His current research focuses on applied statistical modeling and prediction problems in biology and genomics, medicine and industry. This series of three talks takes us on a journey that starts with the introduction of the lasso in by Rob Tibshirani, and brings us to date on some of the vast array of applications that have emerged. These talks will focus on some of the topics from this book.
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The community of people that have worked on sparsity and high-dimensional statistical inference is by now very large the lasso paper alone has over 28K citations! My work with my colleagues and students has concentrated on applied methodology, and in particular algorithms and software for employing these powerful tools. All the applications I present are accompanied by software mostly in R that my students and I actively support and improve.
I motivate the need for sparsity with wide data, and then chronicle the invention of lasso and the quest for good software. After some early starts, my colleagues and I have settled on an algorithm known as coordinate descent, which is surprisingly efficient for fitting a sequence or path of sparse models.
Along with our so-called strong rules for hedging the active set, our glmnet package in R also python and matlab has remained popular. Several examples will be given, culminating with a special adaptation of glmnet called snpnet for fitting lasso models for polygenic traits using GWAS truly massive data.
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I end with a survey of some active areas of research not covered in the remaining two talks. With real applications, we often encounter missing data, typically regarded as a nuisance. Depending on the application, we have different ways of sweeping the problem under the rug, some more natural than others. With principal components and the SVD, there is a natural way of accommodating NAs, which appears to have been in the statistical folklore for a long time.
Matrix completion re-emerged during the Netflix competition as a way to compute a low-rank SVD in the presence of a large amount of missing data, and for imputing missing values. I discuss some aspects of this problem, and describe several algorithms for finding a path of solutions. Here sparsity comes in two forms: sparsity in the entries in the observed matrix, and sparsity in the singular values of the solutions. I illustrate with applications in a variety of areas, including recommender systems and the modeling of sparse longitudinal multivariate data.
As the sparsity literature has progressed over the years, some ingenious extensions have been proposed. I briefly outline three projects that have employed these ideas; two concerning generalized additive model selection, and one for selecting interactions in a linear model.
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Then, in a different direction, the graphical lasso builds sparse inverse covariance matrices to capture the conditional independencies in multivariate Gaussian data. I discuss this approach and extensions, and then illustrate its use for anomaly detection and imputation with high-dimensional data. Name required. Mail will not be published required.
IMS awards , Lectures and Addresses. The tools described are all ones that we have the responsibility to appreciate as we interact with patients in order to improve medical care for them and others.
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The book has four short chapters dealing with causation, study methods, prevention and screening, and an examination of the patterns of life and death. Each section offers a readable account with clear explanations of some difficult concepts: confounding; bias; intention to treat analysis; confidence intervals; whether or not screening for a disease is worthwhile. How we know whether anything we do or offer to our patients has any benefit depends on the collection of accurate information, without bias, and its fair application to medical knowledge.
Whether we are ourselves involved in large epidemiological or clinical studies, or simply need to seek and offer useful advice that will benefit our patients, or just complete a death certificate, our knowledge will be significantly enhanced by reading this book and, at only eighty pages long, is something we can all do. SMD Home.