Injuries have a great impact on professional soccer, due to their large influence on team performance and the considerable costs of rehabilitation for players. Existing studies in the literature provide just a preliminary understanding of which factors mostly affect injury risk, while an evaluation of the potential of statistical models in forecasting injuries is still missing. In this paper, we propose a multidimensional approach to injury prediction in professional soccer which is based on GPS measurements and machine learning. By using GPS tracking technology, we collect data describing the training workload of players in a professional soccer club during a season. We show that our injury predictors are both accurate and interpretable by providing a set of case studies of interest to soccer practitioners. Our approach opens a novel perspective on injury prevention, providing a set of simple and practical rules for evaluating and interpreting the complex relations between injury risk and training performance in professional soccer.

In this paper we consider the cluster estimation problem under the Stochastic Block Model. We show that the semidefinite programming (SDP) formulation for this problem achieves an error rate that decays exponentially in the signal-to-noise ratio. The error bound implies weak recovery in the sparse graph regime with bounded expected degrees, as well as exact recovery in the dense regime. An immediate corollary of our results yields error bounds under the Censored Block Model. Moreover, these error bounds are robust, continuing to hold under heterogeneous edge probabilities and a form of the so-called monotone attack. Significantly, this error rate is achieved by the SDP solution itself without any further pre- or post-processing, and improves upon existing polynomially-decaying error bounds proved using the Grothendieck\textquoteright s inequality. Our analysis has two key ingredients: (i) showing that the graph has a well-behaved spectrum, even in the sparse regime, after discounting an exponentially small number of edges, and (ii) an order-statistics argument that governs the final error rate. Both arguments highlight the implicit regularization effect of the SDP formulation.

Stop words typically remove such things as "a, an, the, it". Often this can be beneficial when we are classifying based on topics, which are well described by nouns and adjectives. However some text classification tasks are more abstract. Consider classifying fiction and non-fiction articles on the same topic, what would the difference between these two writing styles be? They would probably use the same nouns but what about the frequency of "the" vs "an" or "he" vs "they"?

We present an efficient feature selection method that can find all multiplicative combinations of continuous features that are statistically significantly associated with the class variable, while rigorously correcting for multiple testing. The key to overcome the combinatorial explosion in the number of candidates is to derive a lower bound on the $p$-value for each feature combination, which enables us to massively prune combinations that can never be significant and gain more statistical power. While this problem has been addressed for binary features in the past, we here present the first solution for continuous features. In our experiments, our novel approach detects true feature combinations with higher precision and recall than competing methods that require a prior binarization of the data.

A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand, discounting statistical fluctuations. This problem can be approached using two principled criteria that at first may seem equivalent: selecting the most plausible model in terms of its posterior probability; or selecting the model with the highest predictive performance in terms of identifying missing links. Here we show that while these two approaches yield consistent results in most of cases, there are also notable instances where they do not, that is, where the most plausible model is not the most predictive. We show that in the latter case the improvement of predictive performance can in fact lead to overfitting both in artificial and empirical settings. Furthermore, we show that, in general, the predictive performance is higher when we average over collections of models that are individually less plausible, than when we consider only the single most plausible model.

Various problems in data analysis and statistical genetics call for recovery of a column-sparse, low-rank matrix from noisy observations. We propose ReFACTor, a simple variation of the classical Truncated Singular Value Decomposition (TSVD) algorithm. In contrast to previous sparse principal component analysis (PCA) algorithms, our algorithm can provably reveal a low-rank signal matrix better, and often significantly better, than the widely used TSVD, making it the algorithm of choice whenever column-sparsity is suspected. Empirically, we observe that ReFACTor consistently outperforms TSVD even when the underlying signal is not sparse, suggesting that it is generally safe to use ReFACTor instead of TSVD and PCA. The algorithm is extremely simple to implement and its running time is dominated by the runtime of PCA, making it as practical as standard principal component analysis.

Adversarial training has been shown to regularize deep neural networks in addition to increasing their robustness to adversarial examples. However, its impact on very deep state of the art networks has not been fully investigated. In this paper, we present an efficient approach to perform adversarial training by perturbing intermediate layer activations and study the use of such perturbations as a regularizer during training. We use these perturbations to train very deep models such as ResNets and show improvement in performance both on adversarial and original test data. Our experiments highlight the benefits of perturbing intermediate layer activations compared to perturbing only the inputs. The results on CIFAR-10 and CIFAR-100 datasets show the merits of the proposed adversarial training approach. Additional results on WideResNets show that our approach provides significant improvement in classification accuracy for a given base model, outperforming dropout and other base models of larger size.

The action starts Saturday night with NXT TakeOver: Chicago, followed by Backlash 2017 Sunday night with members of the "SmackDown Live" roster. In total, 13 matches are scheduled for the two cards, both of which have 8 p.m. EDT start times. NXT TakeOver: Chicago can only be seen on WWE Network, which costs $9.99 per month. Fans can watch Backlash on the network or by ordering the pay-per-view for $54.99. New subscribers to the network can watch both shows with a free live stream, given that they won't be charged for the first month.

This article was posted by Manish Saraswat on Analytics Vidhya. Manish who works in marketing and Data Science at Analytics Vidhya believes that education can change this world. R, Data Science and Machine Learning keep him busy. Machine learning and data science are being looked as the drivers of the next industrial revolution happening in the world today. This also means that there are numerous exciting startups looking for data scientists.

For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models such as Lasso. This work proposes learning the feature nonlinearities by binning feature values and finding the best fit in each quantile using non-convex regularized linear regression. The algorithm first captures the dependence between neighboring quantiles by enforcing smoothness via piecewise-constant/linear approximation and then selects a sparse subset of good features. We prove that the proposed algorithm is statistically and computationally efficient. In particular, it achieves linear rate of convergence while requiring near-minimal number of samples. Evaluations on synthetic and real datasets demonstrate that algorithm is competitive with current state-of-the-art and accurately learns feature nonlinearities. Finally, we explore an interesting connection between the binning stage of our algorithm and sparse Johnson-Lindenstrauss matrices.