The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section.

An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates is considered. Modeling the structure of the interactions by a graph, our goal is to recover the interaction graph from independently identically distributed (i.i.d.) samples of the covariates and the outcome. When viewed as a feature selection problem, a simple quantity called influence is proposed as a measure of the marginal effects of the interaction terms on the outcome. For the case when the underlying interaction graph is known to be acyclic, it is shown that a simple algorithm that is based on a maximum-weight spanning tree with respect to the plug-in estimates of the influences not only has strong theoretical performance guarantees, but can also outperform generic feature selection algorithms for recovering the interaction graph from i.i.d. samples of the covariates and the outcome. Our results can also be extended to the model that includes both individual effects and pairwise interactions via the help of an auxiliary covariate.

Any author would like to know if his/her article will be successful or not. Here is an attempt to deal with this task. We obtained 5000 most significant articles (Analytic Bridge and Data Science Central) from here (see Paragraph 6) We created simple crawler based on Python BeautifulSoup library We used Python pattern.en We crawled 5000 URLs and for each URL we downloaded the title, body of the article and parameters: number of likes (not including Facebook likes), number of comments, number of views, article creation date and date of the last comment. First, we got rid of empty (or deleted), very short (less than 100 characters long) and "not found" articles, thus getting 2000 articles with associated parameters. Then we removed articles with missing parameters and ended up with only 1207 articles.

Many of those who call themselves statisticians just won't admit that data science heavily relies on and uses (heretical, rule-breaking) statistical science, or they don't recognize the true statistical nature of these data science techniques (some are 15-year old), or are opposed to the modernization of their statistical arsenal. They already missed the train when machine learning became a popular discipline (also heavily based on statistics) more than 15 years ago. Now machine learning professionals, who are statistical practitioners working on problems such as clustering, far outnumber statisticians. Many times, I have interacted with statisticians who think that anyone not calling himself statistician, knows nothing or little about statistics; see my recent bio published here, or visit the LinkedIn profiles of many data scientists, to debunk this myth. Any statistical technique that is not in their old books are considered heretical at best, or non-statistic at worst, or most of the time, not understood.

Problems of this nature occur in fields as diverse as business, medicine, astrophysics, and public policy. Why estimate f? How do we estimate f? Suppose we observe and for We believe that there is a relationship between Y and at least one of the X's. We can model the relationship as Where f is an unknown function and ε is a random error with mean zero. Why Do We Estimate f? Statistical Learning, and this course, are all about how to estimate f. The term statistical learning refers to using the data to "learn" f. Why do we care about estimating f? There are 2 reasons for estimating f, Prediction and Inference.

Most tasks in Machine Learning can be reduced to classification tasks. For example, we have a medical dataset and we want to classify who has diabetes (positive class) and who doesn't (negative class). We have a dataset from the financial world and want to know which customers will default on their credit (positive class) and which customers will not (negative class). To do this, we can train a Classifier with a'training dataset' and after such a Classifier is trained (we have determined its model parameters) and can accurately classify the training set, we can use it to classify new data (test set). If the training is done properly, the Classifier should predict the class probabilities of the new data with a similar accuracy.

Many real-world systems can be studied in terms of pattern recognition tasks, so that proper use (and understanding) of machine learning methods in practical applications becomes essential. While a myriad of classification methods have been proposed, there is no consensus on which methods are more suitable for a given dataset. As a consequence, it is important to comprehensively compare methods in many possible scenarios. In this context, we performed a systematic comparison of 7 well-known clustering methods available in the R language. In order to account for the many possible variations of data, we considered artificial datasets with several tunable properties (number of classes, separation between classes, etc). In addition, we also evaluated the sensitivity of the clustering methods with regard to their parameters configuration. The results revealed that, when considering the default configurations of the adopted methods, the spectral approach usually outperformed the other clustering algorithms. We also found that the default configuration of the adopted implementations was not accurate. In these cases, a simple approach based on random selection of parameters values proved to be a good alternative to improve the performance. All in all, the reported approach provides subsidies guiding the choice of clustering algorithms.

In stochastic convex optimization the goal is to minimize a convex function $F(x) \doteq {\mathbf E}_{{\mathbf f}\sim D}[{\mathbf f}(x)]$ over a convex set $\cal K \subset {\mathbb R}^d$ where $D$ is some unknown distribution and each $f(\cdot)$ in the support of $D$ is convex over $\cal K$. The optimization is commonly based on i.i.d.~samples $f^1,f^2,\ldots,f^n$ from $D$. A standard approach to such problems is empirical risk minimization (ERM) that optimizes $F_S(x) \doteq \frac{1}{n}\sum_{i\leq n} f^i(x)$. Here we consider the question of how many samples are necessary for ERM to succeed and the closely related question of uniform convergence of $F_S$ to $F$ over $\cal K$. We demonstrate that in the standard $\ell_p/\ell_q$ setting of Lipschitz-bounded functions over a $\cal K$ of bounded radius, ERM requires sample size that scales linearly with the dimension $d$. This nearly matches standard upper bounds and improves on $\Omega(\log d)$ dependence proved for $\ell_2/\ell_2$ setting by Shalev-Shwartz et al. (2009). In stark contrast, these problems can be solved using dimension-independent number of samples for $\ell_2/\ell_2$ setting and $\log d$ dependence for $\ell_1/\ell_\infty$ setting using other approaches. We further show that our lower bound applies even if the functions in the support of $D$ are smooth and efficiently computable and even if an $\ell_1$ regularization term is added. Finally, we demonstrate that for a more general class of bounded-range (but not Lipschitz-bounded) stochastic convex programs an infinite gap appears already in dimension 2.

Orange is a component based data mining and machine learning software suite written in the Python language. It is an Open source data visualization and analysis for novice and experts. Data mining can be done through visual programming or Python scripting. It has components for machine learning. There are add ons for bioinformatics and text mining.

Regression is a modelling technique for predicting the values of an outcome variable from one or more explanatory variables. Logistic Regression is a specific approach for describing a binary outcome variable (for example yes/no). Let's assume you are own a new boutique shop. You have a list of potential clients you are thinking of inviting to a special event with the aim of maximizing the number of sales – who should you invite? Data on previous events you have run is a great starting point here, allowing you to predict an individual's likelihood of buying given the information you have on them.