Donald B. Rubin

Bio: Donald B. Rubin is an academic researcher from Tsinghua University. The author has contributed to research in topics: Causal inference & Missing data. The author has an hindex of 132, co-authored 515 publications receiving 262632 citations. Previous affiliations of Donald B. Rubin include University of Chicago & Harvard University.

Missing Data in Experiments

Abstract: Application of simple methods Complete case analysis and variable mean imputation Download from the website, and into R a dataset called ceo.dat. The dataset contains information on 6 variables of fortune 500 companies in 1999. It has 447 cases. Originally, the fortune 500 consists of 500 cases, but 53 cases were deleted due to missing values. The six variables are • salary: 1999 CEO salary plus bonuses (thousand $) • totcomp: 1999 CEO total compensation (thousand $) • tenure: number of years as CEO (is 0 if less than 6 months) • age: age of CEO in years • sales: total 1998 sales revenue of firm i (million $) • profits: 1998 profits for firm i (million $) • assets: total assets of firm i in 1998 (million $) In this problem you will generate missing data yourself using three mechanisms (MCAR, MAR, NMAR). Next, you will apply two different missing data methods (complete case analysis and variable mean imputation), and compute means, variances, and the correlation matrix. Also, we are interested in salary as a function of profits (salary= a + b·profits). Since the data set is complete, and you generate missing data yourself, you will be able to compare the results from the two missing data methods to the population values (obtained from the complete data). We will assume that missing data occurs only the variables salary, totcomp, and age. The other three variables will not have missing values. Do the following: 1. Simulate 25% nonresponse in the three variables described; you will obtain three data sets, one for each scenario. Think about how you can get MCAR, MAR, and NMAR. 2. For each incomplete data set, compute the means, variances, the correlation matrix, and the regression described above. 3. Compare the results with the complete data means, variances, the correlation matrix, and the regression. 4. Write a report (2 page max) in which you describe the findings. Also describe how you generated MCAR, MAR, and NMAR, and why your method of generating nonresponse resulted in that particular mechanism. 6. Include R programs you wrote and R commands you used on a separate page. Use the materials from chapter 2, and the handout to find the least squares estimates for the missing observations in the data set called carsmiss. Download it from the website, and into R using the command carsmiss <-read.table("carsmiss.txt",T,sep=","). The data set carsmiss has four …

Tasks in statistical inference for studying variation in medicine.

Abstract: When studying variation in medicine, traditional hypothesis-testing procedures are too limited to obtain useful inferences except in special situations. More generally, full probability modelling is necessary. Even a relatively simple example can illustrate this point rather dramatically. The development and application of full-probability methods for medical problems comprise exciting areas for statistical and medical researchers, especially if working together.

Fitting Linear Mixed-Effects Models Using lme4

Abstract: Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

Deep Learning

Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Latent dirichlet allocation

Abstract: We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.