With unsupervised learning, the idea of class attributes and explicit class membership does not exist; in fact, one of the dominant forms of unsupervised learning -- data clustering -- aims to approximate class membership by minimizing interclass instance similarity and maximizing intraclass similarity. We will have a look at 2 particular popular methods for attempting to answer this question: the elbow method and the silhouette method. It should be self-evident that, in order to plot this variance against varying numbers of clusters, varying numbers of clusters must be tested. The silhouette method measures the similarity of an object to its own cluster -- called cohesion -- when compared to other clusters -- called separation.

I would probably spend the time on simple (yet useful) algorithms that are representative of these fields (and maybe save reinforcement learning for later).

In this paper, we propose hybrid principal component analysis (HPCA) to extract appearance feature of a face and inter-age group variation-based classifier (IAGVC) with regression to estimate age of a person. The proposed age estimation system is robust and less sensitive to outliers where nonuniform distribution of images at different age groups is existing. Under HPCA, we introduce two novel methods, extended SpPCA and extended SubXPCA. The issues, such as summarization of variance, variable component selection, computational complexity and classification accuracy of HPCA, have been addressed as well. The proposed HPCA operates on subpattern and whole pattern at a time and extracts appearance feature based on both local and global variation of faces.

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence and that their sample complexity is independent of the condition number of the unknown true low-rank matrix. By leveraging recent advances in low-rank matrix approximation techniques, we show that our algorithms achieve computational speed-ups over existing methods. Finally, we complement our theory with some numerical experiments.

We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a non-asymptotic convergence analysis of our framework and derive computational and sample complexities for our algorithm to converge to an $\epsilon$-stationary point in expectation. In addition, extensive experiments for a wide class of SMF formulations demonstrate that our framework consistently yields faster convergence and a more accurate output dictionary vis-\`a-vis state-of-the-art frameworks.

We consider the stochastic composition optimization problem proposed in \cite{wang2017stochastic}, which has applications ranging from estimation to statistical and machine learning. We propose the first ADMM-based algorithm named com-SVR-ADMM, and show that com-SVR-ADMM converges linearly for strongly convex and Lipschitz smooth objectives, and has a convergence rate of $O( \log S/S)$, which improves upon the $O(S^{-4/9})$ rate in \cite{wang2016accelerating} when the objective is convex and Lipschitz smooth. Moreover, com-SVR-ADMM possesses a rate of $O(1/\sqrt{S})$ when the objective is convex but without Lipschitz smoothness. We also conduct experiments and show that it outperforms existing algorithms.

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We propose a general framework for such methods, for which we prove almost sure convergence to stationary points and analyze its worst-case iteration complexity. When a randomly chosen iterate is returned as the output of such an algorithm, we prove that in the worst-case, the SFO-calls complexity is $O(\epsilon^{-2})$ to ensure that the expectation of the squared norm of the gradient is smaller than the given accuracy tolerance $\epsilon$. We also propose a specific algorithm, namely a stochastic damped L-BFGS (SdLBFGS) method, that falls under the proposed framework. {Moreover, we incorporate the SVRG variance reduction technique into the proposed SdLBFGS method, and analyze its SFO-calls complexity. Numerical results on a nonconvex binary classification problem using SVM, and a multiclass classification problem using neural networks are reported.

Kaggle's 2017 March Machine Learning Mania competition challenged Kagglers to do what millions of sports fans do every year–try to predict the winners and losers of the US men's college basketball tournament. In this winner's interview, 1st place winner, Andrew Landgraf, describes how he cleverly analyzed his competition to optimize his luck. I am interested in sports analytics and have followed the previous competitions on Kaggle. Reading last year's winner's interview, I realized that luck is a major component of winning this competition, just like all brackets. I wanted to see if there was a way of maximizing my luck.

This book provides an introduction to statistical learning methods. It is aimed for upper level undergraduate students, masters students and Ph.D. students in the non-mathematical sciences. The book also contains a number of R labs with detailed explanations on how to implement the various methods in real life settings, and should be a valuable resource for a practicing data scientist.

Seeing Theory is a project designed and created by Daniel Kunin with support from Brown University's Royce Fellowship Program. The goal of the project is to make statistics more accessible to a wider range of students through interactive visualizations. Yet, for all the increased importance and demand for statistical competence, the pedagogical approaches in statistics have barely changed. Using Mike Bostock's data visualization software, D3.js, Seeing Theory visualizes the fundamental concepts covered in an introductory college statistics or Advanced Placement statistics class.