Categorical regressor variables are usually handled by introducing a set of indicator variables, and imposing a linear constraint to ensure identifiability in the presence of an intercept, or equivalently, using one of various coding schemes. As proposed in Yuan and Lin [J. R. Statist. Soc. B, 68 (2006), 49-67], the group lasso is a natural and computationally convenient approach to perform variable selection in settings with categorical covariates. As pointed out by Simon and Tibshirani [Stat. Sin., 22 (2011), 983-1001], "standardization" by means of block-wise orthonormalization of column submatrices each corresponding to one group of variables can substantially boost performance. In this note, we study the aspect of standardization for the special case of categorical predictors in detail. The main result is that orthonormalization is not required; column-wise scaling of the design matrix followed by re-scaling and centering of the coefficients is shown to have exactly the same effect. Similar reductions can be achieved in the case of interactions. The extension to the so-called sparse group lasso, which additionally promotes within-group sparsity, is considered as well. The importance of proper standardization is illustrated via extensive simulations.

We propose a supervised approach incorporating groupfeature sparsity in multi-class kernel logistic regression(GFR-MKLR). The need for group sparsity arises inseveral practical situations where a subset of a set offactors can explain a predicted variable and each factorconsists of a group of variables. We apply our approachfor predicting human interactions based on bodyparts motion (e.g., hands, legs, head, etc.) where imagefeatures are organised in groups corresponding to bodyparts. Our approach, leads to sparse models by assigningweights to groups of features having the highest discriminationbetween different types of interactions. Experimentsconducted on the UT-Interaction dataset havedemonstrated the performance of our method with regardto stat-of-art methods.

As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known effect Z, i.e., E(Y|X, Z) = E(Y|Z). Assuming that E(Y|Z) and Z are linearly related, we reformulate an equivalent notion of conditional mean independence through transformation, which is approximated in practice. We apply the martingale difference divergence (Shao and Zhang, 2014) to measure conditional mean dependence, and show that the estimation error from approximation is negligible, as it has no impact on the asymptotic distribution of the test statistic under some regularity assumptions. The implementation of our test is demonstrated by both simulations and a financial data example.

Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC, high-dimensional data and costly simulations still remain a bottleneck. There is also no consensus as to how to best assess the performance of such methods without knowing the true posterior. We show how a nonparametric conditional density estimation (CDE) framework, which we refer to as ABC-CDE, help address three key challenges in ABC: (i) how to efficiently estimate the posterior distribution with limited simulations and different types of data, (ii) how to tune and compare the performance of ABC and related methods in estimating the posterior itself, rather than just certain properties of the density, and (iii) how to efficiently choose among a large set of summary statistics based on a CDE surrogate loss. We provide theoretical and empirical evidence that justify ABC-CDE procedures that directly estimate and assess the posterior based on an initial ABC sample, and we describe settings where standard ABC and regression-based approaches are inadequate.

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It explores main concepts from basic to expert level which can help you achieve better grades, develop your academic career, apply your knowledge at work or make business forecasting related decisions. Learning multiple regression analysis is indispensable for business analysis, financial analysis or data science applications in areas such as consumer analytics, finance, banking, health care, science, e-commerce and social media. It is also essential for academic careers in data science, applied statistics, economics, econometrics or quantitative finance. And it is necessary for any business forecasting related decision. But as learning curve can become steep as complexity grows, this course helps by leading you through step by step real world practical examples for greater effectiveness.

Linear Regression – Simple Linear Regression- there is only independent variable. Multiple Linear Regression- refers to defining a relationship between independent and dependent variables Logistic Regression – A super simple form of regression analysis in which the outcome variable is binary or dichotomous. Helps to estimate adjusted prevalence rates, adjusted for potential confounders (sociodemographic or clinical characteristics) Linear Discriminant Analysis – A generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. Classification and Regression Trees- Decision trees are are an important type of algorithm for predictive modeling machine learning. A greedy algorithm based on divide and conquer rule.

This course will take you through the process of predictive analytics/predictive modeling. A statistical technique or machine learning algorithm is borrowed to help predict an outcome. The goal of this course is to start you on your journey to becoming a top data scientist. To do that, you need to understand the methodology or methods at your disposal in solving these problems. By using a famous example (the titanic disaster), we will show you how to understand the problem in-front of you, how to explore your data, pre-process your data, how to create your first model, how to improve model accuracy, and look at some evaluation metrics.

There are many important regression problems in real-world brain-computer interface (BCI) applications, e.g., driver drowsiness estimation from EEG signals. This paper considers offline analysis: given a pool of unlabeled EEG epochs recorded during driving, how do we optimally select a small number of them to label so that an accurate regression model can be built from them to label the rest? Active learning is a promising solution to this problem, but interestingly, to our best knowledge, it has not been used for regression problems in BCI so far. This paper proposes a novel enhanced batch-mode active learning (EBMAL) approach for regression, which improves upon a baseline active learning algorithm by increasing the reliability, representativeness and diversity of the selected samples to achieve better regression performance. We validate its effectiveness using driver drowsiness estimation from EEG signals. However, EBMAL is a general approach that can also be applied to many other offline regression problems beyond BCI.

Active learning (AL) [33], a subfield of machine learning, considers the following problem: if the learning algorithm can choose the training data, then which training samples should it choose to maximize the learning performance, under a fixed budget, e.g., the maximum number of labeled training samples? As an example, consider emotion estimation in affective computing [28]. Emotions can be represented as continuous numbers in the 2D space of arousal and valence [30], or in the 3D space of arousal, valence, and dominance [26]. However, emotions are very subjective, subtle, and uncertain. So, usually multiple human assessors are needed to obtain the groundtruth emotion values for each affective sample (video, audio, image, physiological signal, etc). For example, 14-16 assessors were used to evaluate each video clip in the DEAP dataset [21], six to 17 assessors for each utterance in the VAM (Vera am Mittag in German, Vera at Noon in English) spontaneous speech corpus [16], and at least 110 assessors for each sound in the IADS-2 (International Affective Digitized Sounds 2nd Edition) dataset [4]. This is very time-consuming and labor-intensive. How should we optimally select the affective samples to label so that an accurate regression model can be built with the minimum cost (i.e., the minimum number of labeled samples)?