It is online only book developed by Chester Ismay and Albert Y. Kim and covers the basics of using R to analyze data and create data stories using R and statistics. Check the samples of "data stories" from one of the classes here from one of the authors of the book.

Data science, also known as data-driven decision, is an interdisciplinery field about scientific methods, process and systems to extract knowledge from data in various forms, and take descision based on this knowledge. A data scientist should not only be evaluated only on his/her knowledge on mahine learning, but he/she should also have good expertise on statistics. I will try to start from very basics of data science and then slowly move to expert level. Supervised machine learning requires training labeled data. Unsupervised machine learning doesn't required labeled data.

Real data can be messy, and, in many fields, it can include very few observations, making statistical analyses a challenge and pushing machine learning algorithms to their limit. Sometimes, data breaks the assumptions of most extant methods in statistics, complicating analysis and muddying the validity of results. However, recent developments in a field called topological data analysis (TDA) has provided a set of tools to wrangle messy and/or small data in a robust manner. TDA--and the approach of applying topological concepts to statistical problems--is subfield of analytics developed from ideas in algebraic and differential topology. Though the theory is rooted in graduate level mathematics, a basic understanding and a package implementation of the algorithms allow it to be more accessible to data miners, particularly those with a strong mathematical background.

Elementary learning is performed in this phase.

We present an efficient second-order algorithm with $\tilde{O}(\frac{1}{\eta}\sqrt{T})$ regret for the bandit online multiclass problem. The regret bound holds simultaneously with respect to a family of loss functions parameterized by $\eta$, for a range of $\eta$ restricted by the norm of the competitor. The family of loss functions ranges from hinge loss ($\eta=0$) to squared hinge loss ($\eta=1$). This provides a solution to the open problem of (J. Abernethy and A. Rakhlin. An efficient bandit algorithm for $\sqrt{T}$-regret in online multiclass prediction? In COLT, 2009). We test our algorithm experimentally, showing that it also performs favorably against earlier algorithms.

Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood (ML) principle, which seeks to maximize the likelihood under the assumption that the positive definite covariance matrix can be decomposed as the sum of a low rank positive semidefinite matrix and a diagonal matrix with nonnegative entries. This leads to a challenging rank constrained nonconvex optimization problem. We reformulate the low rank ML Factor Analysis problem as a nonlinear nonsmooth semidefinite optimization problem, study various structural properties of this reformulation and propose fast and scalable algorithms based on difference of convex (DC) optimization. Our approach has computational guarantees, gracefully scales to large problems, is applicable to situations where the sample covariance matrix is rank deficient and adapts to variants of the ML problem with additional constraints on the problem parameters. Our numerical experiments demonstrate the significant usefulness of our approach over existing state-of-the-art approaches.

We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space $\mathcal{X}$ and the goal is to order all possible observations x in $\mathcal{X}$ by means of a scoring function $s:\mathcal{X}\rightarrow \mathbb{R}$ so that s(X) and Y tend to increase or decrease together with highest probability. This problem generalizes bi/multi-partite ranking to a certain extent and the task of finding optimal scoring functions s(x) can be naturally cast as optimization of a dedicated functional criterion, called the IROC curve here, or as maximization of the Kendall ${\tau}$ related to the pair (s(X), Y ). From the theoretical side, we describe the optimal elements of this problem and provide statistical guarantees for empirical Kendall ${\tau}$ maximization under appropriate conditions for the class of scoring function candidates. We also propose a recursive statistical learning algorithm tailored to empirical IROC curve optimization and producing a piecewise constant scoring function that is fully described by an oriented binary tree. Preliminary numerical experiments highlight the difference in nature between regression and continuous ranking and provide strong empirical evidence of the performance of empirical optimizers of the criteria proposed.

In this technical report, we consider an approach that combines the PPO objective and K-FAC natural gradient optimization, for which we call PPOKFAC. We perform a range of empirical analysis on various aspects of the algorithm, such as sample complexity, training speed, and sensitivity to batch size and training epochs. We observe that PPOKFAC is able to outperform PPO in terms of sample complexity and speed in a range of MuJoCo environments, while being scalable in terms of batch size. In spite of this, it seems that adding more epochs is not necessarily helpful for sample efficiency, and PPOKFAC seems to be worse than its A2C counterpart, ACKTR.

Kernel-based methods exhibit well-documented performance in various nonlinear learning tasks. Most of them rely on a preselected kernel, whose prudent choice presumes task-specific prior information. Especially when the latter is not available, multi-kernel learning has gained popularity thanks to its flexibility in choosing kernels from a prescribed kernel dictionary. Leveraging the random feature approximation and its recent orthogonality-promoting variant, the present contribution develops a scalable multi-kernel learning scheme (termed Raker) to obtain the sought nonlinear learning function `on the fly,' first for static environments. To further boost performance in dynamic environments, an adaptive multi-kernel learning scheme (termed AdaRaker) is developed using weighted combinations of advices from hierarchical ensembles of experts. The weights account not only for each kernel's contribution to the learning, but also for the unknown dynamics. Performance is analyzed in terms of both static and dynamic regrets. AdaRaker is uniquely capable of tracking nonlinear learning functions in environments with unknown dynamics, with analytic performance guarantees. Tests with synthetic and real datasets are carried out to showcase the effectiveness of the novel algorithms, and their performance.

The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance. Indeed, most well-known theoretical properties of the lasso, including recent advances in selective inference with the lasso, are established under the assumption that the underlying error variance is known. Yet the error variance in practice is, of course, unknown. In this paper, we propose the natural lasso estimator for the error variance, which maximizes a penalized likelihood objective. A key aspect of the natural lasso is that the likelihood is expressed in terms of the natural parameterization of the multiparameter exponential family of a Gaussian with unknown mean and variance. The result is a remarkably simple estimator with provably good performance in terms of mean squared error. These theoretical results do not require placing any assumptions on the design matrix or the true regression coefficients. We also propose a companion estimator, called the organic lasso, which theoretically does not require tuning of the regularization parameter. Both estimators do well compared to preexisting methods, especially in settings where successful recovery of the true support of the coefficient vector is hard.