In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which ensures exact recovery in the noiseless case and stable recovery in the noisy case with high probability. The non-asymptotic analysis sheds light on an interplay between optimization error and statistical error. The proposed procedure is shown to be rate-optimal under certain conditions. As a technical by-product, novel high-order concentration inequalities are derived for studying high-moment sub-Gaussian tensors. An interesting tensor formulation illustrates the potential application to high-order interaction pursuit in high-dimensional linear regression.

You ran a linear regression analysis and the stats software spit out a bunch of numbers. The results were significant (or not). You might think that you're done with analysis. After running a regression analysis, you should check if the model works well for data. We can check if a model works well for data in many different ways.

DevOps methodologies are increasingly generating large and diverse data sets across the entire application lifecycle -- from development, to deployment, to application performance management, and only a robust monitoring and analysis layer can truly harness this data for the ultimate DevOps goal of end-to-end automation. The recent rise of machine learning -- and related capabilities such as predictive analytics and artificial intelligence -- has started to push organizations to explore the implementation of a new data analysis model that relies on mathematical algorithms. Despite the promised benefit of helping teams optimize operations and gain more visibility into their data, adoption of machine learning into the DevOps toolbox is limited. Let's try and examine why. Let's start with understanding how machine learning can fit into and benefit the DevOps methodology.

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.

I am provided with 3 years worth of Sales data (broken down by month) along with data for multiple potential independent variables like Ad Spend (broken down by TV and Digital), Population Increase, Consumer purchase index. I am required to a) Forecast Sales data and B) find the effect of these dependent variables on Sales and what is the optimal mix of Ad spend (TV vs Digital) for Sales. I wish to run an equivalent of multiple linear regression in Python but for Time Series data. All the examples that I have read for Time Series focus on 1 independent variable. How can I incorporate multiple independent variables into a linear regression model for Time Series?

How to calculate the p value, r squared and adjusted r squared value in a linear regression model in python??

We present a simple generative framework for learning to predict previously unseen classes, based on estimating class-attribute-gated class-conditional distributions. We model each class-conditional distribution as an exponential family distribution and the parameters of the distribution of each seen/unseen class are defined as functions of the respective observed class attributes. These functions can be learned using only the seen class data and can be used to predict the parameters of the class-conditional distribution of each unseen class. Unlike most existing methods for zero-shot learning that represent classes as fixed embeddings in some vector space, our generative model naturally represents each class as a probability distribution. It is simple to implement and also allows leveraging additional unlabeled data from unseen classes to improve the estimates of their class-conditional distributions using transductive/semi-supervised learning. Moreover, it extends seamlessly to few-shot learning by easily updating these distributions when provided with a small number of additional labelled examples from unseen classes. Through a comprehensive set of experiments on several benchmark data sets, we demonstrate the efficacy of our framework.

About this course: Regression Analysis is perhaps the single most important Business Statistics tool used in the industry. Regression is the engine behind a multitude of data analytics applications used for many forms of forecasting and prediction. This is the fourth course in the specialization, "Business Statistics and Analysis". The course introduces you to the very important tool known as Linear Regression. You will learn to apply various procedures such as dummy variable regressions, transforming variables, and interaction effects.

If you want to learn how to perform the most useful statistical analyses in the R program, you have come to the right place. Now you don't have to scour the web endlessly in order to find how to do a Pearson or Spearman correlation, an independent t test or a factorial ANOVA, how to perform a sequential regression analysis or how to compute the Cronbach's alpha. Everything is here, in this course, explained visually, step by step. So, what will you learn in this course? First of all, you will learn how to perform association tests in R, both parametric and non-parametric: the Pearson correlation, the Spearman and Kendall correlation, the partial correlation and the chi-square test for independence.