Robert Tibshirani

Bio: Robert Tibshirani is an academic researcher from Stanford University. The author has contributed to research in topics: Lasso (statistics) & Elastic net regularization. The author has an hindex of 147, co-authored 593 publications receiving 326580 citations. Previous affiliations of Robert Tibshirani include University of Toronto & University of California.

Inference with Transposable Data: Modeling the Effects of Row and Column Correlations

Abstract: We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Often this data is transposable, meaning that both the row variables and column variables are of potential interest. An example of this scenario is detecting significant genes in microarrays when the samples or arrays may be dependent due to underlying relationships. We study the effect of both row and column correlations on commonly used test-statistics, null distributions, and multiple testing procedures, by explicitly modeling the covariances with the matrix-variate normal distribution. Using this model, we give both theoretical and simulation results revealing the problems associated with using standard statistical methodology on transposable data. We solve these problems by estimating the row and column covariances simultaneously, with transposable regularized covariance models, and de-correlating or sphering the data as a pre-processing step. Under reasonable assumptions, our method gives test statistics that follow the scaled theoretical null distribution and are approximately independent. Simulations based on various models with structured and observed covariances from real microarray data reveal that our method offers substantial improvements in two areas: 1) increased statistical power and 2) correct estimation of false discovery rates.

Moving Beyond Linearity

Abstract: So far in this book, we have mostly focused on linear models. Linear models are relatively simple to describe and implement, and have advantages over other approaches in terms of interpretation and inference. However, standard linear regression can have significant limitations in terms of predictive power. This is because the linearity assumption is almost always an approximation, and sometimes a poor one. In Chapter 6 we see that we can improve upon least squares using ridge regression, the lasso, principal components regression, and other techniques. In that setting, the improvement is obtained by reducing the complexity of the linear model, and hence the variance of the estimates. But we are still using a linear model, which can only be improved so far! In this chapter we relax the linearity assumption while still attempting to maintain as much interpretability as possible. We do this by examining very simple extensions of linear models like polynomial regression and step functions, as well as more sophisticated approaches such as splines, local regression, and generalized additive models.

This Provisional PDF corresponds to the article as it appeared upon acceptance. Copyedited and fully formatted PDF and full text (HTML) versions will be made available soon. A shared transcriptional program in early breast neoplasias despite genetic and clinical distinctions

Abstract: BackgroundThe earliest recognizable stages of breast neoplasia are lesions that represent a heterogeneous collection of epithelial proliferations currently classified based on morphology. Their role in the development of breast cancer is not well understood but insight into the critical events at this early stage will improve efforts in breast cancer detection and prevention. These microscopic lesions are technically difficult to study so very little is known about their molecular alterations.ResultsTo characterize the transcriptional changes of early breast neoplasia, we sequenced 3′- end enriched RNAseq libraries from formalin-fixed paraffin-embedded tissue of early neoplasia samples and matched normal breast and carcinoma samples from 25 patients. We find that gene expression patterns within early neoplasias are distinct from both normal and breast cancer patterns and identify a pattern of pro-oncogenic changes, including elevated transcription of ERBB2, FOXA1, and GATA3 at this early stage. We validate these findings on a second independent gene expression profile data set generated by whole transcriptome sequencing. Measurements of protein expression by immunohistochemistry on an independent set of early neoplasias confirms that ER pathway regulators FOXA1 and GATA3, as well as ER itself, are consistently upregulated at this early stage. The early neoplasia samples also demonstrate coordinated changes in long non-coding RNA expression and microenvironment stromal gene expression patterns.ConclusionsThis study is the first examination of global gene expression in early breast neoplasia, and the genes identified here represent candidate participants in the earliest molecular events in the development of breast cancer.

Scikit-learn: Machine Learning in Python

Abstract: Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems. This package focuses on bringing machine learning to non-specialists using a general-purpose high-level language. Emphasis is put on ease of use, performance, documentation, and API consistency. It has minimal dependencies and is distributed under the simplified BSD license, encouraging its use in both academic and commercial settings. Source code, binaries, and documentation can be downloaded from http://scikit-learn.sourceforge.net.

Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2

Abstract: In comparative high-throughput sequencing assays, a fundamental task is the analysis of count data, such as read counts per gene in RNA-seq, for evidence of systematic changes across experimental conditions. Small replicate numbers, discreteness, large dynamic range and the presence of outliers require a suitable statistical approach. We present DESeq2, a method for differential analysis of count data, using shrinkage estimation for dispersions and fold changes to improve stability and interpretability of estimates. This enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression. The DESeq2 package is available at http://www.bioconductor.org/packages/release/bioc/html/DESeq2.html .

Regression Shrinkage and Selection via the Lasso

Abstract: SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.

Going deeper with convolutions

Abstract: We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

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.