Guest blog by Kevin Gray.. Kevin is president of Cannon Gray, a marketing science and analytics consultancy. Regression is arguably the workhorse of statistics. Despite its popularity, however, it may also be the most misunderstood. The answer might surprise you: There is no such thing as Regression. The Dependent Variable is something you want to predict or explain.

This post is the second part in a series where we will build a real-time example for analysis and monitoring of Uber car GPS trip data. If you have not already read the first part of this series, you should read that first. The first post discussed creating a machine learning model using Apache Spark's K-means algorithm to cluster Uber data based on location. This second post will discuss using the saved K-means model with streaming data to do real-time analysis of where and when Uber cars are clustered. The example data set is Uber trip data, which you can read more about in part 1 of this series.

In SAS, a quick-and-dirty approach to outliers using cluster analysis is PROC FASTCLUS. The documentation for this procedure includes an example to detect outliers. Try several different options (especially the LEAST option of the PROC FASTCLUS statement) to determine whether this procedure works for your data. Note that PROC FASTCLUS works only with interval/ratio/continuous valued variables, unless you stratify your data using separate analyses for nominal variables using the SAS BY statement.

In the last few years, more than one thousand single-nucleotide polymorphisms (SNPs) have been reproducibly associated with more than two hundred phenotypes and quantitative traits in genome-wide association studies (GWAS) [1]. These loci are usually identified by linear or logistic regression analysis which is performed separately for each SNP. The resulting p-values are then used to rank the SNPs and to select those with a p-value smaller than a pre-specified significance level which is adjusted for the large number of statistical tests. In such a scenario, comparable to analyses of other genomic data sets such as gene expression, p-values are not used in a confirmatory setting but rather as a screening tool to identify associated, i.e. important, SNPs while controlling the number of false positive findings. Nonparametric, model-free statistical learning machines provide a promising alternative to classical, model-based statistical methods for the selection of important variables in high dimensional data sets.

Machine Learning is a subfield within Artificial Intelligence that builds algorithms that allow computers to learn to perform tasks from data instead of being explicitly programmed. We can make machines learn to do things! The first time I heard that, it blew my mind. That means that we can program computers to learn things by themselves! The ability of learning is one of the most important aspects of intelligence. Translating that power to machines, sounds like a huge step towards making them more intelligent. And in fact, Machine Learning is the area that is making most of the progress in Artificial Intelligence today; being a trendy topic right now and pushing the possibility to have more intelligent machines.

The goal of machine learning is to program computers to use example data or past experience to solve a given problem. Many successful applications of machine learning exist already, including systems that analyze past sales data to predict customer behavior, optimize robot behavior so that a task can be completed using minimum resources, and extract knowledge from bioinformatics data. Introduction to Machine Learning is a comprehensive textbook on the subject, covering a broad array of topics not usually included in introductory machine learning texts. Subjects include supervised learning; Bayesian decision theory; parametric, semi-parametric, and nonparametric methods; multivariate analysis; hidden Markov models; reinforcement learning; kernel machines; graphical models; Bayesian estimation; and statistical testing. Machine learning is rapidly becoming a skill that computer science students must master before graduation.

The format is very similar to a BIG cheat sheet. It is based on literature and in-class material from courses of the statistics department at the University of California in Berkeley but also influenced by other sources . To read the PDF version, click here.

One of the most common analyses we perform is to look for patterns in data. What market segments can we divide our customers into? How do we find clusters of individuals in a network of users? It's possible to answer these questions with Machine Learning. Even when you don't know which specific segments to look for, or have unstructured data, you can use a variety of techniques to algorithmically find emergent patterns in your data and properly segment or classify outcomes.

Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational and statistical properties have been recently studied, the performance of convex clustering has not yet been investigated in the high-dimensional clustering scenario, where the data contains a large number of features and many of them carry no information about the clustering structure. In this paper, we demonstrate that the performance of convex clustering could be distorted when the uninformative features are included in the clustering. To overcome it, we introduce a new clustering method, referred to as Sparse Convex Clustering, to simultaneously cluster observations and conduct feature selection. The key idea is to formulate convex clustering in a form of regularization, with an adaptive group-lasso penalty term on cluster centers. In order to optimally balance the tradeoff between the cluster fitting and sparsity, a tuning criterion based on clustering stability is developed. In theory, we provide an unbiased estimator for the degrees of freedom of the proposed sparse convex clustering method. Finally, the effectiveness of the sparse convex clustering is examined through a variety of numerical experiments and a real data application.

A generative model based on training deep architectures is proposed. The model consists of K networks that are trained together to learn the underlying distribution of a given data set. The process starts with dividing the input data into K clusters and feeding each of them into a separate network. After few iterations of training networks separately, we use an EM-like algorithm to train the networks together and update the clusters of the data. We call this model Mixture of Networks. The provided model is a platform that can be used for any deep structure and be trained by any conventional objective function for distribution modeling. As the components of the model are neural networks, it has high capability in characterizing complicated data distributions as well as clustering data. We apply the algorithm on MNIST hand-written digits and Yale face datasets. We also demonstrate the clustering ability of the model using some real-world and toy examples.