Tree boosting has empirically proven to be efficient for predictive mining for both classification and regression. For many years, MART (multiple additive regression trees) has been the tree boosting method of choice. But a starting from 2015, a first to try, always winning algorithm surged to the surface: XGBoost. This algorithm re-implements the tree boosting and gained popularity by winning Kaggle and other data science competition. The paper introduce in first place the supervised learning task and discuss the model selection techniques.

For machine learning, you can also use these libraries to build learning models. However, doing so requires that you have a strong appreciation of the mathematical foundation for the various machine learning algorithms.

When I was beginning my way in data science, I often faced the problem of choosing the most appropriate algorithm for my specific problem. If you're like me, when you open some article about Machine Learning algorithms, you see dozens of detailed descriptions. The paradox is that they don't ease the choice. In this article, I will try to explain basic concepts and give some intuition of using different kinds of Machine Learning algorithms in different tasks. At the end of the article, you'll find the structured overview of the main features of described algorithms.

Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to first identify and remove outliers by looking at the data then to fit OLS and form confidence intervals and p-values on the remaining data as if this were the original data collected. We show in this paper that this "detect-and-forget" approach can lead to invalid inference, and we propose a framework that properly accounts for outlier detection and removal to provide valid confidence intervals and hypothesis tests. Our inferential procedures apply to any outlier removal procedure that can be characterized by a set of quadratic constraints on the response vector, and we show that several of the most commonly used outlier detection procedures are of this form. Our methodology is built upon recent advances in selective inference (Taylor & Tibshirani 2015), which are focused on inference corrected for variable selection. We conduct simulations to corroborate the theoretical results, and we apply our method to two classic data sets considered in the outlier detection literature to illustrate how our inferential results can differ from the traditional detect-and-forget strategy. A companion R package, outference, implements these new procedures with an interface that matches the functions commonly used for inference with lm in R.

A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is shown that the new procedure outperforms standard regularized empirical risk minimization procedures such as lasso or slope in heavy-tailed problems.

We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative procedure is developed to recover both the important covariates and the regression function. Theoretically, we prove that the favored smoothing bandwidth based screening possesses the model selection consistency property.

Keras models follow Scikit-learn's interface of fit/predict with some notable extensions.

Ok, I recognize that the call to summary() just barfed out a whole lot of information onto the screen.

Now there's something to get you out of bed in the morning! Still, they're an essential element and means for identifying potential problems of any statistical model. For example, the residuals from a linear regression model should be homoscedastic. If not, this indicates an issue with the model such as non-linearity in the data. This post will cover various methods for visualising residuals from regression-based models.

High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a {\em regularization factor}, and solve them by the parametric simplex method (PSM). Our parametric simplex method offers significant advantages over other competing methods: (1) PSM naturally obtains the complete solution path for all values of the regularization parameter; (2) PSM provides a high precision dual certificate stopping criterion; (3) PSM yields sparse solutions through very few iterations, and the solution sparsity significantly reduces the computational cost per iteration. Particularly, we demonstrate the superiority of PSM over various sparse learning approaches, including Dantzig selector for sparse linear regression, LAD-Lasso for sparse robust linear regression, CLIME for sparse precision matrix estimation, sparse differential network estimation, and sparse Linear Programming Discriminant (LPD) analysis. We then provide sufficient conditions under which PSM always outputs sparse solutions such that its computational performance can be significantly boosted. Thorough numerical experiments are provided to demonstrate the outstanding performance of the PSM method.