The availability of massive data about sports activities offers nowadays the opportunity to quantify the relation between performance and success. In this study, we analyze more than 6,000 games and 10 million events in six European leagues and investigate this relation in soccer competitions. We discover that a team's position in a competition's final ranking is significantly related to its typical performance, as described by a set of technical features extracted from the soccer data. Moreover we find that, while victory and defeats can be explained by the team's performance during a game, it is difficult to detect draws by using a machine learning approach. We then simulate the outcomes of an entire season of each league only relying on technical data, i.e. excluding the goals scored, exploiting a machine learning model trained on data from past seasons. The simulation produces a team ranking (the PC ranking) which is close to the actual ranking, suggesting that a complex systems' view on soccer has the potential of revealing hidden patterns regarding the relation between performance and success.

Traditional medicine typically applies one-size-fits-all treatment for the entire patient population whereas precision medicine develops tailored treatment schemes for different patient subgroups. The fact that some factors may be more significant for a specific patient subgroup motivates clinicians and medical researchers to develop new approaches to subgroup detection and analysis, which is an effective strategy to personalize treatment. In this study, we propose a novel patient subgroup detection method, called Supervised Biclustring (SUBIC) using convex optimization and apply our approach to detect patient subgroups and prioritize risk factors for hypertension (HTN) in a vulnerable demographic subgroup (African-American). Our approach not only finds patient subgroups with guidance of a clinically relevant target variable but also identifies and prioritizes risk factors by pursuing sparsity of the input variables and encouraging similarity among the input variables and between the input and target variables

One of the first models I learned when I started my data science journey was Logistic Regression. The name Logistic Regression is highly misleading. Logisitic regression actually is a classification algorithm and not a regression algorithm. Logistic regression can be used to solve problems like classifying images. The image above shows a bunch of training digits (observations) from the MNIST dataset whose category membership is known (labels 0–9).

What is the effect of programming languages on software quality? This question has been a topic of much debate for a very long time. In this study, we gather a very large data set from GitHub (728 projects, 63 million SLOC, 29,000 authors, 1.5 million commits, in 17 languages) in an attempt to shed some empirical light on this question. This reasonably large sample size allows us to use a mixed-methods approach, combining multiple regression modeling with visualization and text analytics, to study the effect of language features such as static versus dynamic typing and allowing versus disallowing type confusion on software quality. By triangulating findings from different methods, and controlling for confounding effects such as team size, project size, and project history, we report that language design does have a significant, but modest effect on software quality. Most notably, it does appear that disallowing type confusion is modestly better than allowing it, and among functional languages, static typing is also somewhat better than dynamic typing. We also find that functional languages are somewhat better than procedural languages. It is worth noting that these modest effects arising from language design are overwhelmingly dominated by the process factors such as project size, team size, and commit size. However, we caution the reader that even these modest effects might quite possibly be due to other, intangible process factors, for example, the preference of certain personality types for functional, static languages that disallow type confusion. A variety of debates ensue during discussions whether a given programming language is "the right tool for the job." While some of these debates may appear to be tinged with an almost religious fervor, most agree that programming language choice can impact both the coding process and the resulting artifact. Advocates of strong, static typing tend to believe that the static approach catches defects early; for them, an ounce of prevention is worth a pound of cure. Dynamic typing advocates argue, however, that conservative static type checking is wasteful of developer resources, and that it is better to rely on strong dynamic type checking to catch type errors as they arise. These debates, however, have largely been of the armchair variety, supported only by anecdotal evidence. This is perhaps not unreasonable; obtaining empirical evidence to support such claims is a challenging task given the number of other factors that influence software engineering outcomes, such as code quality, language properties, and usage domains.

All dimensions in the brain data (i.e., voxel variables) are This is where random field theory comes to the rescue. For instance, signals from "brain regions" are

For python programmers, scikit-learn is one of the best libraries to build Machine Learning applications with. It is ideal for beginners because it has a really simple interface, it is well documented with many examples and tutorials. Besides supervised machine learning (classification and regression), it can also be used for clustering, dimensionality reduction, feature extraction and engineering, and pre-processing the data. The interface is consistent over all of these methods, so it is not only easy to use, but it is also easy to construct a large ensemble of classifiers/regression models and train them with the same commands. In this blog lets have a look at how to build, train, evaluate and validate a classifier with scikit-learn and in this way get familiar with the scikit-learn library.

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. "Big data," "data science," and "machine learning" have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on a journey through the revolution in data analysis following the introduction of electronic computation in the 1950s.

We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional non-Gaussian setting. Our estimators leverage the score function based second-order Stein's lemma and do not require Gaussian or elliptical symmetry assumptions made in the literature. Moreover, to handle score functions and response variables that are heavy-tailed, our estimators are constructed via carefully thresholding their empirical counterparts. We show that our estimator achieves near- optimal statistical rate of convergence in several settings. We supplement our theoretical results via simulation experiments that confirm the theory.

We introduce a mixed-effects model to learn spatiotempo-ral patterns on a network by considering longitudinal measures distributed on a fixed graph. The data come from repeated observations of subjects at different time points which take the form of measurement maps distributed on a graph such as an image or a mesh. The model learns a typical group-average trajectory characterizing the propagation of measurement changes across the graph nodes. The subject-specific trajectories are defined via spatial and temporal transformations of the group-average scenario, thus estimating the variability of spatiotemporal patterns within the group. To estimate population and individual model parameters, we adapted a stochastic version of the Expectation-Maximization algorithm, the MCMC-SAEM. The model is used to describe the propagation of cortical atrophy during the course of Alzheimer's Disease. Model parameters show the variability of this average pattern of atrophy in terms of trajectories across brain regions, age at disease onset and pace of propagation. We show that the personalization of this model yields accurate prediction of maps of cortical thickness in patients.

Here is an extremely simple logistic problem. Logistic regression is an estimation of Logit function. Following are the first and second derivative of log likelihood function. Here is a recap of Newton Raphson method.