD performance. The proposed framework also exhibits substantial computational savings compared to state-of-the-art methods.

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is to faithfully recover the tensor from highly incomplete measurements in a statistically and computationally efficient manner. Harnessing the low-rank structure of tensors in the Tucker decomposition, this paper develops a scaled gradient descent (ScaledGD) algorithm to directly recover the tensor factors with tailored spectral initializations, and shows that it provably converges at a linear rate independent of the condition number of the ground truth tensor for two canonical problems -- tensor completion and tensor regression -- as soon as the sample size is above the order of $n^{3/2}$ ignoring other dependencies, where $n$ is the dimension of the tensor. This leads to an extremely scalable approach to low-rank tensor estimation compared with prior art, which suffers from at least one of the following drawbacks: extreme sensitivity to ill-conditioning, high per-iteration costs in terms of memory and computation, or poor sample complexity guarantees. To the best of our knowledge, ScaledGD is the first algorithm that achieves near-optimal statistical and computational complexities simultaneously for low-rank tensor completion with the Tucker decomposition. Our algorithm highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation, where the iteration-varying preconditioners promote desirable invariance properties of the trajectory with respect to the underlying symmetry in low-rank tensor factorization.

We prove that three strategy video games from the Sid Meier's Civilization series: Sid Meier's Civilization: Beyond Earth, Sid Meier's Civilization V, and Sid Meier's Civilization VI, are Turing complete. We achieve this by building three universal Turing machines-one for each game-using only the elements present in the games, and using their internal rules and mechanics as the transition function. The existence of such machines imply that under the assumptions made, the games are undecidable. We show constructions of these machines within a running game session, and we provide a sample execution of an algorithm-the three-state Busy Beaver-with one of our machines.

Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs. It has recently been shown that the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms and by finite variable counting logics. The correspondence has even led to new, higher-order GNNs corresponding to the WL algorithm in higher dimensions. The purpose of this paper is to explain these descriptive characterisations of GNNs.

It is hard to directly implement Graph Neural Networks (GNNs) on large scaled graphs. Besides of existed neighbor sampling techniques, scalable methods decoupling graph convolutions and other learnable transformations into preprocessing and post classifier allow normal minibatch training. By replacing redundant concatenation operation with attention mechanism in SIGN, we propose Scalable and Adaptive Graph Neural Networks (SAGN). SAGN can adaptively gather neighborhood information among different hops. To further improve scalable models on semi-supervised learning tasks, we propose Self-Label-Enhance (SLE) framework combining self-training approach and label propagation in depth. We add base model with a scalable node label module. Then we iteratively train models and enhance train set in several stages. To generate input of node label module, we directly apply label propagation based on one-hot encoded label vectors without inner random masking. We find out that empirically the label leakage has been effectively alleviated after graph convolutions. The hard pseudo labels in enhanced train set participate in label propagation with true labels. Experiments on both inductive and transductive datasets demonstrate that, compared with other sampling-based and sampling-free methods, SAGN achieves better or comparable results and SLE can further improve performance.

Artificial intelligence products improve wildlife conservation in Africa. The latest breakthrough in this field is the work of Dr Olga Isupova.

Artificial intelligence (AI) at the edge is changing healthcare, retail and Audi cars, as Intel's IoT Group vice president, John Healy tells Jeremy Cowan and George Malim. Plus we learn how chipmakers globally are tackling supply problems that have halted vehicle production. The semiconductor industry is facing an "awakening", says Healy, as it shape-shifts to meet "insatiable demand" for silicone. Finally, we hear which African country is a leader in satellite cartography, and how Amazon is playing games with its warehouse staff. Hi, and welcome to the latest Trending Tech Podcast brought to you by The Evolving Enterprise, IoT Now, and VanillaPlus.com. This is Jeremy Cowan, and I want to thank you for joining the latest, sometimes serious, sometimes light-hearted look at enterprise digital transformation. I am delighted to welcome today two guests, who are John Healy, from California-based international technology company, Intel, known among other things, for the processors that power so many of our devices. John is vice president of the IoT Group. John, thank you very much for making the time to be here. Good to have you on again, George. Okay, today, we'll be looking at some key tech news stories that deserve a bit of a deeper dive.

The Covid-19 pandemic was devastating for many industries, but it only accelerated the use of artificial intelligence across the U.S. economy. Amid the crisis, companies scrambled to create new services for remote workers and students, beef up online shopping and dining options, make customer call centers more efficient and speed development of important new drugs. Even as applications of machine learning and perception platforms become commonplace, a thick layer of hype and fuzzy jargon clings to AI-enabled software.That makes it tough to identify the most compelling companies in the space--especially those finding new ways to use AI that create value by making humans more efficient, not redundant. With this in mind, Forbes has partnered with venture firms Sequoia Capital and Meritech Capital to create our third annual AI 50, a list of private, promising North American companies that are using artificial intelligence in ways that are fundamental to their operations. To be considered, businesses must be privately-held and utilizing machine learning (where systems learn from data to improve on tasks), natural language processing (which enables programs to "understand" written or spoken language) or computer vision (which relates to how machines "see"). AI companies incubated at, largely funded through or acquired by large tech, manufacturing or industrial firms aren't eligible for consideration. Our list was compiled through a submission process open to any AI company in the U.S. and Canada. The application asked companies to provide details on their technology, business model, customers and financials like funding, valuation and revenue history (companies had the option to submit information confidentially, to encourage greater transparency). Forbes received several hundred entries, of which nearly 400 qualified for consideration. From there, our data partners applied an algorithm to identify 100 companies with the highest quantitative scores--and that also made diversity a priority. Next, a panel of expert AI judges evaluated the finalists to find the 50 most compelling companies (they were precluded from judging companies in which they have a vested interest). Among trends this year are what Sequoia Capital's Konstantine Buhler calls AI workbench companies--building of platforms tailored to different enterprises, including Dataiku, DataRobot Domino Data and Databricks.

We address the problem of modeling constrained hospital resources in the midst of the COVID-19 pandemic in order to inform decision-makers of future demand and assess the societal value of possible interventions. For broad applicability, we focus on the common yet challenging scenario where patient-level data for a region of interest are not available. Instead, given daily admissions counts, we model aggregated counts of observed resource use, such as the number of patients in the general ward, in the intensive care unit, or on a ventilator. In order to explain how individual patient trajectories produce these counts, we propose an aggregate count explicit-duration hidden Markov model, nicknamed the ACED-HMM, with an interpretable, compact parameterization. We develop an Approximate Bayesian Computation approach that draws samples from the posterior distribution over the model's transition and duration parameters given aggregate counts from a specific location, thus adapting the model to a region or individual hospital site of interest. Samples from this posterior can then be used to produce future forecasts of any counts of interest. Using data from the United States and the United Kingdom, we show our mechanistic approach provides competitive probabilistic forecasts for the future even as the dynamics of the pandemic shift. Furthermore, we show how our model provides insight about recovery probabilities or length of stay distributions, and we suggest its potential to answer challenging what-if questions about the societal value of possible interventions.

This paper studies linear convergence of the subspace constrained mean shift (SCMS) algorithm, a well-known algorithm for identifying a density ridge defined by a kernel density estimator. By arguing that the SCMS algorithm is a special variant of a subspace constrained gradient ascent (SCGA) algorithm with an adaptive step size, we derive linear convergence of such SCGA algorithm. While the existing research focuses mainly on density ridges in the Euclidean space, we generalize density ridges and the SCMS algorithm to directional data. In particular, we establish the stability theorem of density ridges with directional data and prove the linear convergence of our proposed directional SCMS algorithm.