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.

In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the two-block coordinate descent algorithms tackling the non-convex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms, namely, accelerated hierarchical alternating least squares (A-HALS) and alternating nonnegative least squares (ANLS), using synthetic, image and document data sets.

Recent work has managed to learn cross-lingual word embeddings without parallel data by mapping monolingual embeddings to a shared space through adversarial training. However, their evaluation has focused on favorable conditions, using comparable corpora or closely-related languages, and we show that they often fail in more realistic scenarios. This work proposes an alternative approach based on a fully unsupervised initialization that explicitly exploits the structural similarity of the embeddings, and a robust self-learning algorithm that iteratively improves this solution. Our method succeeds in all tested scenarios and obtains the best published results in standard datasets, even surpassing previous supervised systems. Our implementation is released as an open source project at https://github.com/artetxem/vecmap

About this course: This course describes Bayesian statistics, in which one's inferences about parameters or hypotheses are updated as evidence accumulates. You will learn to use Bayes' rule to transform prior probabilities into posterior probabilities, and be introduced to the underlying theory and perspective of the Bayesian paradigm. The course will apply Bayesian methods to several practical problems, to show end-to-end Bayesian analyses that move from framing the question to building models to eliciting prior probabilities to implementing in R (free statistical software) the final posterior distribution. Additionally, the course will introduce credible regions, Bayesian comparisons of means and proportions, Bayesian regression and inference using multiple models, and discussion of Bayesian prediction. We assume learners in this course have background knowledge equivalent to what is covered in the earlier three courses in this specialization: "Introduction to Probability and Data," "Inferential Statistics," and "Linear Regression and Modeling."

Machine learning is a branch in computer science that studies the design of algorithms that can learn. Typical tasks are concept learning, function learning or "predictive modeling", clustering and finding predictive patterns. These tasks are learned through available data that were observed through experiences or instructions, for example. The hope that comes with this discipline is that including the experience into its tasks will eventually improve the learning. But this improvement needs to happen in such a way that the learning itself becomes automatic so that humans like ourselves don't need to interfere anymore is the ultimate goal. Today's scikit-learn tutorial will introduce you to the basics of Python machine learning: If you're more interested in an R tutorial, take a look at our Machine Learning with R for Beginners tutorial. The first step to about anything in data science is loading in your data. This is also the starting point of this scikit-learn tutorial. This discipline typically works with observed data. This data might be collected by yourself or you can browse through other sources to find data sets. But if you're not a researcher or otherwise involved in experiments, you'll probably do the latter.

In Pandas Data Cleaning and Modeling with Python LiveLessons, Daniel Y. Chen builds upon the foundation he built in Pandas Data Analysis with Python Fundamentals LiveLessons. In this LiveLesson Dan teaches you the techniques and skills you need to know to be able to clean and process your data. Dan shows you how to do data munging using some of the built-in Python libraries that can be used to clean data loaded into Pandas. Once your data is clean you are going to want to analyze it, so next Dan introduces you to other libraries that are used for model fitting. Daniel Y. Chen is a graduate student in the interdisciplinary Ph.D. program in Genetics, Bioinformatics & Computational Biology (GBCB) at Virginia Tech.

This course is for you If you are being fascinated by the field of Machine Learning? This course is designed to cover one of the most interesting areas of machine learning called classification. I will take you step-by-step in this course and will first cover the basics of MATLAB. Following that we will look into the details of how to use different machine learning algorithms using MATLAB. Specifically, we will be looking at the MATLAB toolbox called statistic and machine learning toolbox.We will implement some of the most commonly used classification algorithms such as K-Nearest Neighbor, Naive Bayes, Discriminant Analysis, Decision Tress, Support Vector Machines, Error Correcting Ouput Codes and Ensembles. Following that we will be looking at how to cross validate these models and how to evaluate their performances.

In my spare time, I love learning new technologies and going to hackathons. Our hackathon project Pantrylogs using Artificial Intelligence was selected as one of the 10 Microsoft Imagine Cup UK finalists. I'm interested in learning more about AI, Data Science, and Machine Learning to improve the performances of our application. In this article, I would love to share my experience of using Azure Machine Learning Studio with you. Azure Machine Learning Studio is a very powerful browser-based, visual drag-and-drop authoring environment.

Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance operators and have been shown to be closely related to the conditional mean embedding framework developed by the machine learning community. The goal of this paper is to show how the dominant eigenfunctions of these operators in combination with gradient-based optimization techniques can be used to detect long-lived coherent patterns in high-dimensional time-series data. The results will be illustrated using video data and a fluid flow example.

We introduce the open-ended, modular, self-improving Omega AI unification architecture which is a refinement of Solomonoff's Alpha architecture, as considered from first principles. The architecture embodies several crucial principles of general intelligence including diversity of representations, diversity of data types, integrated memory, modularity, and higher-order cognition. We retain the basic design of a fundamental algorithmic substrate called an "AI kernel" for problem solving and basic cognitive functions like memory, and a larger, modular architecture that re-uses the kernel in many ways. Omega includes eight representation languages and six classes of neural networks, which are briefly introduced. The architecture is intended to initially address data science automation, hence it includes many problem solving methods for statistical tasks. We review the broad software architecture, higher-order cognition, self-improvement, modular neural architectures, intelligent agents, the process and memory hierarchy, hardware abstraction, peer-to-peer computing, and data abstraction facility.