This article was written by Jim Frost from Minitab. He came to Minitab with a background in a wide variety of academic research. His role was the "data/stat guy" on research projects that ranged from osteoporosis prevention to quantitative studies of online user behavior. Essentially, his job was to design the appropriate research conditions, accurately generate a vast sea of measurements, and then pull out patterns and meanings from it. After you have fit a linear model using regression analysis, ANOVA, or design of experiments (DOE), you need to determine how well the model fits the data. To help you out, Minitab statistical software presents a variety of goodness-of-fit statistics.

An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to the assumptions of Euclidean geometry. Rather, they occupy non-linear spaces, a.k.a. manifolds, where it is difficult to define concepts such as coordinates, vectors and expected values. In this work, we construct a non-parametric predictive methodology for manifold-valued objects, based on a distance modification of the Random Forest algorithm. Our method is versatile and can be applied both in cases where the response space is a well-defined manifold, but also when such knowledge is not available. Model fitting and prediction phases only require the definition of a suitable distance function for the observed responses. We validate our methodology using simulations and apply it on a series of illustrative image completion applications, showcasing superior predictive performance, compared to various established regression methods.

We present a new variable selection method based on model-based gradient boosting and randomly permuted variables. Model-based boosting is a tool to fit a statistical model while performing variable selection at the same time. A drawback of the fitting lies in the need of multiple model fits on slightly altered data (e.g. cross-validation or bootstrap) to find the optimal number of boosting iterations and prevent overfitting. In our proposed approach, we augment the data set with randomly permuted versions of the true variables, so called shadow variables, and stop the step-wise fitting as soon as such a variable would be added to the model. This allows variable selection in a single fit of the model without requiring further parameter tuning. We show that our probing approach can compete with state-of-the-art selection methods like stability selection in a high-dimensional classification benchmark and apply it on gene expression data for the estimation of riboflavin production of Bacillus subtilis.

This paper studies robust regression in the settings of Huber's $\epsilon$-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of $\epsilon$-contamination models for various regression problems including nonparametric regression, sparse linear regression, reduced rank regression, etc. We also discuss a general notion of depth function for linear operators that has potential applications in robust functional linear regression.

This contribution is from David Corliss. David teaches a class on this subject, giving a (very brief) description of 23 regression methods in just an hour, with an example and the package and procedures used for each case. Here you can check the webcast done for Central Michigan University. The slide deck can be found here. Below is the presentation transcript.

In this paper, we investigate how to automatically extract attractive summaries for news propagation on microblogs and propose a novel system called ATSUM to achieve this goal via text attractiveness analysis. It first analyzes the sentences in a news article and automatically predict the attractiveness score of each sentence by using the support vector regression method. The predicted attractiveness scores are then incorporated into a summarization system. Experimental results on a manually labeled dataset verify the effectiveness of the proposed methods.

One fundamental problem in causal inference is the treatment effect estimation in observational studies when variables are confounded. Control for confounding effect is generally handled by propensity score. But it treats all observed variables as confounders and ignores the adjustment variables, which have no influence on treatment but are predictive of the outcome. Recently, it has been demonstrated that the adjustment variables are effective in reducing the variance of the estimated treatment effect. However, how to automatically separate the confounders and adjustment variables in observational studies is still an open problem, especially in the scenarios of high dimensional variables, which are common in big data era. In this paper, we propose a Data-Driven Variable Decomposition (D$^2$VD) algorithm, which can 1) automatically separate confounders and adjustment variables with a data driven approach, and 2) simultaneously estimate treatment effect in observational studies with high dimensional variables. Under standard assumptions, we show experimentally that the proposed D$^2$VD algorithm can automatically separate the variables precisely, and estimate treatment effect more accurately and with tighter confidence intervals than the state-of-the-art methods on both synthetic data and real online advertising dataset.

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and extreme data, least squares cannot explain their central tendency or tail distributions, yielding undesired estimates. In this paper, we propose expectile matrix factorization by introducing asymmetric least squares, a key concept in expectile regression analysis, into the matrix factorization framework. We propose an efficient algorithm to solve the new problem based on alternating minimization and quadratic programming. We prove that our algorithm converges to a global optimum and exactly recovers the true underlying low-rank matrices when noise is zero. For synthetic data with skewed noise and a real-world dataset containing web service response times, the proposed scheme achieves lower recovery errors than the existing matrix factorization method based on least squares in a wide range of settings.

For Android malware detection, precise ground truth is a rare commodity. As security knowledge evolves, what may be considered ground truth at one moment in time may change, and apps once considered benign may turn out to be malicious. The inevitable noise in data labels poses a challenge to inferring effective machine learning classifiers. Our work is focused on approaches for learning classifiers for Android malware detection in a manner that is methodologically sound with regard to the uncertain and ever-changing ground truth in the problem space. We leverage the fact that although data labels are unavoidably noisy, a malware label is much more precise than a benign label. While you can be confident that an app is malicious, you can never be certain that a benign app is really benign, or just undetected malware. Based on this insight, we leverage a modified Logistic Regression classifier that allows us to learn from only positive and unlabeled data, without making any assumptions about benign labels. We find Label Regularized Logistic Regression to perform well for noisy app datasets, as well as datasets where there is a limited amount of positive labeled data, both of which are representative of real-world situations.

Clustering is a fundamental research topic in data mining. A balanced clustering result is often required in a variety of applications. Many existing clustering algorithms have good clustering performances, yet fail in producing balanced clusters. In this paper, we propose a novel and simple method for clustering, referred to as the Balanced Clustering with Least Square regression (BCLS), to minimize the least square linear regression, with a balance constraint to regularize the clustering model. In BCLS, the linear regression is applied to estimate the class-specific hyperplanes that partition each class of data from others, thus guiding the clustering of the data points into different clusters. A balance constraint is utilized to regularize the clustering, by minimizing which can help produce balanced clusters. In addition, we apply the method of augmented Lagrange multipliers (ALM) to help optimize the objective model. The experiments on seven real-world benchmarks demonstrate that our approach not only produces good clustering performance but also guarantees a balanced clustering result.