Seeding - the task of finding initial cluster centers - is critical in obtaining high-quality clusterings for k-Means. However, k-means++ seeding, the state of the art algorithm, does not scale well to massive datasets as it is inherently sequential and requires k full passes through the data. It was recently shown that Markov chain Monte Carlo sampling can be used to efficiently approximate the seeding step of k-means++. However, this result requires assumptions on the data generating distribution. We propose a simple yet fast seeding algorithm that produces *provably* good clusterings even *without assumptions* on the data. Our analysis shows that the algorithm allows for a favourable trade-off between solution quality and computational cost, speeding up k-means++ seeding by up to several orders of magnitude. We validate our theoretical results in extensive experiments on a variety of real-world data sets.

Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled *with* replacement. In contrast, sampling *without* replacement is far less understood, yet in practice it is very common, often easier to implement, and usually performs better. In this paper, we provide competitive convergence guarantees for without-replacement sampling under several scenarios, focusing on the natural regime of few passes over the data. Moreover, we describe a useful application of these results in the context of distributed optimization with randomly-partitioned data, yielding a nearly-optimal algorithm for regularized least squares (in terms of both communication complexity and runtime complexity) under broad parameter regimes. Our proof techniques combine ideas from stochastic optimization, adversarial online learning and transductive learning theory, and can potentially be applied to other stochastic optimization and learning problems.

Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms through a handful of popular theorems. We present a new theorem which shows that ``Bregman distortions'' (employing a potentially non-convex generator) may be exactly re-written as a scaled Bregman divergence computed over transformed data. This property can be viewed from the standpoints of geometry (a scaled isometry with adaptive metrics) or convex optimization (relating generalized perspective transforms). Admissible distortions include {geodesic distances} on curved manifolds and projections or gauge-normalisation. Our theorem allows one to leverage to the wealth and convenience of Bregman divergences when analysing algorithms relying on the aforementioned Bregman distortions. We illustrate this with three novel applications of our theorem: a reduction from multi-class density ratio to class-probability estimation, a new adaptive projection free yet norm-enforcing dual norm mirror descent algorithm, and a reduction from clustering on flat manifolds to clustering on curved manifolds. Experiments on each of these domains validate the analyses and suggest that the scaled Bregman theorem might be a worthy addition to the popular handful of Bregman divergence properties that have been pervasive in machine learning.

Techniques known as Nonlinear Set Membership prediction, Lipschitz Interpolation or Kinky Inference are approaches to machine learning that utilise presupposed Lipschitz properties to compute inferences over unobserved function values. Provided a bound on the true best Lipschitz constant of the target function is known a priori they offer convergence guarantees as well as bounds around the predictions. Considering a more general setting that builds on Hoelder continuity relative to pseudo-metrics, we propose an online method for estimating the Hoelder constant online from function value observations that possibly are corrupted by bounded observational errors. Utilising this to compute adaptive parameters within a kinky inference rule gives rise to a nonparametric machine learning method, for which we establish strong universal approximation guarantees. That is, we show that our prediction rule can learn any continuous function in the limit of increasingly dense data to within a worst-case error bound that depends on the level of observational uncertainty. We apply our method in the context of nonparametric model-reference adaptive control (MRAC). Across a range of simulated aircraft roll-dynamics and performance metrics our approach outperforms recently proposed alternatives that were based on Gaussian processes and RBF-neural networks. For discrete-time systems, we provide stability guarantees for our learning-based controllers both for the batch and the online learning setting.

In this paper we propose a fast online Kernel SVM algorithm under tight budget constraints. We propose to split the input space using LVQ and train a Kernel SVM in each cluster. To allow for online training, we propose to limit the size of the support vector set of each cluster using different strategies. We show in the experiment that our algorithm is able to achieve high accuracy while having a very high number of samples processed per second both in training and in the evaluation.

Artificial intelligence (AI) made incredible strides in 2016, and the growth appears set to accelerate as we enter the New Year. A team of Microsoft researchers has released a dataset of 100,000 questions and answers that other AI researchers can use – for free – in their quest to create systems that can read and answer questions as well as a human. The MS MARCO dataset is based on anonymized real-world data from Bing and Cortana queries and is part of an attempt to spur the breakthroughs in machine reading that are already happening in image and speech recognition. The move is also aimed at facilitating advances toward "artificial general intelligence," or machines that can think like humans – and can read and understand a document as well as a person. Meanwhile, AI helped a musician in Norway sing a new tune for the holidays this year: a Christmas carol that was created by Microsoft's AI technology.

Big data continues to be the fastest-growing segment of the information management software market. New findings released by leading global data, market research, and advisory firm Ovum estimate that the big data market will grow from $1.7bn in 2016 to $9.4bn by 2020, comprising 10% of the overall market for information management tooling. Ovum's 2017 Trends to Watch: Big Data report highlights that while the breakout use case for big data in 2017 will be streaming, machine learning will be the factor that disrupts the landscape the most. Under the covers, machine learning is already becoming ubiquitous as it is embedded in many services that consumers take for granted. Increasingly, machine learning is becoming embedded in enterprise software and tooling for integrating and preparing data.

In recent years, AI (artificial intelligence) researchers have finally cracked problems that they've worked on for decades, from Go to human-level speech recognition. A key piece was the ability to gather and learn on mountains of data, which pulled error rates past the success line. In short, big data has transformed AI, to an almost unreasonable level. Blockchain technology could transform AI too, in its own particular ways. Some applications of blockchains to AI are mundane, like audit trails on AI models. Some appear almost unreasonable, like AI that can own itself -- AI DAOs. All of them are opportunities. This article will explore these applications. Before we discuss applications, let's first review what's different about blockchains compared to traditional big-data distributed databases like MongoDB. We can think of blockchains as "blue ocean"databases: they escape the "bloody red ocean" of sharks competing in an existing market, opting instead to be in a blue ocean of uncontested market space.

The buzzwords "Industry 4.0" and "digital business" represent the start of a complex transformational process that will deeply affect industry and society during the next decade. This transformation is based on the convergence of the real (analog) world and the virtual (digital) world by means of machineto- machine (M2M) communication, autonomous systems (for example, robotics) and the Internet of Things (IoT). The German government uses the term "Industry 4.0" as the title of a government project promoting the computerization of traditional industries and the creation of intelligent factories (smart factories) that will be supported by cyberphysical systems and the IoT. The digits "4.0" in Industry 4.0 stand for the fourth industrial revolution: the transition of production from digital processing to fully interconnected processes, products and services. It follows the evolution of production processes for tradable goods from manufacturing to industry production (the first revolution), the move from steam-driven machine production to electricity-driven production (the second revolution) and the shift from analog processing to digital processing and microelectronics (the third revolution). One of the major features of Industry 4.0 is the ability of machines and devices to communicate with each other without a human interface.

Nazi WWII encryption technology is being used to create the bank cards of the future. Technology from the German's Enigma ciphering machines, famously decoded by British mathematician Alan Turing, will be used to create ultra-secure encryption cards. The new cards will have machines in them to replace the existing three-digit CVV security number found on the back strip of most bank cards today, and could kill off the pin-entry card reader entirely. Technology from the German's Enigma ciphering machines, famously decoded by British mathematician Alan Turing, will be used to create credit cards. Pictured is a scene from the 2014 film'The Imitation Game' in which Benedict Cumberbatch plays Alan Turing Encryption technology during the second world war relied on frequently changing'cyphers'.