This paper analyses properties of localized kernel based, nonparametric statistical machine learning methods, in particular of support vector machines (SVMs) and methods close to them. Caused by the enormous research activities there is abundance of general introductions to this field of computer science and statistics. Beside many publications in international journals there are summarizing textbooks like for example Cristianini & Shawe-Taylor (2000), Schölkopf & Smola (2001), Steinwart & Christmann (2008) or Cucker & Zhou (2007) from a mathematical or statistical point of view. Nevertheless, we want to give a short overview over the analyzed topic. Support vector machines were initially introduced by Boser, Guyon & Vapnik (1992) und Cortes & Vapnik (1995), based on earlier work like the Russian original of Vapnik, Chervonenkis & Červonenkis (1979).

There is more to a story than meets the eye, and some stories deserve to be presented from more than just one perspective. With Flipboard 4.0, we have released story roundups, a new feature that adds coverage from multiple sources to a story and provides you with a fuller picture of an event. With our scale of millions of articles and constant stream of documents, it's impossible to generate these roundups manually. So, we have developed a clustering algorithm that's both fast and scalable, and in this blog post, I will explain how we create these roundups on Flipboard. Although there are many sophisticated automatic clustering algorithms, such as K-means or Agglomerative clustering, story clustering is a non-trivial problem.

This article was written by Roopam Upadhyay. Roopam is a seasoned professional of advanced analytics with more than a decade of experience in statistical modeling, data science, predictive analytics, optimization, & business consulting. They learn the same way as humans. Humans learn from experience and so do machines. For machines, experience is in the form of data.

Singular values of a data in a matrix form provide insights on the structure of the data, the effective dimensionality, and the choice of hyper-parameters on higher-level data analysis tools. However, in many practical applications such as collaborative filtering and network analysis, we only get a partial observation. Under such scenarios, we consider the fundamental problem of recovering spectral properties of the underlying matrix from a sampling of its entries. We are particularly interested in directly recovering the spectrum, which is the set of singular values, and also in sample-efficient approaches for recovering a spectral sum function, which is an aggregate sum of the same function applied to each of the singular values. We propose first estimating the Schatten $k$-norms of a matrix, and then applying Chebyshev approximation to the spectral sum function or applying moment matching in Wasserstein distance to recover the singular values. The main technical challenge is in accurately estimating the Schatten norms from a sampling of a matrix. We introduce a novel unbiased estimator based on counting small structures in a graph and provide guarantees that match its empirical performance. Our theoretical analysis shows that Schatten norms can be recovered accurately from strictly smaller number of samples compared to what is needed to recover the underlying low-rank matrix. Numerical experiments suggest that we significantly improve upon a competing approach of using matrix completion methods.

No matter how many books you read, tutorials you finish or problems you solve, there will always be a data set you might come across where you get clueless. Specially, when you are in your early days of Machine Learning. In this blog post, you'll learn some essential tips on building machine learning models which most people learn with experience. These tips were shared by Marios Michailidis (a.k.a Kazanova), Kaggle Grandmaster, Current Rank #3 in a webinar happened on 5th March 2016. The key to succeeding in competitions is perseverance. Marios said, 'I won my first competition (Acquired valued shoppers challenge) and entered kaggle's top 20 after a year of continued participation on 4 GB RAM laptop (i3)'. Were you planning to give up? While reading Q & As, if you have any questions, please feel free to drop them in comments!

They learn the same way as humans. Humans learn from experience and so do machines. For machines, experience is in the form of data. Machines use powerful algorithms to make sense of the data. They identify underlining patterns within the data to learn things about the world.

Graph-based semi-supervised learning is one of the most popular methods in machine learning. Some of its theoretical properties such as bounds for the generalization error and the convergence of the graph Laplacian regularizer have been studied in computer science and statistics literatures. However, a fundamental statistical property, the consistency of the estimator from this method has not been proved. In this article, we study the consistency problem under a non-parametric framework. We prove the consistency of graph-based learning in the case that the estimated scores are enforced to be equal to the observed responses for the labeled data. The sample sizes of both labeled and unlabeled data are allowed to grow in this result. When the estimated scores are not required to be equal to the observed responses, a tuning parameter is used to balance the loss function and the graph Laplacian regularizer. We give a counterexample demonstrating that the estimator for this case can be inconsistent. The theoretical findings are supported by numerical studies.

An important topic in the multi-label learning research is how to exploit the relationship between different classes of labels in order to improve the learning accuracy or reduce the number of required labels. When labels are partially observed, the low-rank matrix model is one of the most popular models to deal with missing labels. As human-labeling is usually expensive and time-consuming, it is critical to design a robust algorithm which is able to learn the underlying low-rank matrix model on datasets with noisy heavily missing labels. In this work, we consider an extreme scenario where each training instance only has one single label being annotated in binary set 1 out of multiple classes of labels. This scenario is often encountered in realworld systems but less discussed in literatures. For example, it is rare for a user to annotate a news article or a piece of music with many tags, especially when the user is not paid for his annotation. The problem becomes challenging when we have a large number of features and classes. Over the past decades, a number of multi-label learning approaches have been proposed under different settings.

Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling high dimensional constrained problems, as the projection step becomes computationally prohibitive to compute. To address this problem, this paper adopts a projection-free optimization approach, a.k.a.~the Frank-Wolfe (FW) or conditional gradient algorithm. We first develop a decentralized FW (DeFW) algorithm from the classical FW algorithm. The convergence of the proposed algorithm is studied by viewing the decentralized algorithm as an inexact FW algorithm. Using a diminishing step size rule and letting $t$ be the iteration number, we show that the DeFW algorithm's convergence rate is ${\cal O}(1/t)$ for convex objectives; is ${\cal O}(1/t^2)$ for strongly convex objectives with the optimal solution in the interior of the constraint set; and is ${\cal O}(1/\sqrt{t})$ towards a stationary point for smooth but non-convex objectives. We then show that a consensus-based DeFW algorithm meets the above guarantees with two communication rounds per iteration. Furthermore, we demonstrate the advantages of the proposed DeFW algorithm on low-complexity robust matrix completion and communication efficient sparse learning. Numerical results on synthetic and real data are presented to support our findings.

For more on advances in machine learning, prediction, and technology, check out the Data science and advanced analytics sessions at Strata Hadoop World London, May 22-25, 2017. Early price ends April 7. You've probably heard by now that machine learning algorithms can use big data to predict whether a donor will give to a charity, whether an infant in a NICU will develop sepsis, whether a customer will respond to an ad, and on and on. Machine learning can even drive cars and predict elections. I believe it can, but these recent high-profile hiccups should leave everyone who works with data (big or not) and machine learning algorithms asking themselves some very hard questions: do I understand my data? Do I understand the model and answers my machine learning algorithm is giving me? And do I trust these answers? Unfortunately, the complexity that bestows the extraordinary predictive abilities on machine learning algorithms also makes the answers the algorithms produce hard to ...