This is meant to be a practical book. The author's "objective is to provide a thorough discussion of the most useful data-mining tools that goes beyond the typical'black box' description, and to show why these tools work". I think the result of reading and doing the exercises in this book is: 1. I will have acquired some familiarity with regression techniques and a few of the problems they can help with 2. I will have performed the regression techniques in R Over half the text focuses on various kinds of regression. Then there is a little bit on classification, decision trees, clustering, principal components analysis.

We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By collecting the results of exhaustively computing ES-K, various approximate methods for selecting sparse variables can be summarized as density of states. With this density of states, we can compare different methods for selecting sparse variables such as relaxation and sampling. For large problems where the combinatorial explosion of explanatory variables is crucial, the AES-K method enables density of states to be effectively reconstructed by using the replica-exchange Monte Carlo method and the multiple histogram method. Applying the ES-K and AES-K methods to type Ia supernova data, we confirmed the conventional understanding in astronomy when an appropriate K is given beforehand. However, we found the difficulty to determine K from the data. Using virtual measurement and analysis, we argue that this is caused by data shortage.

Traditionally, kernel learning methods requires positive definitiveness on the kernel, which is too strict and excludes many sophisticated similarities, that are indefinite, in multimedia area. To utilize those indefinite kernels, indefinite learning methods are of great interests. This paper aims at the extension of the logistic regression from positive semi-definite kernels to indefinite kernels. The model, called indefinite kernel logistic regression (IKLR), keeps consistency to the regular KLR in formulation but it essentially becomes non-convex. Thanks to the positive decomposition of an indefinite matrix, IKLR can be transformed into a difference of two convex models, which follows the use of concave-convex procedure. Moreover, we employ an inexact solving scheme to speed up the sub-problem and develop a concave-inexact-convex procedure (CCICP) algorithm with theoretical convergence analysis. Systematical experiments on multi-modal datasets demonstrate the superiority of the proposed IKLR method over kernel logistic regression with positive definite kernels and other state-of-the-art indefinite learning based algorithms.

We describe the Customer LifeTime Value (CLTV) prediction system deployed at ASOS.com, a global online fashion retailer. CLTV prediction is an important problem in e-commerce where an accurate estimate of future value allows retailers to effectively allocate marketing spend, identify and nurture high value customers and mitigate exposure to losses. The system at ASOS provides daily estimates of the future value of every customer and is one of the cornerstones of the personalised shopping experience. The state of the art in this domain uses large numbers of handcrafted features and ensemble regressors to forecast value, predict churn and evaluate customer loyalty. Recently, domains including language, vision and speech have shown dramatic advances by replacing handcrafted features with features that are learned automatically from data. We detail the system deployed at ASOS and show that learning feature representations is a promising extension to the state of the art in CLTV modelling. We propose a novel way to generate embeddings of customers, which addresses the issue of the ever changing product catalogue and obtain a significant improvement over an exhaustive set of handcrafted features.

Best Subset Regression method can be used to create a best-fitting regression model. This technique of model building helps to identify which predictor (independent) variables should be included in a multiple regression model(MLR). This method comprises of scrutinizing all of the models created from all possible permutation combination of predictor variables. This technique uses the R Squared value to check for the best model. Considering the level of complexity involved in creating such models it will not be an easy or a fun task to perform this method without using a statistical software program.

We propose generalized random forests, a method for non-parametric statistical estimation based on random forests (Breiman, 2001) that can be used to fit any quantity of interest identified as the solution to a set of local moment equations. Following the literature on local maximum likelihood estimation, our method operates at a particular point in covariate space by considering a weighted set of nearby training examples; however, instead of using classical kernel weighting functions that are prone to a strong curse of dimensionality, we use an adaptive weighting function derived from a forest designed to express heterogeneity in the specified quantity of interest. We propose a flexible, computationally efficient algorithm for growing generalized random forests, develop a large sample theory for our method showing that our estimates are consistent and asymptotically Gaussian, and provide an estimator for their asymptotic variance that enables valid confidence intervals. We use our approach to develop new methods for three statistical tasks: non-parametric quantile regression, conditional average partial effect estimation, and heterogeneous treatment effect estimation via instrumental variables. A software implementation, grf for R and C++, is available from CRAN.

Users of a personalised recommendation system face a dilemma: recommendations can be improved by learning from data, but only if the other users are willing to share their private information. Good personalised predictions are vitally important in precision medicine, but genomic information on which the predictions are based is also particularly sensitive, as it directly identifies the patients and hence cannot easily be anonymised. Differential privacy has emerged as a potentially promising solution: privacy is considered sufficient if presence of individual patients cannot be distinguished. However, differentially private learning with current methods does not improve predictions with feasible data sizes and dimensionalities. Here we show that useful predictors can be learned under powerful differential privacy guarantees, and even from moderately-sized data sets, by demonstrating significant improvements with a new robust private regression method in the accuracy of private drug sensitivity prediction. The method combines two key properties not present even in recent proposals, which can be generalised to other predictors: we prove it is asymptotically consistently and efficiently private, and demonstrate that it performs well on finite data. Good finite data performance is achieved by limiting the sharing of private information by decreasing the dimensionality and by projecting outliers to fit tighter bounds, therefore needing to add less noise for equal privacy. As already the simple-to-implement method shows promise on the challenging genomic data, we anticipate rapid progress towards practical applications in many fields, such as mobile sensing and social media, in addition to the badly needed precision medicine solutions.

We present a novel subset scan method to detect if a probabilistic binary classifier has statistically significant bias -- over or under predicting the risk -- for some subgroup, and identify the characteristics of this subgroup. This form of model checking and goodness-of-fit test provides a way to interpretably detect the presence of classifier bias or regions of poor classifier fit. This allows consideration of not just subgroups of a priori interest or small dimensions, but the space of all possible subgroups of features. To address the difficulty of considering these exponentially many possible subgroups, we use subset scan and parametric bootstrap-based methods. Extending this method, we can penalize the complexity of the detected subgroup and also identify subgroups with high classification errors. We demonstrate these methods and find interesting results on the COMPAS crime recidivism and credit delinquency data.

Linear Regression is still the most prominently used statistical technique in data science industry and in academia to explain relationships between features. A total of 1,355 people registered for this skill test. It was specially designed for you to test your knowledge on linear regression techniques. If you are one of those who missed out on this skill test, here are the questions and solutions. You missed on the real time test, but can read this article to find out how many could have answered correctly.

Given a task of predicting $Y$ from $X$, a loss function $L$, and a set of probability distributions $\Gamma$ on $(X,Y)$, what is the optimal decision rule minimizing the worst-case expected loss over $\Gamma$? In this paper, we address this question by introducing a generalization of the principle of maximum entropy. Applying this principle to sets of distributions with marginal on $X$ constrained to be the empirical marginal from the data, we develop a general minimax approach for supervised learning problems. While for some loss functions such as squared-error and log loss, the minimax approach rederives well-knwon regression models, for the 0-1 loss it results in a new linear classifier which we call the maximum entropy machine. The maximum entropy machine minimizes the worst-case 0-1 loss over the structured set of distribution, and by our numerical experiments can outperform other well-known linear classifiers such as SVM. We also prove a bound on the generalization worst-case error in the minimax approach.